ࡱ> `b$[\]^_hVQVY w K i b ;jbjb /mmX3ZZZZZZZn{{{8{~nD4ƤƤƤƤƤ0,R -Z"ƤƤ"" "ZZƤƤ9""""ZƤZƤ"nnZZZZ"""ZZ" N{"""(O0""""Znnd-0Jnn0Chapter 5 The Giant 1: RATIOS, MEASUREMENT, AND EQUIVALENT FRACTIONS DAYPROBLEMSTOPICMATERIALS:1GO-1-GO-11Ratio Tablesgraph paper, rulers2GO-12-GO-21Fraction Bars, Diamond Problemsresource page (2 per student), scissors, legal sized envelopes or baggies3GO-22-GO-33Giant Ruler (Measurement) and Fraction Blackout Game (Equivalent Fractions)plain paper, crayons, or markers, resource pages, transparency4GO-34-GO-50Fractions, Common Denominators, and Inequalitiesfraction bars, resource page5GO-51-GO-64Identity Property of Multiplication6GO-65-GO-78Three Different Models of Equivalent Fractionsfraction-decimal-percent grids, standard rulers, resource pages, fraction bars, transparency 7GO-79-GO-89Proportionsfraction bars8GO-90-GO-104Proportionsrulers, fraction bars9-10GO-105-GO-122Consolidation and Reviewfraction bars, ruler OVERVIEW This entire chapter lays the groundwork for Chapter 6 where students will write and solve proportions in many contexts and Chapter 7 where students will use standard, formal operations with fractions. The purpose of this chapter is for students to examine ratios and equivalent fractions to build the intuitive understanding that underlies the formal operations. Students who can already do operations with fractions should benefit from rethinking the reasoning behind the operations. The chapter begins with solving problems using ratio tables and linking them to equivalent fractions. Each student makes a set of fraction strips, and then uses the strips to order and compare common fractions. The class will create a giant ruler and use it to practice working with mixed numbers, improper fractions, and equivalent fractions. Students use ratio tables to rewrite and compare equivalent fractions and use the Identity Property of Multiplication to find equivalent fractions. A geometric model is presented to justify the results of multiplication by a fractional form equivalent to 1. Proportions are informally developed using ratio tables, the Identity Property of Multiplication, and rectangular models. Students will: use ratio tables, fraction bars, and measurement with a ruler to understand equivalent fractions. change different denominators to common denominators using the Identity Property of Multiplication. compare fractions using equivalent fractions. recognize equivalent fractions. add mixed numbers and fractions informally using equivalent fractions. find solutions to two variable algebra puzzles. add and multiply integers and fractions. Resource Pages: MENTAL MATH TM (Days 3 and 6: Problems GO-22 and GO-65) Make one transparency. FRACTION FAMILIES RESOURCE PAGE (Day 2: Problem GO-13) Make two copies per student. GIANT RULER RESOURCE PAGE (Day 3: Problem GO-24) Make 12 copies. BLACKOUT SPINNERS RESOURCE PAGE (Days 3 and 6: Problems GO-26 and GO-70) Make one copy per student pair or team. BLACKOUT GAME BOARD RESOURCE PAGE (Days 3 and 6: Problems GO-26 and GO-70) Make one copy per student. FRACTION LIST RESOURCE PAGE (Day 4: Problem GO-34) There are ten identical rows of fractions on this page. Make enough copies so that when you cut the rows apart each student gets one row. EQUIVALENT FRACTION TABLE RESOURCE PAGE (Day 6: Problem GO-66) Make one copy per student. Manipulatives: FRACTION-DECIMAL-PERCENT GRIDS (See Chapter 3) Chapter 5 The Giant 1: RATIOS, MEASUREMENT, AND EQUIVALENT FRACTIONS You will begin this chapter by using tables to show the relationship between pairs of numbers called ratios. The ratio tables will help you solve word problems involving unit costs, rates, and proportions. Throughout the chapter you will practice several methods for finding equivalent fractions. The Fraction Blackout game will help you recognize equivalent fractions. In the Diamond Problems, you practice working with integers. You will practice your measurement skills in several activities. In this chapter you will have the opportunity to: solve problems that include ratios, unit costs, rates, and proportions by using ratio tables. find equivalent fractions using fraction bars, rulers, the Identity Property of Multiplication, and a model. practice integer operations. develop an understanding of inequality. measure and identify lengths with a ruler. GO-0. One for the Giant Patricia Garcia was reading a story to her sister, Ana, about a kindly giant who lived in a very cold place. Ana felt sorry for the giant and wanted to make him a quilt just like hers (only bigger, of course). Anas quilt is 3744 square inches, and it took 104 hours to make. Ana wants the giant quilt to be 9360 square inches. If she makes the giant quilt at the same rate at which she made her quilt, how long will it take to make?    DAY ONE GO-1 through GO-11 OBJECTIVES Students will: make a drawing using ratios. solve problems involving unit cost and rates using ratio tables. graph data from ratio tables to compare slopes between different ratios. MATERIALS graph paper rulers plain paper Todays lesson begins with ratios and ratio tables. Problem GO-1 provides students with examples of how they may have seen ratios written. As you circulate throughout the classroom, check with teams to assess what their past experience with ratios may have been. In problem GO-2 the value for one pound of fruit is the unit cost. Students will find the unit cost valuable as they complete the table. Students will graph the data from problem GO-2 for problem GO-3 and compare the steepness of each graph. They will also examine a ratio table that will not be graphed and predict the slant of the line. This culminates with problem GO-4 where students use ratios to create a proportional drawing. Remind students that problem GO-4 is not a test of their artistic skill; rather, it represents one use of ratio in the real world. GO-1.  RATIOS A RATIO is a comparison of two quantities by division. It can be written in several ways, such as:  EQ \f(2,5)  2 : 5 2 to 5 Make these notes in your Tool Kit to the right of the double-lined box. a) Write the ratio three to seven in the three different forms. [  EMBED "Equation" "Word Object1" \* mergeformat , 3:7, 3 to 7 ] b) Is the order of the numbers in the ratio important? Explain your answer. [ Order is important because it represents division. ] This next activity will give students a chance to work informally with ratios, GO-2. Equivalent ratios can be organized in a ratio table. Complete the following ratio tables to record the cost of different weights of fruit. Be prepared to explain your reasoning, that is, how you determined each ratio. a)Pounds of Melon123568Cost$0.90$1.80$2.70$4.50$5.40$7.20 b)Pounds of Bananas 123689Cost$0.34$0.68$1.02$2.04$2.72$3.06 c)Pounds of Kiwi 123489Cost$2.80$5.60$8.40$11.20$22.40$25.20 GO-3. Use the tables from the previous problem to draw three graphs, one for each data set, on the same coordinate axes. Label the horizontal axis from 1 through 8 and the vertical axis in one-dollar increments. a) If you bought zero pounds of fruit, how much would you spend? Label this point on your graph. [ $0 ] b) What similarities or differences do you see between the graphs? [ All three graphs go through the origin and form straight lines of varying steepness. ] c) Which graph is the steepest? Which graph is the flattest? [ kiwi; bananas ] Examine the table for the cost of candy. Compare it to the data you have graphed, but do not graph the data. Pounds of Candy123458Cost$2.00$4.00$6.00$8.00$10.00$16.00d) Answer these questions without graphing the data. If you were to graph the candy data, which graph(s) would it be steeper than? [ melon and bananas ] e) Which graph(s) would the candy data be flatter than? [ kiwi ] GO-4. Artists use ratios to help them make drawings look like real life. The human face is full of ratios. Use the picture at right to draw a realistic face. You may either draw the face of someone you know or draw a copy of the face provided here. Some guidelines are: a) The face should be 6 units high and 4 units wide. b) The eyes are half-way between the top and bottom of the face. c) Each eye is one unit wide and the space between them is one unit. d) The mouth is one unit wide. e) Finish your drawing using the drawing at right to help you. HOMEWORK for Day 1 begins here. GO-5. Steve drives 65 miles per hour. Copy and complete the ratio table below. Miles65130195260325390Hours123456a) How many hours does it take for Steve to travel from Providence to New York, a distance of 130 miles? [ 2 hours ] b) How far can he travel in four hours? [ 260 miles ] c) How long will it take him to travel 390 miles? [ 6 hours ] d) How far can he travel in eight hours? [ 520 miles ] GO-6. In a class of 20 students, there were nine boys. Copy and use a ratio table like the one below to determine how many boys there would be in a class of 100 students. Number of Boys918273645Total Students20406080100a) Based on the data in your table, about what percent of the class is boys? [ 45% ] b) What percent of the class is girls? [ 55% ] GO-7.  MIXED NUMBERS AND FRACTIONS GREATER THAN ONE The number 4  EQ \f(1,4) is called a mixed number, because it is made from a whole number, 4, and a fraction,  EQ \f(1,4) . It is a mix of a whole number and a fraction. The number  EQ \f(17,4) is a fraction that is greater than one, because the numerator is greater than the denominator. Sometimes fractions that are greater than one are called "improper fractions." Improper does not mean wrong. In mathematics, keeping a fraction in its improper form is often more useful than changing it to a mixed number. Make these notes in your Tool Kit. a) Highlight the words a whole number and a fraction and fraction that is greater than one. b) Write the label Mixed Numbers and give three examples in the space to the right of the double-lined box. c) Write three examples of fractions greater than one to the right of the double-lined box. We begin this new set of Algebra Puzzles to help lead the students to making tables to use to graph lines. The set of Algebra Puzzles will also help them practice adding integers. The answers may include negative integers. Encourage students to write results as ordered pairs (x, y). Part (c) of this Algebra Puzzle requires the use of negative integers and can be used as a discussion of additive inverses. GO-8. Algebra Puzzles Write three pairs of numbers that make each of the following equations true. Write your answers as ordered pairs (x, y). For example, (1, 3) is an answer for part (a). Remember you can use negative numbers as well. a) x + y = 4 [ (0, 4), (1, 3), (2, 2), ... ]b) x + y = 10 [ (0, 10), (1, 9), (2, 8), ... ]c) x + y = 0 [ (0, 0), (1, -1), (-1, 1), ... ]d) x + y = 1 [ (0, 1), (1, 0), (-2, 3), ... ] GO-9. In the trapezoid at right, all dimensions are in feet. Find the perimeter and area. [ 8 + 8.4 + 11 + 21.7 = 49. 1; Area = 52.675 sq. feet ] GO-10. George saved $58 in two weeks. At this rate, approximately how long will it take him to save at least $830? [ A ] (A) 29 weeks (B) 12 weeks (C) 14 weeks (D) 23 weeks GO-11.Now that we have started a new chapter, it is time for you to organize your binder. a) Put the work from the last chapter in order and keep it in a separate folder. b) When this is completed, write, I have organized my binder.  DAY TWO GO-12 through GO-21 OBJECTIVES Students will: compare fractional parts using fraction bars. define and give examples of equivalent fractions. find equivalent fractions using ratio tables. practice addition of fractions using models. solve word problems by setting up and using ratio tables. MATERIALS fraction bar resource page (two per student) scissors legal-sized envelopes We introduce Diamond Problems here to help practice addition and multiplication of integers and fractions. Diamond Problems are useful as a prelude to factoring algebraic expressions in later courses. The top ? is always filled in with the product of the two side #s, while the bottom ? is always filled in with the sum of the two side #s. The diamond icon is not shown for the first problem because the point of the problem is to find how the pattern works. Future diamond problems will show the icon. GO-12. Diamond Problems With your partner, study the examples of Diamond Problems in the table below. See if you can discover a pattern.   In the fourth diamond, can you find the unknowns (?) if you know the numbers (#)? Explain how you would do this. Note that # is a standard symbol for the word number. Copy the Diamond Problems below and use the pattern you found to complete each of them.  a)  [ xy = 12; x + y = 7 ] b)  [ xy = 6; x + y = -5 ] c)  [ x = 3; y = 4 ] d)  [ x = -2; x + y = -4 ] Today students will make fraction bars with the Fraction Families Resource Page. Make one resource page for each student to cut up and then another copy for students to keep intact in their binders. The intent of the lesson is for students to have a hands-on, visual understanding of fractional parts. Students should cut one sheet into six strips and put the strips in a safe place such as an envelope. Keep the individual fractions on each strip intact. There is no need to cut them apart. An effective way to have the students store their fraction bars is to punch holes in a large envelope. They can keep the fraction bars in the envelope in their binder this way. Baggies also work. Keep the other copy intact as a resource page in the students notebook. The intent is for students to create a visual anchor of what the various fractions look like in relation to one another. The four math operations can be modeled with these strips in a more concrete manner that will lead to deeper understanding of the abstract algorithms. Students should fold the strips back to show the desired number. For example, if students want to see  EMBED "Equation" \* mergeformat , they should take the eighths strip and fold back  EMBED "Equation" \* mergeformat . **** GO-13.Today you will be making a set of fraction bars.a) Label each fractional part as shown on both of the resource pages. b) Cut along the darkened (horizontal) lines to create strips. Put your initials on the back of each piece. Do not cut along vertical lines except for the ends of each strip. c) Find two pieces the exact same length to make  EQ \f(1,2) . Write an equation in the form of  EQ \f(1,2) = ____ to explain what you found. [  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  ] d) Find four pieces the exact same length to make  EQ \f(1,2) . Write an equation in the form of  EQ \f(1,2) = ____ to explain what you found. [  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  ] e) Find two pieces the exact same length to make  EQ \f(1,4) . Write an equation in the form of  EQ \f(1,4) = ____ to explain what you found. [  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  ] f) Find four pieces the exact same length to make  EQ \f(2,3) . Write an equation in the form of  EQ \f(2,3) = ____ to explain what you found. [  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  ] g) Find two pieces the exact same length to make  EQ \f(1,3) . Write an equation in the form of  EQ \f(1,3) = ____ to explain what you found. [  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  ] h) Put all of the pieces in an envelope to keep in your binder for later use. GO-14.  EQUIVALENT FRACTIONS Two fractions that name the same number are called EQUIVALENT FRACTIONS. For example, because  EQ \f(1,2) =  EQ \f(3,6) , the fractions  EQ \f(1,2) and  EQ \f(3,6) are equivalent.  Make these notes in your Tool Kit to the right of the double-lined box. a) Explain why  EQ \f(1,3) and  EQ \f(4,12) are equivalent fractions. b) Name two other equivalent fractions. GO-15. Complete the following equivalent fraction ratio tables and make a list of equivalent fractions. You may use your uncut fraction bar resource page for visual assistance. For example, for the ratio table below, where 2N is the variable expression or rule relating N and D,  EQ \f(1,2) =  EQ \f(2,4) =  EQ \f(3,6) is a list of equivalent fractions. numerator (N)123Ndenominator (D)2462N a)N123425ND4812161004N b)N1234ND369123N c)N246860D3691290 GO-16. Look at your uncut fraction bar resource page. Name a fraction that is: a) greater than  EQ \f(1,2) and less than 1. [  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat , ...  EMBED "Equation" \* mergeformat  ] b) greater than  EQ \f(1,4) , less than  EQ \f(3,4) , and not  EQ \f(1,2) . [  EMBED "Equation.3" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat  ] c) greater than  EQ \f(1,4) and less than  EQ \f(5,8) . [  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat  ] d) greater than  EQ \f(3,8) and less than  EQ \f(4,8) . [  EMBED "Equation" \* mergeformat  ]Example:  HOMEWORK for Day 2 begins here. GO-17. Use your cut fraction bars to model the following problems and write each result as one fraction. a)  EQ \f(3,6) +  EQ \f(2,6) [  EMBED "Equation" \* mergeformat  ]b)  EQ \f(1,2) +  EQ \f(1,3) [  EMBED "Equation" \* mergeformat  ] c)  EQ \f(1,4) +  EQ \f(2,4) [  EMBED "Equation" \* mergeformat  ]d)  EQ \f(1,4) +  EQ \f(1,2) [  EMBED "Equation" \* mergeformat  ] e)  EQ \f(5,10) +  EQ \f(2,10) [  EMBED "Equation" \* mergeformat  ]f)  EQ \f(1,2) +  EQ \f(1,5) [  EMBED "Equation" \* mergeformat  ]g) Consider the pairs (a) and (b), (c) and (d), and (e) and (f). What do you notice about the answers to these pairs? [ Each pair is composed of equivalent fractions. ] GO-18. Jeanine earns $5.50 an hour baby-sitting her neighbors three children. Copy and complete the following ratio table to determine how much she should charge her neighbor. a) How much will Jeanine earn if she starts at 7:30 p.m. and ends at 12:30 a.m.? [ $27.50 ] b) How much will she earn if the neighbors do not return for 5  EQ \f(1,2) hours? [ $30.25 ] Hours123456NAmount$5.50$11.00$16.50$22.00$27.50$33.00$5.50N GO-19. A bank teller can count 150 bills each minute. a) How many can he count in five minutes? Ten minutes? Thirty minutes? One hour? Create a ratio table to solve this problem. [ 750; 1500; 4500; 9000 ] b) How many bills will he count each day if he counts for 8 hours a day? [ 72,000 ] c) How many bills can he count in five days, 14 days, and 365 days? You may use another ratio table to solve this problem. [ 360,000; 1,008,000; 26,280,000 ] GO-20. Using the numbers 0, 1, 2, 2 EMBED "Equation.CWEE1" \* mergeformat , 3, 7, 7 EMBED "Equation.CWEE1" \* mergeformat , 9, and 10, answer the following questions. (You may use a number more than once.) a) Find five numbers with a mean of 5. [ 1, 2, 2, 10, 10 ]b) Find five numbers with a mean of 5 and a median of 2 EMBED "Equation.CWEE1" \* mergeformat . [ 1, 2.5, 2.5, 9, 10 ] c) If you have a mean of 5, what is the largest median you can have for this set of numbers? [ The sum should be 25 using as many equal large numbers as possible. Choose 7 EMBED "Equation" \* mergeformat , 7 EMBED "Equation" \* mergeformat , 7 EMBED "Equation" \* mergeformat , 2 EMBED "Equation" \* mergeformat , 0 with a median of 7 EMBED "Equation" \* mergeformat . ] GO-21.Simplify each expression.a) 4 (8 4) + 3 [ 19 ]b) (20 5) 4 8 + 2 [ -15 ]c) 2 3 + 1 + 5 4 [ 27 ]d) 6 2 + 3 8 + 6 [ 42 ] DAY THREE GO-22 through GO-33 OBJECTIVES Students will: create and use a giant ruler to see the fractional parts of an inch. visualize mixed numbers, improper fractions, and equivalent fractions using the giant ruler. practice recognizing equivalent fractions. MATERIALS mental math resource page plain paper four colors of markers or crayons per pair of students Fraction Blackout resource page Giant Ruler resource page (12 copies) In todays lesson students will study the fractional parts of an inch by creating the Giant Ruler by folding a piece of copy paper into the appropriate parts. Directions for making a classroom model of a Giant Foot follow problem GO-24. Students will then apply knowledge of fractional parts when they play the Fraction Blackout game. In Fractional Blackout, students shade in fractional parts of a grid depending on the results of spinning either spinner A or B. Students will only need spinners A and B today. On Day 6 students will need spinners C and D. Use mental math problems MM-23, MM-24, and MM-25. GO-22. Practice mental math according to your teachers directions. Explain in writing how you solved one of the problems. GO-23. Use your fraction bars to solve the following problems and write the result as a fraction. a)  EQ \f(2,6) +  EQ \f(2,6) [  EMBED "Equation" \* mergeformat  ]b)  EQ \f(5,6) +  EQ \f(4,6) [  EMBED "Equation" \* mergeformat  ]c)  EQ \f(3,4) +  EQ \f(3,4) [  EMBED "Equation" \* mergeformat  ] d)  EQ \f(5,8)   EQ \f(3,8) [  EMBED "Equation" \* mergeformat  ] e)  EQ \f(5,10)   EQ \f(2,10) [  EMBED "Equation" \* mergeformat  ] f)  EQ \f(1,2)   EQ \f(1,4) [  EMBED "Equation" \* mergeformat  ] For the next activity, use a standard piece of 8-1/2" x 11" copy paper. **** GO-24.You will create a Giant Inch (we will call it an inch even though it really is not an inch long) as part of the classrooms giant ruler. Your teacher will give you a piece of paper. a) Fold your paper in half as shown. Now unfold your paper and mark the fold line halfway down the paper (from the top) with a black marker. Label it  EQ \f(1,2) . Fold your paper back in half. b) Carefully fold your paper in half once again. Open it up. Mark the new fold lines with a red marker one-fourth of the way down the paper. Label them  EQ \f(1,4) and  EQ \f(3,4) from left to right. Fold your paper back into fourths.c) Carefully fold your paper in half again. Open it up. Mark these new fold lines with a green marker one-eighth of the way down the paper. Label them  EQ \f(1,8) ,  EQ \f(3,8) ,  EQ \f(5,8) , and  EQ \f(7,8) from left to right. Fold your paper back into eighths. d) Fold your paper in half again. Open it up. Mark the new fold lines with a blue marker a little way down (about half of one-eighth). Label them  EQ \f(1,16) ,  EQ \f(3,16) ,  EQ \f(5,16) ,  EQ \f(7,16) ,  EQ \f(9,16) ,  EQ \f(11,16) ,  EQ \f(13,16) , and  EQ \f(15,16) from left to right. e) When you count by fourths, why do you not mark  EQ \f(2,4) ? What fraction is in its place? [  EMBED "Equation" \* mergeformat  ] f) When you count by eighths, which eighths do you not mark? What other names might each one have? [  EMBED "Equation" "Word Object5" \* mergeformat  ] g) When you count by sixteenths, what numbers do you write with names other than sixteenths? What other names might the missing numbers have? [  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat , ... ,  EMBED "Equation" \* mergeformat ;  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat  ] Duplicate twelve rulers from the resource page and staple or tape them to the wall to create a gigantic ruler. Label each inch. Build this ruler in a place where it can stay for a while so you can refer to it as you link together fractions, mixed numbers, and fractions greater than one. Students may refer to this ruler to do problems. GO-25. Write these line lengths using mixed numbers. a) [  EMBED "Equation" \* mergeformat  inches ]  b) [  EMBED "Equation" \* mergeformat  inches ] c) [  EMBED "Equation" \* mergeformat  inches ] d) [  EMBED "Equation" \* mergeformat  inches ]  **** GO-26. Fraction Blackout A game for two players. Mathematical Purpose: To practice finding equivalent fractions. Object: To fill your game board by strategically choosing which fractions to shade and get your name on the board as a winner. Materials: One Fraction Blackout game board and one spinner page with spinner. Note: the fraction in each part of the spinner is the value assigned to that sector, NOT the size of the sector. The spinner is not a pie chart. Scoring: There is no scoring. How to Play the Game: Put your name on your own Fraction Blackout Game Board. Decide who will be First Player and who will be Second Player. If three are playing together, decide who will be Third Player. First Player chooses and spins either Spinner A or Spinner B. First Player records the fraction on the Fraction Blackout Game Board. First Player shades the fraction on the Fraction Blackout Game Board. The player may shade any blocks on the Game Board that add to the fraction spun. Both players must agree that the amount filled in is equal to the fraction spun. Alternate play. If a fraction is spun that is larger than the space the student has left, the student cannot play until the next turn. Players may choose which spinner to use (A or B) with each new play. Ending the Game: Continue to alternate play until one student has filled a Game Board. Other students may continue to play to complete their Game Board. When you have played Fraction Blackout, raise your hands and give the Fraction Blackout Game Board(s) to your teacher and follow her or his instructions. HOMEWORK for Day 3 begins here. GO-27. Copy and fill in the following equivalent fraction ratio tables, then write a list of equivalent fractions. a) [ 4 and 2;  EMBED "Equation" \* mergeformat  =  EMBED "Equation" \* mergeformat  =  EMBED "Equation" \* mergeformat  =  EMBED "Equation" \* mergeformat  ] b) [ 3 and 9;  EMBED "Equation" \* mergeformat  =  EMBED "Equation" \* mergeformat  =  EMBED "Equation" \* mergeformat  ]  GO-28. The perimeter of a rectangle is 40 centimeters. It is 1 centimeter longer than it is wide. Use a Guess and Check table to find its width. It will be easier if you draw a picture first. [ 9.5 centimeters ] GO-29. Use your fraction bars to answer the following questions. a) How many one-fourths are in one-half? [ 2 ] b) How many one-sixths are in two-thirds? [ 4 ] c) How many one-fourths are in six-eighths? [ 3 ] d) How many one-halves are in 3  EQ \f(5,10) ? [ 7 ] GO-30. Use what you know about rulers to complete the equivalent fractions below. a)  EQ \f(2,16) =  EQ \f( ,8) [ 1 ]b)  EQ \f(4,16) =  EQ \f( ,8) [ 2 ]c)  EQ \f(8,16) =  EQ \f( 1 , ) [ 2 ] d)  EQ \f(10,16) =  EQ \f( ,8) [ 5 ]e)  EQ \f(12,16) =  EQ \f( ,4) [ 3 ]f)  EQ \f(14,16) =  EQ \f( ,8) [ 7 ] GO-31.Farrell is a business man who eats lunch at a different place each day. He keeps track of his lunch expenses. On Monday, he spent $5; on Tuesday, $4.50; on Wednesday, $26.50; on Thursday, $4.75; and on Friday, $4.50. a) Calculate the mean of these amounts. Determine the mode and the median. [ mean = $9.05; mode = $4.50; median = $4.75 ] b) If you wanted to describe Farrell's spending habits on lunch as fairly as possible, which measure would you use and why? [ Answers will vary, but citing either median or mode would be fair. ] GO-32. Algebra Puzzles Write three pairs of numbers that make each equation true. a) x y = 5 [ (5, 0), (6, 1), (8, 3), ... ]b) x + y = -5 [ (-1, -4), (-2, -3), (0, -5), ... ] c) x y = -1 [ (0, 1), (1, 2), (2, 3), ... ]d) x y = -5 [ (1, 6), (0, 5), (2, 7), ... ] GO-33. Simplify each expression.  a) (7 + 6) 2 9 + 6 [ 240 ] c) 5 (2 + 4) 7 [ 23 ] b) (6 + 6) 2 4 4 [ -10 ] d) 6.9 + 2 2 (7 + 8) [ 66.9 ] DAY FOUR GO-34 through GO-50 OBJECTIVES Students will: explain how to determine whether a fraction is closest to zero, one-half, or one. find common denominators using equivalent fractions. compare two fractions using equivalent fractions. define and use inequality symbols when comparing integers. MATERIALS fraction bars (for students who need to use them for a visual model) fraction list resource page (GO-34) Cut the rows on the Fraction List resource page apart so that each student can glue or paste one row in his/her notebook. We have found that otherwise students make many errors copying the fractions. Have partners compare and discuss responses after completing the next problem, a problem in which they will mentally estimate the relative size of fractions. Have a quick class discussion about each part only to solicit descriptions of the students methods, especially classifying and grouping fractions. Note that the method for comparing fractions that we teach today is to help with understanding fractional relationships. We arrive at a simpler method on Day 5 using the Giant 1. **** GO-34. List the fractions below on your paper.  EQ \f(1,12) \f(7,6) \f(15,16) \f(13,12) \f(15,9) \f(6,100) \f(10,22) \f(6,7) \f(30,16) \f(2,17) \f(98,100) \f(12,25) \f(2,20) \f(6,11) \f(6,5) \f(6,2) \f(20,11)  a) List the fractions that are close to or greater than 1  EQ \f(1,2) , then cross them off your original list. [  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat  ] b) List the fractions that are close to 1, then cross them out. [  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat  ] c) List the fractions that are close to  EQ \f(1,2) , then cross them out. [  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat  ] d) List the fractions that are close to 0, then cross them out. [  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat  ] GO-35. For each of the following problems, be sure to write the complete fraction on your paper. [ Answers vary. ] a) Complete these fractions to make them close to 0:  EQ \f( ,16) ,  EQ \f( ,10) ,  EQ \f(4, ) ,  EQ \f(10,) . [ sample answers:  EMBED "Equation" "Word Object1" \* mergeformat ,  EMBED "Equation" "Word Object1" \* mergeformat ,  EMBED "Equation" "Word Object1" \* mergeformat ,  EMBED "Equation" "Word Object1" \* mergeformat  ] b) Rewrite these fractions to make them close to  EQ \f(1,2) :  EQ \f( ,15) ,  EQ \f( ,9) ,  EQ \f(4, ) ,  EQ \f(10, ) . [ sample answers:  EMBED "Equation" "Word Object1" \* mergeformat ,  EMBED "Equation" "Word Object1" \* mergeformat ,  EMBED "Equation" "Word Object1" \* mergeformat ,  EMBED "Equation" "Word Object1" \* mergeformat  ] c) Rewrite these fractions to make them greater than 1 but less than 2:  EQ \f(6, ) ,  EQ \f(10, ) ,  EQ \f( ,6) ,  EQ \f( ,3) . [ sample answers:  EMBED "Equation" "Word Object1" \* mergeformat ,  EMBED "Equation" "Word Object1" \* mergeformat ,  EMBED "Equation" "Word Object1" \* mergeformat ,  EMBED "Equation" "Word Object1" \* mergeformat  ] GO-36. Answer each question and write an example for each part below. a) If the numerator is very small compared to the size of the denominator, what whole number will the fraction be closest to on a number line? [ 0 ] b) If the numerator is about half the size of the denominator, where will the fraction be on the number line? [ near  EMBED "Equation" "Word Object1" \* mergeformat  ] c) If the numerator of a fraction is about the same size as the denominator, where will the fraction be on a number line? [ near 1 ] d) If the numerator of a fraction is larger than the denominator, where will the fraction be on the number line? [ beyond 1 ] GO-37. Use equivalent fraction ratio tables or fraction bars to complete parts (a) through (c). a) Write two fractions that are the same as  EQ \f(1,2) . [ Answers vary. ] b) Write two fractions that are the same as  EQ \f(3,5) . [ Answers vary. ] c) Write two fractions that are the same as  EQ \f(4,7) . [ Answers vary. ] GO-38. The sum of  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  + EMBED "Equation" \* mergeformat  is approximately: [ D ] (A) 1 (B) 2 (C) 3 (D) 4 GO-39.Anthony and David each bought a personal pizza. Anthonys pizza was cut into five pieces, and he ate three of them. David ate four of his seven pieces. Answer the questions below to help you decide who ate the most pizza. Remember that listing equivalent fractions is just like making a ratio table. a) Complete the list below to find the first seven equivalent fractions for  EQ \f(3,5) .  EQ \f(3,5) ,  EQ \f(6,10) ,  EQ \f(9,15) , ... [ ...  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat  ] b) Write the first seven equivalent fractions for  EQ \f(4,7) :  EQ \f(4,7) ,  EQ \f(8,14) , ... [ ...  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat  ] c) Find a fraction from the first set you wrote that has the same denominator as a fraction from the second set. Write them next to each other. [  EMBED "Equation" \* mergeformat  and  EMBED "Equation" \* mergeformat  ] d) The fractions  EQ \f(21,35) and  EQ \f(20,35) have common denominators; that is, their denominators are the same (35). By comparing the numerators, you can see which one is the larger fraction. If the pizzas were cut into 35 pieces, how many pieces would Anthony have eaten? How many would David have eaten? [ 21, 20 ] GO-40. Which is larger,  EQ \f(3,4) or  EQ \f(11,16) ? a) Write lists of equivalent fractions for the two values until you find fractions with common (same) denominators. [  EMBED "Equation" \* mergeformat  ] b) Which fraction is larger? [  EMBED "Equation" \* mergeformat  ] GO-41.  INEQUALITY SYMBOLS The symbol > means is greater than and the symbol < means  is less than. These symbols are called INEQUALITY SYMBOLS and are used to compare and order numbers. For example, 5 > 3 and 1 < 7. The symbol e" means  is greater than or equal to and d" means  is less than or equal to. Here is an easy way to remember what each inequality symbol means: the pointed part of the symbol always points to the smaller number, and the open part of the symbol always points to the larger number.  Make these notes in your Tool Kit to the right of the double-lined box. Rewrite the following expressions placing the correct inequality symbol between them. a) 3 ___ -2 [ > ]b) -5 ___ 2 [ < ]c) -3 ___ -7 [ > ]d) How will you help yourself to remember which direction the inequality symbol should go? HOMEWORK for Day 4 begins here. GO-42. Jan drove 120 miles in 3 hours. a) How far would Jan drive in 12 hours if she kept going at the same rate? Use a ratio table. [ 480 miles ] b) How far did Jan drive in half an hour if she always drove at the same rate? [ 20 miles ] c) How long would it take Jan to drive 100 miles? Explain your reasoning. Write your answer as a mixed number. [  EMBED "Equation" \* mergeformat  hours ] GO-43. Use your fraction bars to decide which fraction should replace each variable to make the following equations true. Some problems may have more than one answer. a)  EQ \f(1,4) = A + A [ A =  EMBED "Equation" \* mergeformat  ]b)  EQ \f(3,4) = B + C [ B =  EMBED "Equation" \* mergeformat ; C =  EMBED "Equation" \* mergeformat  ]c)  EQ \f(1,3) = D + E [ D =  EMBED "Equation" \* mergeformat ; E =  EMBED "Equation" \* mergeformat  ] d)  EQ \f(1,2) = F + G + G [ F =  EMBED "Equation" \* mergeformat ; G =  EMBED "Equation" \* mergeformat  ]e)  EQ \f(2,3) = H + I + I [ H =  EMBED "Equation" \* mergeformat ; I =  EMBED "Equation" \* mergeformat  or H =  EMBED "Equation" \* mergeformat ; I =  EMBED "Equation" \* mergeformat  ]f)  EQ \f(7,8) = J + K [ J =  EMBED "Equation" \* mergeformat ; K =  EMBED "Equation" \* mergeformat  or J =  EMBED "Equation" \* mergeformat ; K =  EMBED "Equation" \* mergeformat  ] GO-44. The sum  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  +  EMBED "Equation" \* mergeformat  + EMBED "Equation" \* mergeformat  is approximately: [ B ] (A) 1 (B) 2 (C) 3 (D) 4 GO-45.The local Little League is having its annual Pancake Breakfast, and Josh and Jean are helping their father make the batter. The recipe makes 50 pancakes and calls for 12 cups of flour. a) How much flour would Josh need for 200 pancakes? Use a ratio table or show another method. [ 48 cups] b) How many pancakes can Josh make with 60 cups of flour? [ 250 pancakes ] GO-46.Find the area and perimeter of each of these figures. All dimensions are in feet. Be sure your answers are in proper units. a)  [ A = 81.9 square feet; p = 41.2 feet ]b)  [ A = 152 square feet; p = 61 feet ] GO-47. Rewrite the following statements using >, <, or = to make each one true. Solve them by thinking, not by calculating and not by using a calculator. a)  EQ \f(3,6) ___  EQ \f(11,22) [ = ] b)  EQ \f(2,2) ___  EQ \f(3,4) [ > ] c)  EQ \f(9,7) ___  EQ \f(3,3) [ > ] GO-48. These comparisons are more difficult than those in the previous problem. Complete the steps below for each pair of fractions to write a correct inequality. a) Make a list of equivalent fractions to compare each pair. b) Clearly show the comparisons using a common denominator for each pair. Look at problem GO-39 if you need help. i)  EQ \f(3,4) ___  EQ \f(5,6) [ < ]ii)  EQ \f(4,9) ___  EQ \f(1,3) [ > ]iii)  EQ \f(3,8) ___  EQ \f(1,3) [ > ] Tell students that when they copy Diamond Problems, they should copy only the X, not the whole diamond. GO-49.Diamond Problems Copy the Diamond Problems below and use the pattern you discovered (shown in the icon under the problem number) to complete each. a)  [ x = -2; y = -4 ] b)  [ y = 1; x + y = 5 ] c)  [ xy = 45; x + y = -14 ] d)  [ y = -2; xy = -18 ] GO-50. Written as a percent,  EQ \f(5,4) is equivalent to: [ C ] (A) 54% (B) 80% (C) 125% (D) 45% DAY FIVE GO-51 through GO-64 OBJECTIVES Students will: change different denominators to common denominators using the Identity Property of Multiplication. use a rectangular area model for the Identity Property of Multiplication. MATERIALS ruler Todays lesson introduces two other methods for finding equivalent fractions, the Identity Property of Multiplication followed by a rectangular area model. The last problem of the day asks students to compare the three methods. This is a full day which will require pacing to ensure students complete the entire lesson before leaving class. The homework extends the lesson to teach students a way to compare fractions. GO-51. Answer the following questions regarding multiplication. a) What is 453 1?  EQ \f(1,3)  1? N 1? [ 453;  EMBED "Equation" \* mergeformat ; N ] b) Describe what happens to a number when you multiply it by 1. [ It remains the same. ] GO-52.  IDENTITY PROPERTY OF MULTIPLICATION Any number multiplied by 1 equals itself; that is, it remains unchanged. This is called the IDENTITY PROPERTY OF MULTIPLICATION. 7 1 = 7 -3 1 = -3 x 1 = x  Include these examples of the Identity Property of Multiplication in your Tool Kit to the right of the double-lined box. Complete each equation. a) -4 1 = ___b) 4 1 = ___c) B ___ = B GO-53. Complete the ratio table below to find equivalent fractions for  EQ \f(2,3) . We will refer to this table later. Numerator246812Denominator3691218 GO-54. Write three equivalent fractions for the number 1. [ answers vary ] GO-55.We have previously found equivalent fractions using a ratio table. A quicker method to rename a fraction as an equivalent fraction with a new denominator is to use the Identity Property of Multiplication. In the case at right, the 1 is in disguise as  EQ \f(3,3) . Notice that  EQ \f(6,9) and the original  EQ \f(2,3) are just different names for the same number. By multiplying the original fraction by  EQ \f(3,3) , we have not changed the value of  EQ \f(2,3) ; we have just changed its name. When we use the Identity Property of Multiplication, we multiply by 1 in one of its fractional forms. We can call it the Giant 1 to remind ourselves of what it really represents, the Identity Property of Multiplication. =   Practice using the Giant 1 by doing the problems below. Write the fraction you use for the Giant 1 each time in each part. a)  EQ \f(2,3)  1 =  EQ \f( ,12)  [  EMBED "Equation" \* mergeformat ; 8 ]b)  EQ \f(2,3)  1 =  EQ \f( ,15)  [  EMBED "Equation" \* mergeformat ; 10 ]c)  EQ \f(2,3)  1 =  EQ \f( ,18)  [  EMBED "Equation" \* mergeformat ; 12 ] GO-56.Another way to show the effect of multiplying by  EQ \f(3,3) is to start with a rectangle in which we have represented  EQ \f(2,3) by shading two of the three parts.   EQ \f(2,3)   EQ \f(6,9)  The second rectangle shows the effect of multiplying both the numerator and the denominator of  EQ \f(2,3) by three, and the equation below represents the relationship shown by the rectangles.  EQ \f(2,3)   EQ \f(3,3) =  EQ \f(6,9) a) Draw a rectangle like the first one and label it  EQ \f(2,3) . b) Draw another rectangle like the one you drew in part (a). Then draw horizontal lines to represent multiplying by  EQ \f(4,4) . c) Write an equation that represents the relationship between the two rectangles you drew.  [  EMBED "Equation" \* mergeformat  =  EMBED "Equation" \* mergeformat  ] After students have completed the following problem, lead a class discussion on their answers to summarize the days work. GO-57. Consider the three methods you just used to show equivalent fractions: ratio tables, the Giant 1, and the rectangular area model. How are they similar? How are they different? [ We use the Giant 1 to create equivalent fractions with the Identity Property of Multiplication. We create equivalent fractions using diagrams by comparing parts cut into greater number of smaller parts. In ratio tables we create equivalent fractions by multiplying entries by  EMBED "Equation" \* mergeformat , so they essentially use a Giant 1. ] HOMEWORK for Day 5 begins here. GO-58.Use vertical lines in a rectangle to create and shade  EQ \f(3,4) . Use a horizontal line to double the number of spaces. Write an equation using the Identity Property of Multiplication (Giant 1) to summarize what you did. [  EMBED "Equation" \* mergeformat  ] GO-59. Copy the following problems onto your paper and show how to multiply by 1 to create equivalent fractions. Replace the 1 with a fraction and complete the equivalent fraction. a)  EQ \f(1,3)  1 =  EQ \f( ,24)  [  EMBED "Equation" \* mergeformat ; 8 ]b)  EQ \f( ,12) =  EQ \f(3,4)  1 [ 9;  EMBED "Equation" \* mergeformat  ]c)  EQ \f(2,5)  1 =  EQ \f(12, )  [  EMBED "Equation" \* mergeformat ; 30 ]  d) Copy part (a) in your Tool Kit to the right of the double-lined box for the Identity Property of Multiplication. GO-60. Suppose we want to compare  EQ \f(3,5) and  EQ \f(4,7) . We can use the Giant 1 as a shortcut to compare these fractions. a) List the denominators that  EQ \f(3,5) can have: 5, 10, 15, etc. b) List the denominators that  EQ \f(4,7) can have: 7, 14, 21, etc. c) Circle the smallest denominator that  EQ \f(3,5) and  EQ \f(4,7) can share. [ 35 ] d) Now use the idea of the Giant 1 to change the denominators of both fractions below to the denominator you need.  EQ \f(3,5)  1 =  EQ \f( ,35) [ 21 ]  EQ \f(4,7)  1 =  EQ \f( ,35) [ 20 ]e) Compare the fractions. Which fraction is larger? Write a number sentence to show the relationship using an inequality symbol. [  EMBED "Equation" \* mergeformat  because 21 is greater than 20; therefore,  EMBED "Equation" \* mergeformat . ] f) Compare your work on this problem with the method in problem GO-39. Which method do you prefer? [ In this method you only work with the denominators until you find a common multiple. ] GO-61.Use the Identity Property of Multiplication to change the following pairs of fractions to pairs with common denominators, and then determine which of the two fractions is larger. Write an inequality statement (< or >) to compare  EQ \f(2,3) and  EQ \f(5,8) : Example:  EQ \f(2,3)  1 =  EQ \f(16,24) and  EQ \f(5,8)  1 =  EQ \f(15,24) . Therefore,  EQ \f(2,3) >  EQ \f(5,8) . Use the process above to compare the following fractions. a)  EQ \f(7,10) and  EQ \f(2,3) [ > ] b)  EQ \f(7,10) and  EQ \f(3,4) [ < ]c)  EQ \f(4,5) and  EQ \f(2,3) [ > ] GO-62.Hector is using radar to monitor speeds on a street near his school. He records the following speeds: 34, 37, 39, 40, 36, 35, 55, 40, 35, and 39. a) Calculate the mean of these speeds. [ 39 mph ] b) Find the median. [ 38 mph ] c) Find the mode. [ 35, 39, and 40 mph ] d) Hector wants to show that there is a  speeding problem. Which measure of average would he use? Explain why. [ Mean is highest, while each of the modes is above the probable speed limit. ] e) What do you think the posted speed limit might be? [ probably 35 mph ] GO-63. Simplify each of the following expressions. a) 4 3 (-7 + 4) 2 [ 22 ]b) 7 + 8 (8 40) + 1 [ -248 ] c) (11 3 + (-4)) 3 [  EMBED "Equation" \* mergeformat  ]d)  EQ \f(23 + 13,18 3) [ 6 ] GO-64. Write all the numbers between 1 and 40 that can be written as the sum of consecutive positive integers. For example, 17 = 8 + 9 and 26 = 5 + 6 + 7 + 8. a) Which numbers cannot be written this way? [ 1, 2, 4, 8, 16, 32 ] b) Predict the next three numbers that are impossible to write in this way. How did you decide what they are? [ 64, 128, 256; powers of 2 ] DAY SIX GO-65 through GO-78 OBJECTIVES Students will: use a table to compare three models for equivalent fractions. MATERIALS mental math resource page fraction-decimal-percent grids (students should have them in their binders) standard rulers resource page from Fraction Blackout fraction bars or Giant Ruler (if students need them as a model) equivalent fraction table resource page Today students will compare three methods for finding equivalent fractions. These methods include the ratio table, Giant 1, and a rectangular model. The resource page has been developed to help students readily compare the three models. Students will again play Fraction Blackout today using spinners C and D. Make sure there are copies of Fraction Blackout available for students who may not have the grid from Day 2. The parallelogram in GO-71 will need to be measured to the nearest sixteenth of an inch. Use mental math problems MM-26 and MM-27. GO-65. Practice mental math according to your teachers directions. Explain in writing how you solved one of the problems. **** GO-66. Here is a table that shows the three methods we used to find equivalent fractions. On the resource page your teacher gives you, show each of these methods to find the next three equivalent fractions for parts (a) through (c). Item Ratio Table Giant 1 Rectangular Model  EQ \f(1,2)       a)  EQ \f(1,3) b)  EQ \f(1,4) c)  EQ \f(2,5)  GO-67.Assume Dr. Karydas sees 8 patients every two hours. a) How many people does Dr. Karydas see in three hours? Solve by using a ratio table. [ 12 patients ] b) How many people can Dr. Karydas see in seven hours? Solve by using a ratio table. [ 28 patients ] c) How many patients can Dr. Karydas see in 1 EQ \f(1,2) hours? Solve by using the Identity Property of Multiplication (the Giant 1). [ 6 patients ] d) How many patients can Dr. Karydas see in N hours? [ 4N patients ] e) If P is the number of patients Dr. Karydas sees in N hours, write an equation relating P and N. [ P = 4N ] GO-68. Check your answers to each part of the preceding problem by substituting the number of hours available as the value of N in the formula you just found. For example, if Dr. Karydas worked for five hours (N = 5), she would see 4(5) = 20 patients. Remind your students that |4| = 4 and |-3| = 3. GO-69.The graph of the absolute value is interesting and xydifferent. Fill out the table at right and then plot the points on graph paper to get the graph of y = |x|. Since |-3| = 3, one of the points on the graph will be (-3, 3). [ y-values 1, 2, 3, 4, 1, 2, 3, 4; The graph is V-shaped. ]0 1 2 3 4 -1 -2 -3 -40 Make sure your students still have their resource pages for Fraction Blackout because they will use Spinners C and D for todays game. **** GO-70. Play Fraction Blackout with Spinners C and D instead of Spinners A and B. Remember: the fraction in each part of the spinner is the value assigned to that sector, NOT the size of the sector. The spinner is not a pie chart. Teachers will need to supply the answers to the next problem as the lengths change with the printing process. Be sure to measure the parallelogram in the student text. GO-71.Find the perimeter of the parallelogram at right by measuring. Measure sides to the nearest  EQ \f(1,16) inch.  HOMEWORK for Day 6 begins here. GO-72. Use the Identity Property of Multiplication (the Giant 1) or fraction strips to compare the following pairs of fractions and decide whether the first is less than ( < ), greater than ( > ), or equal to ( = ) the second. If you use fraction strips, draw an accurate picture. a)  EQ \f(4,5)  1 =  EQ \f( ,20) and  EQ \f(3,4)  1 =  EQ \f( ,20) [ > ] b)  EQ \f(3,8) and  EQ \f(2,3) [ < ]c)  EQ \f(2,5) and  EQ \f(3,7) [ < ]d)  EQ \f(10,12) and  EQ \f(7,9) [ > ]e) What is the smallest common denominator for part (d)? [ 36 is the smallest denominator. Check whether students used  EMBED "Equation" \* mergeformat  or  EMBED "Equation" \* mergeformat  when they did part (d). This is an opportunity to discuss reducing fractions, or using the Identity Property of Multiplication backwards. ] GO-73. Using your fraction bars, replace each variable to make the equations true. a)  EQ \f(1,12) =  EQ \f(1,4)  M [ M =  EMBED "Equation" \* mergeformat  ]b)  EQ \f(2,3) =  EQ \f(3,4)  N [ N =  EMBED "Equation" \* mergeformat  ]c)  EQ \f(1,8) =  EQ \f(1,2)  P [ P =  EMBED "Equation" \* mergeformat  ] d)  EQ \f(1,6) =  EQ \f(2,3)  Q [ Q =  EMBED "Equation" \* mergeformat  ]e)  EQ \f(3,4) =  EQ \f(7,8)  R [ R =  EMBED "Equation" \* mergeformat  ]f)  EQ \f(3,12) =  EQ \f(2,3)  T [ T =  EMBED "Equation" \* mergeformat  ] GO-74.Diamond Problems Complete the Diamond Problems below. a)  [ xy = -3; x + y = 2 ] b)  [ x = 5; y = 2 ] c)  [ x = 3; y = 2 ] d)  [ y = 3.5; xy = 1.75 ] GO-75. Use your fraction-decimal-percent grid. Write an equation that lists equivalent expressions for the shaded area in each box. Be sure you name at least one fraction, one decimal, and one percent for each problem. a) [  EMBED "Equation" \* mergeformat  =  EMBED "Equation" \* mergeformat , 0.75, 75% ]b) [  EMBED "Equation" \* mergeformat  =  EMBED "Equation" \* mergeformat , 0.40, 40% ]c) [  EMBED "Equation" \* mergeformat  =  EMBED "Equation" \* mergeformat , 0.40, 40% ] GO-76. Using a straightedge, carefully draw your initials with straight line letters. Measure the length of each line segment to the nearest sixteenth of an inch. Find the length of your initials by adding all the line segments. You may want to use graph paper. An example is shown at right.  GO-77. Which fraction represents 6%? [ D ] (A)  EQ \f(60,100)  (B)  EQ \f(6,1000)  (C)  EQ \f(6,10)  (D)  EQ \f(6,100)  GO-78.Find the perimeter of the white part of the diagram at right. [ 31 units ] DAY SEVEN GO-79 through GO-89 OBJECTIVES Students will: develop the concept of proportion from ratio tables. calculate perimeter and area using subproblems. write variable expressions and equations. MATERIALS fraction bars The primary focus of todays classwork is to tie together the Identity Property of Multiplication, pictures, and ratio tables as useful methods for finding equivalent fractions. The word proportion is introduced today in GO-80. Students will find that they can write and/or solve proportions using ratio tables, the Identity Property of Multiplication (Giant 1), or pictures (rectangular models). GO-79. Exchange your work from problem GO-76 with your partner. Check your partners measurements. Also check the calculation of the total length of your partners initials. When you have completed this task, write checked by and sign your name. GO-80. In this chapter we have been working with equivalent fractions that represent the same amount. Technically, we have been working with proportions.  PROPORTION A PROPORTION is an equation that states that two fractions are equal.  EQ \f(3,8) =  EQ \f(6,16)   EQ \f(4,12) =  EQ \f(6,18)   EQ \f(2,3) =  EQ \f(x,30)  a) Use the Identity Property of Multiplication (Giant 1) to show that  EQ \f(2,3) =  EQ \f(8,12) is a proportion. Write your work in the space to the right of the double-lined box in your Tool Kit. b) Find a value of x so that  EQ \f(x,6) =  EQ \f(2,3) is a proportion. [ x = 4 ] c) Find a value of y so that  EQ \f(10,y) =  EQ \f(2,3) is a proportion. [ y = 15 ] GO-81. Use a ratio table, a rectangular model, or the Identity Property of Multiplication (Giant 1) to decide which of the following ratio pairs could form a correct proportion. Be sure to show your work. [ (a), (c), (d) ] a)  EQ \f(6,16) ,  EQ \f(3,8) b)  EQ \f(5,9) ,  EQ \f(4,8) c)  EQ \f(4,6) ,  EQ \f(6,9) d)  EQ \f(6,10) ,  EQ \f(9,15)  GO-82.Complete these ratio tables which convert quantities. In the last column, write an appropriate variable expression. a)Minutes1461/5MSeconds602403601260M b)Hours121024HMinutes60120600144060H c)Hours145620HSeconds360014400201,60072,0003600Hd) For the problems above, write the three equations which relate seconds (S), minutes (M), and hours (H). For example, from (a) you will see S = 60M. Now write the other two equations. [ M = 60H; S = 3600H ] GO-83. Jeri was buying detergent for washing dishes at home. She knew that the last 12 ounce bottle she bought lasted about 6 weeks. a) Assuming that her family generally uses detergent at the same rate, fill in the following table. Ounces of Detergent1283018Number of Weeks64159b) Use the table above to write an equation relating D (the number of ounces of detergent) and W (the number of weeks the detergent will last) [ W =  EMBED "Equation" \* mergeformat  ] c) Use graph paper to draw a graph relating D and W. The horizontal axis should represent the number of ounces of detergent, and the vertical axis should represent the number of weeks the detergent will last. To help you start, if you have 0 ounces of detergent, it will last 0 weeks, so (0, 0) is one of the points on your graph. GO-84.When Harris returned from Canada he still had 96 Canadian dollars (C). At the time, each U.S. dollar (A) was worth $1.50 in Canadian dollars. Use ratios to find the value of his Canadian dollars in U.S. dollars.  a) Use a ratio table to solve the problem. [ 64 U.S. dollars ] U.S. dollars$1.00$2.00$8.00$16.00$32.00$64.00Canadian dollars$1.50$3.00$12.00$24.00$48.00$96.00b) Suppose Harris had C Canadian dollars and converted them to A U.S. dollars. Write an equation that expresses A in terms of C. [ A =  EMBED "Equation" \* mergeformat C ] HOMEWORK for Day 7 begins here. GO-85. GO-86.Tim earns $6.25 per hour at Roberts Run-Inn Restaurant. He can only work four hours a day at the restaurant. If he actually makes $5 per hour after taxes are deducted, how many days will it take him to earn $325 to buy a CD player? Solve the problem using either a ratio table or a Giant 1 to solve the proportion. [ 17 days ] Use your fraction bars to find the answer to these division problems. a) How many  EQ \f(1,12) s are in  EQ \f(2,3) ? [ 8 ] b) How many  EQ \f(1,8) s are in  EQ \f(3,4) ? [ 6 ]c) How many  EQ \f(1,6) s are in  EQ \f(2,3) ? [ 4 ]d) How many  EQ \f(1,8) s are in  EQ \f(1,2) ? [ 4 ] e) How many  EQ \f(1,6) s are in  EQ \f(4,4) ? [ 6 ] GO-87.Find the perimeter and area of the figure at right. All dimensions are given in feet. Make sure you show all subproblems. Re-draw this figure and sketch the rectangles you will use for the subproblems. [ perimeter = 48 feet; area = 64 sq. ft ] GO-88. Algebra Puzzles Write three pairs of numbers that make each equation true. For each equation, choose at least one value of x that is a mixed number. a) y = x + 9 [ (0, 9), (-1, 8), (-2, 7), (1.5, 10.5), ... ]b) y = x 9 [ (10, 1), (9, 0), (8, -1), (10.5, 1.5), ... ] c) y = 2x 1 [ (0, -1), (1, 1), (2, 3), (1.5, 2), ... ]d) y = 6x 3 [ (0, -3), (1, 3), (2, 9), (1.5, 6), ... ] GO-89. Simplify each expression. a)  EQ \f(4 + 8 2,12 2 1) [ 4 ] b) 3 (9 6) + 3 + 2 5 [ 22 ]  c) 3 (3 + 6) + 3 8 [ 51 ]d)  EQ \f(35 7 5,5 (3 + 2)) [ 1 ] DAY EIGHT GO-90 through GO-104 OBJECTIVES Students will: set up proportions to solve problems. find equivalent fractions using ratio tables. solve algebraic equations using variables and fraction bars. MATERIALS ruler fraction bars Todays lesson begins with additional practice using ratio tables and writing and solving equations before students solve the theme problem GO-94. In the theme problem students are asked in part (c) to describe the method they used to solve the problem. As you circulate throughout the classroom today, make note of the different ways students used to solve the problem. You may want student teams to create posters of their work as comparisons how the problem was solved. Depending upon the time frame you have for Days 9 and 10, this poster option could be saved as a part of the Chapter Summary and/or review for those days. GO-90. We often use letters or variables the same way we use blanks in ratio tables. 4x8101520a) Find what x would be in this ratio table. [ x = 6 ] b) Since the ratios are equal, write a proportion using x from the table above. [  EMBED "Equation" \* mergeformat  or  EMBED "Equation" \* mergeformat  ] GO-91. Five members of the school band were planning the annual band dinner and concert fund-raiser. Last year they found that 16 pounds of spaghetti feeds 40 people. This year they hope to feed 160 people in the cafeteria and 360 more in the gym. Decide how much spaghetti they will need in each location. a) Answer this question by using a ratio table. b) Answer this question by using a Giant 1. [ 64 pounds; 144 pounds ] GO-92. Mai found she needed 20 ounces of noodles to feed 6 people. She wanted to know how many ounces of noodles would be needed to feed 9 people. a) Solve the problem using a ratio table. [ 30 ] People6912Ounces of Noodles20x40b) If Mai were buying noodles for 45 people, how many ounces of noodles would she need to buy? [ 150 ounces ] GO-93. Copy and complete the equivalent fraction ratio table. N612306042 D 15 30 75 150 10 5a) Write any three fraction ratios from the table as proportions. b) Write an equation that relates N and D. [ D = 2.5 N ] GO-94. Patricia Garcia was reading a story to her sister, Ana, about a kindly giant who lived in a very cold place. Ana felt sorry for the giant and wanted to make him a quilt just like hers (only bigger, of course). Anas quilt is 3744 square inches, and it took 104 hours to make. Ana wants the giant quilt to be 9360 square inches. If she makes the giant quilt at the same rate at which she made her quilt, how long will it take to make it? a) How many hours will it take to make the quilt? How many days? [ 260 hours; 10 days 20 hours ] b) How much bigger is the giants quilt than Anas? [ 2.5 times larger ] c) Describe the method you used to solve this problem. GO-95. The dog chewed up part of Marcos homework paper so that all that was left of the first problem was  EQ \f(4,33) =  EQ \f(,1782) . What was the missing numerator? [ 216 ] GO-96. We are going to arrange fractions along a number line. a) Draw a number line from 0 to 1 like the one below.  b) Mentally sort the fractions below into three groups: closest to 0, closest to  EQ \f(1,2) , and closest to 1.  EQ \f(5,8) \f(3,16) \f(3,8) \f(16,16) \f(1,4) \f(1,8) \f(3,4) \f(7,8)  c) Now write the fractions on the number line where they belong. You may need to find a common denominator to compare fractions. [  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat ,  EMBED "Equation" \* mergeformat , ] GO-97. Use a ruler to draw a line segment with each of the following lengths. Draw the four line segments end-to-end so they make one straight line. Be sure to mark the starting and stopping place for each line segment. Start near the left edge of your paper. a) 3  EQ \f(3,8) inchesb) 2  EQ \f(3,16) inchesc) 1  EQ \f(3,4) inchesd)  EQ \f(1,2) inchese) Add to find the total length of the line segment composed of parts (a) and (b). Check your work by measuring. [  EMBED "Equation" \* mergeformat  inches ] f) Add, then measure to check the total length of the line segments composed of parts (c) and (d). [  EMBED "Equation" \* mergeformat  inches ] g) Find the total length of the line segments in parts (b), (c), and (d). [  EMBED "Equation" \* mergeformat  inches ] h) Find the total length of all four line segments by adding the fractions. You may use your fraction bars. Check your work by measuring. [  EMBED "Equation" \* mergeformat  inches ] HOMEWORK for Day 8 begins here. GO-98.Complete these tables which convert linear measures: a)feet1465finches1248726012f b)miles121011mfeet528010,56052,80058,0805280m c)yards1456111yfeet3121683333y GO-99.To find her usual bedtime, Zoe kept a record of what time she went to bed. These are the times she recorded: 9:30 p.m., 10:30 p.m., 10:00 p.m., 9:00 p.m., 11:00 p.m., 9:00 p.m., 9:30 p.m., 10:00 p.m., 11:00 p.m., and 9:00 p.m. a) Find the mode of Zoes bedtimes. [ 9:00 p.m. ] b) Find the median. [ 9:45 p.m. ] c) When you calculate the mean, what values will you use for 9:30 p.m. and 10:30 p.m.? [ 9.5 and 10.5 ]d) Calculate the mean. [ 9.85 or 9:51 p.m. ] e) If Zoe wants to convince her parents that she usually goes to bed early and should be allowed to stay up late this Friday, which measure of central tendency will she use? Explain. [ She should use the mode, because that is the earliest time. She can also argue that she is in bed before 10:00 p.m. in each of the measures. ] GO-100. Use your fraction bars to solve these mixed practice problems: a)  EQ \f(11,12) = W + Y [  EMBED "Equation" \* mergeformat  and  EMBED "Equation" \* mergeformat , other answers are possible ]b)  EQ \f(3,8) =  EQ \f(3,6)  K [  EMBED "Equation" \* mergeformat  ]c)  EQ \f(1,4) = N  EQ \f(7,12)  [  EMBED "Equation" \* mergeformat  ]d) How many groups of two-thirds are in 3  EQ \f(2,3) ? [  EMBED "Equation" \* mergeformat  ] e) How many  EQ \f(1,12) s are in 1  EQ \f(1,4) ? [ 15 ] GO-101.The Garcias plan to carpet 1962 square feet of their house. Carpet is sold by the square yard, and the carpet Maria Garcia has chosen costs $15.00 per square yard. a) How many square yards are there in the Garcias house? Remember that one square yard is equal to nine square feet. [ 218 square yards ] b) How much will it cost for the Garcias to carpet their house? [ 218 square yards $15 = $3270 ] GO-102.Victor and Hugo were shooting baskets. Hugo made 6 of his 10 shots. Victor made 12 out of 15 shots. Who is the better shooter? a) Answer this question by using a ratio table. b) Answer this question using a Giant 1. c) Answer this question using a proportion. [ Victor is the better shooter because  EMBED "Equation" \* mergeformat  is greater than  EMBED "Equation" \* mergeformat . ] Many equations take the form y = mx + b. In todays Algebra Puzzles, we introduce a coefficient in front of the x, our first m in this context. Familiarity with this form will be useful later. GO-103. Algebra Puzzles Write three ordered pairs that make each of the following equations true. Use at least one fraction greater than one for x in each equation. a) y = -2x + 1 [ (0, 1), (-2, 5), ( EMBED "Equation" "Word Object1" \* mergeformat , -2), ( EMBED "Equation" "Word Object1" \* mergeformat , -4), ... ]b) y = -2x 1 [ (0, -1), (-1, 1), ( EMBED "Equation" "Word Object1" \* mergeformat , -4), (- EMBED "Equation" "Word Object1" \* mergeformat , 2), ... ] GO-104. Simplify each expression. a) 2 (3 4 + 8) + 6 2 [ 52 ]b) 7 + 5 (2 3 + 6) 2 + 7 [ 134 ] c) (4 9) (6 3) 2 + 4 [ 4 ]d) 8 + 7 (6 + 18 3) + 28 2 [ 106 ] DAYS NINE AND TEN GO-105 through GO-122 OBJECTIVES Students will: compare ratios to solve problems. solve problems using ratio tables. summarize the chapters main ideas. MATERIALS fraction bars These two days provide time for summary, self-evaluation, and review problems. We suggest giving class time to start the summary. Give a few more review problems for homework and save most of them for the second day. You may also choose to revisit the theme problem that was solved on Day 8. Depending on the pace of your class these two days would provide the time to present the different approaches used by the students. GO-105. Chapter Summary It is time to summarize and review what you have learned in this chapter. a) Go back and read problem GO-57. Explain how to find an equivalent fraction for  EQ \f(5,7) using all three models. b) Explain how to compare two fractions. GO-106. Self Evaluation When you finish a chapter, you need to reflect on how well you have learned the material. One way to check your understanding at the end of a chapter is to try a problem from each objective and then evaluate your confidence with that objective. Try these five problems which match the five objectives from this chapter. a) Find the equivalent fraction:  EQ \f(2,5) =  EQ \f(8,x) . [ 20;  EMBED "Equation" \* mergeformat  ] b) Show how to use the Giant 1 to show  EQ \f(3,4) =  EQ \f(15,20) . [  EMBED "Equation" \* mergeformat  ] c) Complete this ratio table.x62430y31215d) Write an equation based on the ratio table in (c) that relates y to x. [ y =  EMBED "Equation" \* mergeformat  ] When students have finished these problems, display the correct answers so students can evaluate their progress in learning these objectives. e) Your teacher will tell your class the answers to the four questions. After you check your answers, write the objective name and then use the scale described below. For example, you might write, Equivalent fraction ability = 3. The other objectives would be Giant 1, ratio tables, and writing equations from ratio tables. On a scale of 1 through 5, evaluate your understanding of the objective. 1 = I dont understand this skill. 2 = I do not understand it well. 3 = I usually understand this idea, but I might need a little more practice. 4 = I understand this topic quite well. 5 = Bring on the quiz! I understand this idea very well. How you use the rest of the problems will depend on how much time you used on Day 9 for the chapter summary and self-evaluation. Use some of the problems to make a complete assignment for Day 9 and homework for that day. The rest of the problems should be used for Day 10 classwork and homework as a day for the consolidation of the chapter ideas. GO-107.Draw a rectangle, use vertical lines, and shade  EQ \f(3,5) . Then draw in the number of horizontal lines needed to show multiplication by  EQ \f(4,4) . a) What fraction now represents the shaded part? [  EMBED "Equation" \* mergeformat  ] b) The shaded part is also represented by  EQ \f(3,5) . Write an equation to show the relationship between the two representations. [  EMBED "Equation" \* mergeformat  =  EMBED "Equation" \* mergeformat  ] c) Copy and complete this table to verify the relationship you wrote in part (b). Numerator36912Denominator5101520 GO-108.Diamond Problems Complete the Diamond Problems below. a)  [ x = -6; y = 1 ] b)  [ x = 3; y = -2 ] c)  [ x = -2; x + y = -7 ] d)  [ x = -7; y = 3 ] GO-109. Complete these ratio tables. a)Hours1271013HPay$5.25$10.50$36.75$52.50$68.255.25Hb) Write the equation which relates H, hours worked, and P, pay received. [ P = 5.25H ] c)Sodas235615SCost$0.90$1.35$2.25$2.70$6.750.45Sd) Write the equation which relates S, the number of sodas, and C, their cost. [ C = 0.45S ] GO-110. Fill in the ratio table to find other fractions equivalent to  EQ \f(3,8) . N363060033-3-6 D 8 16 80 1600 88 -8 -16 GO-111. Terry thinks he is a better basketball shooter than Larry because he made 17 out of 30 shots while Larry only made 12 out of 20 shots. Use the method of your choice to determine who is the better shooter. [  EMBED "Equation" "Word Object4" \* mergeformat  >  EMBED "Equation" "Word Object5" \* mergeformat ; Larry has a higher ratio and is a better shooter. ] GO-112. Jawbreakers are 3 for $0.15. a) Fill in the following ratio table: Number1235143NCost$0.05$0.10$0.15$0.25$7.150.05Nb) How much will 213 jawbreakers cost? [ $10.65 ] GO-113. Use your fraction bars to answer the following questions. a) How many groups of  EQ \f(5,12) s are in  EQ \f(5,6) ? [ 2 ] b) How many groups of  EQ \f(3,8) s are in  EQ \f(3,4) ? [ 2 ] c) How many one-halves are in  EQ \f(3,4) ? [  EMBED "Equation" \* mergeformat  ] d) How many one-sixths are in  EQ \f(5,12) ? [  EMBED "Equation" \* mergeformat  ] e) How many one-thirds are in 1 EQ \f(1,2) ? [  EMBED "Equation" \* mergeformat  ] GO-114.While Mrs. Poppington was visiting the historic battleground at Gettysburg, she began talking to the workmen who were replacing the sod in a park near the visitors center. The part of the lawn being replaced is shown in the diagram at right. (Measurements are in yards. The diagram is not drawn to scale, but all corners are right angles.)a) Use your ruler to make a scale drawing of the park. Let  EQ \f(1,4) inch equal 1 yard. b) How many square yards of sod will be needed? [ 54 square yards ] c) At $2.43 a square yard, how much will the sod cost? [ $131.22 ] d) The area will be surrounded by a temporary fence which costs $0.25 per linear foot. How many feet will be needed, and how much will it cost? [ 120 feet; $30 ] e) How much will it cost to replace the sod? [ $161.22 ] GO-115. Write each line length shown below using mixed numbers. a) [  EMBED "Equation" \* mergeformat  inches ]  b) [  EMBED "Equation" \* mergeformat  inches ] c) [  EMBED "Equation" \* mergeformat  inches ] d) [  EMBED "Equation" \* mergeformat  inches ]  GO-116.Every summer, Jacques mother takes him to see her familyAge (years)Height (cm) GO-117.in Luxembourg. The day he arrives, his grandfather measures him. The table at right gives his height (in centimeters) each year. Plot Jacques growth on graph paper. The horizontal axis should be his age, and the vertical axis should be his height. On the horizontal axis use one space for each year of age; on the vertical axis use one space for each 10 centimeters of height. It costs $21 to buy enough potato salad to feed 40 people. How much will it cost to buy enough potato salad for 180 people? Set up a ratio table to answer the question. [ $94.50 ] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1661 89 96 99 103 107 112 119 126 134 142 151 160 169 177 182 G0-118. Take your pulse for 10 seconds. Remember to use your index and middle fingers, not your thumb. Assume that your pulse rate will be fairly constant over the time periods mentioned below. Use a ratio table or the Identity Property of Multiplication (the Giant 1) to solve each part. a) How many times does your heart beat in 10 seconds? [ answers vary ] b) 30 seconds?c) 60 seconds?d) 5 minutes? e) 60 minutes? f) 24 hours? GO-119.Find the perimeter and area of the figure at right. All dimensions given are in meters. Make sure you show all subproblems. [ P = 67.2 meters; A = 171.99 sq. meters ] Part (f) of the next problem requires extra thought. GO-120. Using your fraction bars, replace each variable to make the equations true. a)  EQ \f(1,3) =  EQ \f(1,4) + H [ H =  EMBED "Equation" \* mergeformat  ]b)  EQ \f(2,3) =  EQ \f(1,2) + L [ L =  EMBED "Equation" \* mergeformat  ]c)  EQ \f(5,8) =  EQ \f(1,4) + W [ W =  EMBED "Equation" \* mergeformat  ] d)  EQ \f(5,6) = Q +  EQ \f(1,3)  [ Q =  EMBED "Equation" \* mergeformat  ]e)  EQ \f(3,4) =  EQ \f(3,8) + B [ B =  EMBED "Equation" \* mergeformat  ]f)  EQ \f(7,8) = D +  EQ \f(5,12)  [ D =  EMBED "Equation" \* mergeformat  ] GO-121. For which equation is (3, 6) a solution? [ C ] (A) 3x = y (B) x y = 3 (C) x + y = 9 (D)  EQ \f(x, y) = 2 GO-122. What We Have Done in This Chapter Below is a list of the Tool Kit entries from this chapter.  GO-1 Ratios GO-7 Mixed Numbers and Fractions Greater Than One GO-14 Equivalent Fractions GO-41 Inequality Symbols GO-52 Identity Property of Multiplication (also GO-61) GO-80 Proportion Review all the entries and read the notes you made in your Tool Kit. Make a list of any questions, terms, or notes you do not understand. Ask your partner or study team members for help. If anything is still unclear, ask your teacher. 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wNll*FE77,zTi, Nh{U@x>\sBhbȘ鼲bx[ -rNysnəS($Qjm:`t2J;taʡC\2sB+^0m*O)2S R٧dZo ׄ`kyU۸L REԽj+.$Sh(*naU3rhq;ZjH D۔ހȆY8H.ٻWUԻ,PICT tCompObj UObjInfo"OlePres000#(" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 26 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 25 521 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 207 0 rlineto stroke end d%MATH  58l FMathType 5.0 Equation1ELOEquation.DSMT4  58 Equationd`Ole10Native$Ole10FmtProgID % _1148924022FXr0Xr0Ole &PIC 'dPICT )tCompObj3UObjInfo5    t dxpr   " currentpoint ",Times .+3* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 523 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 207 0 rlineto stroke end d%MATH  38l FMathType 5.0 Equation1ELOEquation.DSMT4  38OlePres0006(Ole10Native7Ole10FmtProgID 8 _11489240211 #FXr0Xr0 Equationd`|t dxpr   " currentpoint ",Times .+1* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint transOle 9PIC  ":dPICT <tCompObj!%FUlate 64 57 translate 23 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 208 0 rlineto stroke end d%MATH  14l FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoHOlePres000$&I(Ole10Native'JOle10FmtProgID K   14 Equationd`|t dxpr   " _1148924020,FXr0Xr0Ole LPIC )+MdPICT Ot currentpoint ",Times .+1* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 23 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 208 0 rlineto stroke end d%MATH  14l FMathType 5.0 Equation1ELOEquation.DSMT4  14 EquationCompObj*.YUObjInfo[OlePres000-/\(Ole10Native0]Ole10FmtProgID ^ _1148924019:(5FXr0Xr0Ole _PIC 24`dd`t dxpr   " currentpoint ",Times .+1* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfontPICT btCompObj37lUObjInfonOlePres00068o( dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18l FMathType 5.0 Equation1ELOEquation.DSMT4Ole10Native9pOle10FmtProgID q _1148924018>FXr0Xr0Ole r  18 Equationd`t dxpr   " currentpoint ",Times .+1* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 PIC ;=sdPICT utCompObj<@UObjInforoll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18l FMathType 5.0 Equation1ELOEquation.DSMT4  18 Equationd`OlePres000?A(Ole10NativeBOle10FmtProgID  _1148924017gGFXr0Xr0Ole PIC DFdPICT tCompObjEIUt dxpr   " currentpoint ",Times .+1* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18l FMathType 5.0 Equation1ELOEquation.DSMT4  18 EquationObjInfoOlePres000HJ(Ole10NativeKOle10FmtProgID  _1148924016PFXr0Xr0Ole PIC MOdPICT td`t dxpr   " currentpoint ",Times .+1* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18l FMathType 5.0 Equation1ELOEquation.DSMT4CompObjNRUObjInfoOlePres000QS(Ole10NativeT  18 Equationd`t dxpr   " currentpoint ",Times .+1* 8Ole10FmtProgID  _1148924015^LYFXr0Xr0Ole PIC VXdPICT tCompObjW[UObjInfoOlePres000Z\(" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18l FMathType 5.0 Equation1ELOEquation.DSMT4  18 Equationd`Ole10Native]Ole10FmtProgID  _1148924014bFXr0Xr0Ole PIC _adPICT tCompObj`dUObjInfot dxpr   " currentpoint ",Times .+1* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18l FMathType 5.0 Equation1ELOEquation.DSMT4  18OlePres000ce(Ole10NativefOle10FmtProgID  _1148924013yUkFXr0Xr0 Equationd`t dxpr   " currentpoint ",Times .+1* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint transOle PIC hjdPICT tCompObjimUlate 64 57 translate 21 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 23 518 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 205 0 rlineto stroke end d%MATH  16l FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoOlePres000ln(Ole10NativeoOle10FmtProgID    16 Equationd`t dxpr   " _1148924012tFXr0Xr0Ole PIC qsdPICT t currentpoint ",Times .+1* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 21 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 23 518 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 205 0 rlineto stroke end d%MATH  16l FMathType 5.0 Equation1ELOEquation.DSMT4  16 EquationCompObjrvUObjInfoOlePres000uw(Ole10NativexOle10FmtProgID  _1148924011p}FXr0Xr0Ole PIC z|dd`t dxpr   " currentpoint ",Times .+1* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 21 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfontPICT tCompObj{UObjInfoOlePres000~( !"#$%&'()+2456789:;<>EGHIJKLMNOQXZ[\]^_`abdkmnopqrstuw~ dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 23 518 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 205 0 rlineto stroke end d%MATH  16l FMathType 5.0 Equation1ELOEquation.DSMT4Ole10NativeOle10FmtProgID   _1148924010FXr0Xr0Ole    16 Equationd`t dxpr   " currentpoint ",Times .+1* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 PIC  dPICT  tCompObjUObjInforoll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 21 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 23 518 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 205 0 rlineto stroke end d%MATH  16l FMathType 5.0 Equation1ELOEquation.DSMT4  16 Equationd`OlePres000(Ole10NativeOle10FmtProgID  _1148924009CFXr0Xr0Ole PIC dPICT  tCompObj*Ut dxpr   " currentpoint ",Times .+1* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 21 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 23 518 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 205 0 rlineto stroke end d%MATH  16l FMathType 5.0 Equation1ELOEquation.DSMT4  16 EquationObjInfo,OlePres000-(Ole10Native.Ole10FmtProgID / _1148924008FXr0Xr0Ole 0PIC 1dPICT 3td`t dxpr   " currentpoint ",Times .+1* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 21 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 23 518 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 205 0 rlineto stroke end d%MATH  16l FMathType 5.0 Equation1ELOEquation.DSMT4CompObj=UObjInfo?OlePres000@(Ole10NativeA  16 Equationd`    t dxpr   " currentpoint ",Times .+2* 3Ole10FmtProgID B _1148924007FXr0Xr0Ole CPIC DdPICT FtCompObjPUObjInfoROlePres000S(" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 29 516 moveto (3) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 210 0 rlineto stroke end d%MATH  23l FMathType 5.0 Equation1ELOEquation.DSMT4  23 Equationd`|Ole10NativeTOle10FmtProgID U _1148924006FXr0Xr0Ole VPIC WdPICT YtCompObjcUObjInfoe    t dxpr   " currentpoint ",Times .+3* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 53 translate 28 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 521 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 208 0 rlineto stroke end d%MATH  34l FMathType 5.0 Equation1ELOEquation.DSMT4  34OlePres000f(Ole10NativegOle10FmtProgID h _1148924005FXr0Xr0 Equationd`    t dxpr   " currentpoint ",Times .+4* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint transOle iPIC jdPICT ltCompObjvUlate 64 60 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (4) show 25 515 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 208 0 rlineto stroke end d%MATH  46l FMathType 5.0 Equation1ELOEquation.DSMT4"      #!%D$'&)(*+,-./103245687:9<;>=@?ABECGdFIHKJMLONPQRSTUVWXYZ[\^]`_baecgfhikjmlonqprstuvwxzy|{}~ObjInfoxOlePres000y(Ole10NativezOle10FmtProgID {   46 Equationd`      dxpr _1148924004FXr0Xr0Ole |PIC }dPICT    " currentpoint ",Times .  +5* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 26 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 25 521 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 207 0 rlineto stroke end d%MATH  58l FMathType 5.0 Equation1ELOEquation.DSMT4  58 EquationCompObjUObjInfoOlePres000(Ole10NativeOle10FmtProgID  _1148924003FXr0Xr0Ole PIC dd`    t dxpr   " currentpoint ",Times .+6* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 54 translate 24 218 moveto /fs 0 def /sf {exch dup /fs ePICT tCompObjUObjInfoOlePres000(xch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 25 522 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 207 0 rlineto stroke end d%MATH  68l FMathType 5.0 Equation1ELOEquation.DSMT4  68 Equationd`t dxpr   " currentpoint ",Times .+7* 8Ole10NativeOle10FmtProgID  _1148924002FXr0Xr0Ole PIC dPICT tCompObjUObjInfo" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (7) show 25 516 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 207 0 rlineto stroke end d%MATH  78l FMathType 5.0 Equation1ELOEquation.DSMT4  78 Equationd,OlePres000(Ole10NativeOle10FmtProgID  _1148924001FXr0Xr0Ole PIC dPICT ~CompObjU    ~dxpr  " currentpoint ",Times .+15* 16"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 14 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (15) show 13 525 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 355 0 rlineto stroke end d+MATH#  1516 /FMathType 5.0 Equation1ELOEquation.DSMT4  1516ObjInfoOlePres000(Ole10Native#Ole10FmtProgID  Equationd` dxpr   " currentpoint " +1* 3" /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint transl_1148924000FXr0Xr0Ole PIC dPICT ate 64 57 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Times-Bold f1 (1) 22 220 sh (3) 27 518 sh end MTsave restore d%MATH  13;FMathType 5.0 Equation1ELOEquation.DSMT4 Equation.3CompObjUObjInfoOlePres000(Ole10FmtProgID Equation Native 5_1148923999FXr0Xr0Ole PIC d  13d`    t dxpr   " currentpoint ",Times .+2* 3" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint transPICT tCompObjUObjInfoOlePres000(late 64 59 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 29 516 moveto (3) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 210 0 rlineto stroke end d%MATH  23l FMathType 5.0 Equation1ELOEquation.DSMT4  23 Equationd`    t dxpr   " Ole10NativeOle10FmtProgID  _1148923998FXr0Xr0Ole PIC dPICT tCompObjUObjInfo     !"#$%&(/123456789:<CEFGHIJKLMOVXYZ[\]^_`biklmnopqrsu|~ currentpoint ",Times .+2* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 26 516 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 210 0 rlineto stroke end d%MATH  26l FMathType 5.0 Equation1ELOEquation.DSMT4  26 EquationOlePres000(Ole10NativeOle10FmtProgID  _1148923997 FXr0Xr0Ole PIC dPICT  tCompObjUd`    t dxpr   " currentpoint ",Times .+4* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (4) show 25 515 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 208 0 rlineto stroke end d%MATH  46l FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoOlePres000(Ole10NativeOle10FmtProgID    46 Equationd`    t dxpr   " currentpoint ",Times .+3* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 _1148923996FXr0Xr0Ole PIC dPICT troll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 523 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 207 0 rlineto stroke end d%MATH  38l FMathType 5.0 Equation1ELOCompObj'UObjInfo)OlePres000*(Ole10Native+Equation.DSMT4  38 Equationd`    Ole10FmtProgID , _1148923994 FXr0Xr0Ole -PIC   .dPICT 0CompObj ;UObjInfo=OlePres000>(  dxpr    " currentpoint ",Times .  +5* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 26 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 25 521 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 207 0 rlineto stroke end d%MATH  58l FMathType 5.0 Equation1ELOEquation.DSMT4  58Ole10Native?Ole10FmtProgID @ _1148923993FXr0Xr0Ole A Equationd,jdxpr  " currentpoint " +4(12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 60 traPIC BdPICT DjCompObjNUObjInfoPnslate 99 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (4) show 13 517 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 356 0 rlineto stroke end d(MATHc  412ubFMathType 5.0 Equation1ELOEquation.DSMT4  412 Equationd,    }dxpr  "OlePres000Q(Ole10NativeR Ole10FmtProgID S _1148923992FXr0Xr0Ole TPIC UdPICT W}CompObj!aU currentpoint ",Times .+5(12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 101 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 13 522 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 356 0 rlineto stroke end d(MATHd  512ubFMathType 5.0 Equation1ELOEquation.DSMT4  512 EquationObjInfocOlePres000 "d(Ole10Native#e Ole10FmtProgID f _1148923991(FXr0Xr0Ole gPIC %'hdPICT j}d,    }dxpr  " currentpoint ",Times .+7(12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 100 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (7) show 13 517 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 356 0 rlineto stroke end d(MATHf  712ubFMathType 5.0 Equation1ELOEquation.DSMT4CompObj&*tUObjInfovOlePres000)+w(Ole10Native,x   712 Equationd,    }dxpr  " currentpoint ",Times .+8(12"  30 dict begin currentpoint 3 -1 roll sub neg Ole10FmtProgID y _11489239906$1FXr0Xr0Ole zPIC .0{dPICT }}CompObj/3UObjInfoOlePres00024(3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 100 219 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (8) show 13 524 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 356 0 rlineto stroke end d(MATHg  812FMathType 5.0 Equation1ELOEquation.DSMT4  812 Equationd`    Ole10Native5 Ole10FmtProgID  _1148923989:FXr0Xr0Ole PIC 79dPICT tCompObj8<UObjInfot dxpr   " currentpoint ",Times .+1* 3" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (3) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  13l FMathType 5.0 Equation1ELOEquation.DSMT4  13 EquationOlePres000;=(Ole10Native>Ole10FmtProgID  _1148923988Q-CFXr0Xr0Ole PIC @BdPICT tCompObjAEUd`|    t dxpr   " currentpoint ",Times .+1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoOlePres000DF(Ole10NativeGOle10FmtProgID    12 Equationd`    t dxpr   " currentpoint ",Times .+2* 6_1148923987LFXr0Xr0Ole PIC IKdPICT t" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 26 516 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 210 0 rlineto stroke end d%MATH  26l CompObjJNUObjInfoOlePres000MO(Ole10NativePFMathType 5.0 Equation1ELOEquation.DSMT4  26 Equationd`Ole10FmtProgID  _1148923986ZHUFXr0Xr0Ole PIC RTd    t dxpr   " currentpoint ",Times .+3* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3)PICT tCompObjSWUObjInfoOlePres000VX( show 24 522 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 207 0 rlineto stroke end d%MATH  36l FMathType 5.0 Equation1ELOEquation.DSMT4  36Ole10NativeYOle10FmtProgID  _1148923985^FXr0Xr0Ole  Equationd`    t dxpr   " currentpoint ",Times .+4* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint transPIC []dPICT tCompObj\`UObjInfolate 64 60 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (4) show 26 516 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 208 0 rlineto stroke end d%MATH  48l FMathType 5.0 Equation1ELOEquation.DSMT4  48 Equationd`      dxpr OlePres000_a(Ole10NativebOle10FmtProgID  _1148923984?gFXr0Xr0Ole PIC dfdPICT CompObjeiU   " currentpoint ",Times .  +5* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 26 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 25 521 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 207 0 rlineto stroke end d%MATH  58l FMathType 5.0 Equation1ELOEquation.DSMT4  58 EquationObjInfoOlePres000hj(Ole10NativekOle10FmtProgID  _1148923983pFXr0Xr0Ole PIC modPICT }    !(*+,-./0124;=>?@ABCDEGNPQRSTUVWXZacdefghijkmtvwxyz{|}~d,    }dxpr  " currentpoint ",Times .+5(12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 101 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 13 522 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 356 0 rlineto stroke end d(MATHd  512ubFMathType 5.0 Equation1ELOEquation.DSMT4CompObjnr UObjInfoOlePres000qs(Ole10Nativet   512 Equationd,    |dxpr  " currentpoint ",Times .+6(Ole10FmtProgID  _1148923982~lyFXr0Xr0Ole PIC vxdPICT |CompObjw{ UObjInfo"OlePres000z|#(12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 54 translate 99 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 13 523 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 356 0 rlineto stroke end d(MATHe  612ubFMathType 5.0 Equation1ELOEquation.DSMT4  612 Equationd,Ole10Native}$ Ole10FmtProgID % _1148923981FXr0Xr0Ole &PIC 'dPICT )}CompObj3UObjInfo5    }dxpr  " currentpoint ",Times .+7(12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 100 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (7) show 13 517 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 356 0 rlineto stroke end d(MATHf  712ubFMathType 5.0 Equation1ELOEquation.DSMT4  712OlePres0006(Ole10Native7 Ole10FmtProgID 8 _1148923980uFXr0Xr0 Equationd,    }dxpr  " currentpoint ",Times .+5(12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint tOle 9PIC :dPICT <}CompObjFUranslate 64 55 translate 101 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 13 522 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 356 0 rlineto stroke end d(MATHd  512ubFMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoHOlePres000I(Ole10NativeJ Ole10FmtProgID K   512 Equationd`    t dxpr   " _1148923979FXr0Xr0Ole LPIC MdPICT Ot currentpoint ",Times .+5* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 23 520 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 205 0 rlineto stroke end d%MATH  56l FMathType 5.0 Equation1ELOEquation.DSMT4  56 EquationCompObjYUObjInfo[OlePres000\(Ole10Native]Ole10FmtProgID ^ _1148923978FXr0Xr0Ole _PIC `dd`    t dxpr   " currentpoint ",Times .+5* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfontPICT btCompObjlUObjInfonOlePres000o( dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 23 520 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 205 0 rlineto stroke end d%MATH  56l FMathType 5.0 Equation1ELOEquation.DSMT4Ole10NativepOle10FmtProgID q _1148923977FXr0Xr0Ole r  56 Equationd`|    t dxpr   " currentpoint ",Times .+3* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 PIC sdPICT utCompObjUObjInforoll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 53 translate 28 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 521 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 208 0 rlineto stroke end d%MATH  34l FMathType 5.0 Equation1ELOEquation.DSMT4  34 Equationd`|    OlePres000(Ole10NativeOle10FmtProgID  _1148923976cFXr0Xr0Ole PIC dPICT bCompObjUb dxpr   " currentpoint " +3* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 53 translate 28 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 521 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 208 0 rlineto stroke end d%MATH  34l FMathType 5.0 Equation1ELOEquation.DSMT4  34 EquationObjInfoOlePres000(Ole10NativeOle10FmtProgID  _1148923975FXr0Xr0Ole PIC dPICT }d,    }dxpr  " currentpoint ",Times .+7(10"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 100 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (7) show 13 517 moveto (10) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 356 0 rlineto stroke end d(MATHd  710ubFMathType 5.0 Equation1ELOEquation.DSMT4CompObjUObjInfoOlePres000(Ole10Native   710 Equationd,    kdxpr  " currentpoint " +7(10"  Ole10FmtProgID  _1148923974FXr0Xr0Ole PIC dPICT kCompObjUObjInfoOlePres000(30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 100 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (7) show 13 517 moveto (10) show /thick 0 def /th { dup setlinewidth /thick exch 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{]1]!BiɁ)#?j|~o76ݱ5잻$!q°ôܣ;4*Pgl}+CEo5+]T`/%'c@y jwl.#dU[6W/(I!jitk5^I~\!`aBGHmh )ܲum>2EAdTޛP9TpUk0\f/cc:.8~5].1\ԇB3R8u*:Nr`xĶ$8wQ#?:F4>=P9eL[}' s [k>&oo/% 7Ջ-]ŤnTNf}m+AVX`8* 5Vwgä$lG".oE7WY#W{mL :i~pv=E@IS:8waۼGQ7xԳ'7/2y q< "gܶuh%e{ ;N|PA411Њ[Tj߂0nQ͸w#YotTI _o~XAǎv\78 [/BAo s7ː/vJR_8(X ß0q PKI r&AT!ssvj"k^U-vL/w%]9hʂ?ޣE} !*X[0R\^R󯳰{a-7=l2n:+[*ܿu/sUC ny&-[8qoQ  ]Aj m!uOn\=;  gō]߅YP:B7STWĺPW<$@o/sgg&f )|}[ֈG f]1'd;0{L5>`/Ɠ:XX|8D>KsgMךAvnjOK{IX(BmL Po'h|G^cD. ,T B~ IB3ڂܷ){G- +iV(,4r/tc|;Iv q$>Ur#<Gu&!ɾtt#^q1m@Tnn(; W&KsE'*Yc#Enn,R ŀ|T3?Μ# u_,2L &/2Ы }=WƒDB̉ysP["YT8+;bTjQX9׏*hͷFQ\3ZE;ew)ls)PC ^Xnl/ /Z8;s@fA&7dI:gz;`6 eb_{O зҾJ8^̢A?|{o=(lPФ'({΂HQq8rQܡn3c9 }&0(GI9Zq{noPIC dPICT CompObj;ObjInfo dxpr CWEE Grphbj  " currentpoint " +1*2"/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 288 div 480 3 -1 roll exch div scale currentpoint translate 64 61 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 192 moveto 164 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 224 /Times-Roman f1 (1) 26 152 sh (2) 26 384 sh end MTsave restore d%MATH  12jOaFEquation.CWEE11ELO  12Equation.CWEE1d=,OlePres000(Ole10NativeOle10FmtProgID _1148923972aFXr0Xr0Ole PIC dPICT CompObj; dxpr CWEE Grphbj  " currentpoint " +1*2"/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 288 div 480 3 -1 roll exch div scale currentpoint translate 64 61 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 192 moveto 164 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 224 /Times-Roman f1 (1) 26 152 sh (2) 26 384 sh end MTsave restore d%MATH  12jOaFEquation.CWEE11ELOObjInfoOlePres000(Ole10NativeOle10FmtProgID   12Equation.CWEE1d=, dxpr CWEE Grphbj _1148923971aFXr0Xr0Ole PIC dPICT  " currentpoint " +1*2"/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 288 div 480 3 -1 roll exch div scale currentpoint translate 64 61 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 192 moveto 164 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 224 /Times-Roman f1 (1) 26 152 sh (2) 26 384 sh end MTsave restore d%MATH  12jOaFEquation.CWEE11ELOCompObj;ObjInfoOlePres000(Ole10Native      !"$+-./0123457>@ABCDEFGHJQSTUVWXYZ[]dfghijklmnopqrt{}~  12Equation.CWEE1d`|    b dxpr   " currentpoint " +1* 2" 30 Ole10FmtProgID _1148923970FXr0Xr0Ole PIC dPICT bCompObjUObjInfoOlePres000(dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4  12 Equationd`|Ole10NativeOle10FmtProgID  _1148923969FXr0Xr0Ole PIC dPICT bCompObj#UObjInfo%    b dxpr   " currentpoint " +1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4  12OlePres000&(Ole10Native'Ole10FmtProgID ( _1148923968FXr0Xr0 Equationd`|    b dxpr   " currentpoint " +1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translaOle )PIC *dPICT ,bCompObj6Ute 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfo8OlePres0009(Ole10Native:Ole10FmtProgID ;   12 Equationd`|    b dxpr   " _1148923967FXr0Xr0Ole <PIC =dPICT ?b currentpoint " +1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4  12 EquationCompObjIUObjInfoKOlePres000L(Ole10NativeMOle10FmtProgID N _1148923966 FXr0Xr0Ole OPIC Pdd`|    b dxpr   " currentpoint " +1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def PICT RbCompObj \UObjInfo^OlePres000  _(sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4Ole10Native `Ole10FmtProgID a _1148923965FXr0Xr0Ole b  12 EquationdE"dxpr  """ currentpoint ",Times .+4* 6"  ( or (2* 3" H30 dict begin curPIC cdPICT eECompObjsUObjInfourentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 25 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (4) show 25 516 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 208 0 rlineto stroke 311 357 moveto 384 /Times-Bold f1 (or) show 802 218 moveto 320 /Times-Bold f1 (2) show 804 516 moveto (3) show 775 258 moveto 210 0 rlineto stroke end dBMATH6  46 or 23ivFMathType 5.0 Equation1ELOEquation.DSMT46  46 or 23OlePres000v(Ole10Nativew:Ole10FmtProgID x _1148923964)FXr0Xr0 Equationd4    m)dxpr  )") currentpoint ",Times .+9* 6"  ( or)1 (!1* 2" i30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1312 div 640 3 -1 rOle yPIC zdPICT |mCompObjUoll exch div scale currentpoint translate 64 54 translate 24 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (9) show 23 521 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 205 0 rlineto stroke 308 362 moveto 384 /Times-Bold f1 (or) show 749 362 moveto 384 /Times-Bold f1 (1) show 1009 223 moveto 320 ns (1) show 1012 521 moveto (2) show 985 263 moveto 210 0 rlineto stroke end dEMATH9S  96 or1 1264FMathType 5.0 Equation1ELOEquation.DSMT49  96 or1 12 EquationObjInfoOlePres000(Ole10Native=Ole10FmtProgID  _1148923963$FXr0Xr0Ole PIC !#dPICT md4|m)dxpr  )") currentpoint ",Times .+6* 4"  ( or)1 (!1* 2" i30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1312 div 608 3 -1 roll exch div scale currentpoint translate 64 54 translate 25 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 25 520 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 208 0 rlineto stroke 311 362 moveto 384 /Times-Bold f1 (or) show 752 362 moveto 384 /Times-Bold f1 (1) show 1012 223 moveto 320 ns (1) show 1015 521 moveto (2) show 988 263 moveto 210 0 rlineto stroke end dEMATH9N  64 or1 1260FMathType 5.0 Equation1ELOEquation.DSMT49  64 or1 12 EquationCompObj"&UObjInfoOlePres000%'(Ole10Native(=Ole10FmtProgID  _11489239622 -FXr0Xr0Ole PIC *,dd    E"dxpr  """ currentpoint ",Times .+2* 8"  ( or (1* 4" H30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 27 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale maPICT ECompObj+/UObjInfoOlePres000.0(kefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 27 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke 313 359 moveto 384 /Times-Bold f1 (or) show 800 220 moveto 320 /Times-Bold f1 (1) show 802 517 moveto (4) show 777 260 moveto 208 0 rlineto stroke end dBMATH6  28 or 14ivFMathType 5.0 Equation1ELOEquation.DSMT46  28 or 14 Equationd,Ole10Native1:Ole10FmtProgID  _11489239616FXr0Xr0Ole PIC 35dPICT }CompObj48UObjInfo    }dxpr  " currentpoint ",Times .+3(10"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 102 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 13 524 moveto (10) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 356 0 rlineto stroke end d(MATH`  310ubFMathType 5.0 Equation1ELOEquation.DSMT4  310OlePres00079(Ole10Native: Ole10FmtProgID  _1148923960{?FXr0Xr0 Equationd`|    t dxpr   " currentpoint ",Times .+1* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint transOle PIC <>dPICT tCompObj=AUlate 64 57 translate 23 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 208 0 rlineto stroke end d%MATH  14l FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoOlePres000@B(Ole10NativeCOle10FmtProgID    14 Equationd`|    t dxpr   " _1148923959HFXr0Xr0Ole PIC EGdPICT t currentpoint ",Times .+1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4  12 EquationCompObjFJUObjInfoOlePres000IK(Ole10NativeLOle10FmtProgID  _1148923958VDQFXr0Xr0Ole PIC NPdd     dxpr  " currentpoint " +2* 8"  ( : (1* 4"  ( , (!4(16"  ( *; (14* 8" 0 ( 8: (?1* 2" > ( F, (M2* 4" M ( U, (^8([16" [ ( g; (n6* 8" m ( u: (|3* 4" { ( PICT  CompObjOS!UObjInfo#OlePres000RT$(      "&'(,./01234568?ABCDEFGHIKRTUVWXYZ[\^eghijklmnoqxz{|}~, (12* 16" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4832 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 27 224 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 27 523 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 210 0 rlineto stroke 243 363 moveto 384 /Times-Bold f1 (:) show 472 224 moveto 320 /Times-Bold f1 (1) show 474 521 moveto (4) show 449 264 moveto 208 0 rlineto stroke 707 363 moveto 384 /Times-Bold f1 (,) show 999 224 moveto 320 /Times-Bold f1 (4) show 914 524 moveto (16) show 901 264 moveto 355 0 rlineto stroke 1288 363 moveto 384 /Times-Bold f1 (;) show 1525 224 moveto 320 /Times-Bold f1 (4) show 1526 523 moveto (8) show 1500 264 moveto 208 0 rlineto stroke 1741 363 moveto 384 /Times-Bold f1 (:) show 1971 224 moveto 320 /Times-Bold f1 (1) show 1974 522 moveto (2) show 1947 264 moveto 210 0 rlineto stroke 2207 363 moveto 384 /Times-Bold f1 (,) show 2428 224 moveto 320 /Times-Bold f1 (2) show 2427 521 moveto (4) show 2401 264 moveto 210 0 rlineto stroke 2661 363 moveto 384 /Times-Bold f1 (,) show 2954 219 moveto 320 /Times-Bold f1 (8) show 2868 524 moveto (16) show 2855 264 moveto 355 0 rlineto stroke 3242 363 moveto 384 /Times-Bold f1 (;) show 3478 219 moveto 320 /Times-Bold f1 (6) show 3479 523 moveto (8) show 3454 264 moveto 207 0 rlineto stroke 3694 363 moveto 384 /Times-Bold f1 (:) show 3928 218 moveto 320 /Times-Bold f1 (3) show 3925 521 moveto (4) show 3900 264 moveto 208 0 rlineto stroke 4158 363 moveto 384 /Times-Bold f1 (,) show 4365 224 moveto 320 /Times-Bold f1 (12) show 4366 524 moveto (16) show 4352 264 moveto 356 0 rlineto stroke end dMATHr  28 : 14 , 416 ; 48 : 12 , 24 , 816 ; 68 : 34 , 1216h FMathType 5.0 Equation1ELOEquation.DSMT4  28 : 14 , 416 ; 48 : 12 , 24 , 816 ; 68Ole10NativeU%Ole10FmtProgID ) _1148923957ZFXr0Xr0Ole * : 34 , 1216 Equationd,|dxpr  " currentpoint ",Times .+2(16"  30 dict begin currentpoint 3 -1 roll sub neg PIC WY+dPICT -|CompObjX\7UObjInfo93 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 99 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 13 518 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 355 0 rlineto stroke end d(MATHe  216ubFMathType 5.0 Equation1ELOEquation.DSMT4  216 Equationd,OlePres000[]:(Ole10Native^; Ole10FmtProgID < _1148923956qMcFXr0Xr0Ole =PIC `b>dPICT @|CompObjaeJU|dxpr  " currentpoint ",Times .+4(16"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 98 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (4) show 13 517 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 355 0 rlineto stroke end d(MATHg  416ubFMathType 5.0 Equation1ELOEquation.DSMT4  416 EquationObjInfoLOlePres000dfM(Ole10NativegN Ole10FmtProgID O _1148923955lFXr0Xr0Ole PPIC ikQdPICT S~d,~dxpr  " currentpoint ",Times .+14* 16"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 13 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (14) show 14 520 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 356 0 rlineto stroke end d+MATH"  1416neFMathType 5.0 Equation1ELOEquation.DSMT4CompObjjn]UObjInfo_OlePres000mo`(Ole10Nativepa#  1416 Equationd`t dxpr   " currentpoint ",Times .+1* 8Ole10FmtProgID b _1148923954zhuFXr0Xr0Ole cPIC rtddPICT ftCompObjswpUObjInforOlePres000vxs(" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18l FMathType 5.0 Equation1ELOEquation.DSMT4  18 Equationd`|Ole10NativeytOle10FmtProgID u _1148923953~FXr0Xr0Ole vPIC {}wdPICT ytCompObj|UObjInfot dxpr   " currentpoint ",Times .+1* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 23 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1)"      #!%@$&'(*),+.-0/21346587:9<;=>?BADCFEHGIJLKNMPOSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ show 25 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 208 0 rlineto stroke end d%MATH  14l FMathType 5.0 Equation1ELOEquation.DSMT4  14OlePres000(Ole10NativeOle10FmtProgID  _1148923952_FXr0Xr0 Equationd`t dxpr   " currentpoint ",Times .+3* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint transOle PIC dPICT tCompObjUlate 64 53 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 523 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 207 0 rlineto stroke end d%MATH  38l FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoOlePres000(Ole10NativeOle10FmtProgID    38 Equationd`|t dxpr   " _1148923951FXr0Xr0Ole PIC dPICT t currentpoint ",Times .+1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4  12 EquationCompObjUObjInfoOlePres000(Ole10NativeOle10FmtProgID  _1148923950FXr0Xr0Ole PIC dd`t dxpr   " currentpoint ",Times .+5* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 26 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfontPICT tCompObjUObjInfoOlePres000( dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 25 521 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 207 0 rlineto stroke end d%MATH  58l FMathType 5.0 Equation1ELOEquation.DSMT4Ole10NativeOle10FmtProgID  _1148923949FXr0Xr0Ole   58 Equationd`|t dxpr   " currentpoint ",Times .+3* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 PIC dPICT tCompObjUObjInforoll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 53 translate 28 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 521 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 208 0 rlineto stroke end d%MATH  34l FMathType 5.0 Equation1ELOEquation.DSMT4  34 Equationd`OlePres000(Ole10NativeOle10FmtProgID  _1148923948FXr0Xr0Ole PIC dPICT tCompObjUt dxpr   " currentpoint ",Times .+7* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (7) show 25 516 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 207 0 rlineto stroke end d%MATH  78l FMathType 5.0 Equation1ELOEquation.DSMT4  78 EquationObjInfoOlePres000(Ole10NativeOle10FmtProgID  _1148923947FXr0Xr0Ole PIC dPICT dWT|dxpr  " currentpoint ",Times .+ 2 ( 1* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 544 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate -6 359 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Bold f1 (2) show 262 220 moveto 320 ns (1) show 264 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 239 260 moveto 208 0 rlineto stroke end d(MATHc 2 14FMathType 5.0 Equation1ELOEquation.DSMT4CompObjUObjInfoOlePres000(Ole10Native  2 14 EquationdWT|dxpr  "Ole10FmtProgID  _1148923946FXr0Xr0Ole PIC dPICT CompObj UObjInfo OlePres000 (  &()*+,-./013:<=>?@ABCDFMOPQRSTUVWY`bcdefghijlsuvwxyz{|}~ currentpoint ",Times .+ 1 ( 1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 544 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate -23 359 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Bold f1 (1) show 237 220 moveto 320 ns (1) show 240 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 213 260 moveto 210 0 rlineto stroke end d(MATH` 1 12ubFMathType 5.0 Equation1ELOEquation.DSMT4 1 12 EquationOle10Native Ole10FmtProgID  _1148923944F 0 0Ole dWT|dxpr  " currentpoint ",Times .+ 1 ( 1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 544 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate -23 359 moveto /fs 0 def /sf {excPIC dPICT CompObjUObjInfo h dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Bold f1 (1) show 237 220 moveto 320 ns (1) show 240 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 213 260 moveto 210 0 rlineto stroke end d(MATH` 1 12ubFMathType 5.0 Equation1ELOEquation.DSMT4 1 12 Equationddxpr  "OlePres000!(Ole10Native" Ole10FmtProgID # _1148923943F 0 0Ole $PIC %dPICT 'CompObj2U currentpoint ",Times .+ 2 ( 1( 16" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 704 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate -6 359 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Bold f1 (2) show 335 220 moveto 320 ns (1) show 252 520 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 239 260 moveto 355 0 rlineto stroke end d+MATH  2 116neFMathType 5.0 Equation1ELOEquation.DSMT4 2 116 EquationObjInfo4OlePres0005(Ole10Native6#Ole10FmtProgID 7 _1148923942F 0 0Ole 8PIC 9dPICT ;td`|    t dxpr   " currentpoint ",Times .+1* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 23 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 208 0 rlineto stroke end d%MATH  14l FMathType 5.0 Equation1ELOEquation.DSMT4CompObjEUObjInfoGOlePres000H(Ole10NativeI  14 Equationd,    |dxpr  " currentpoint ",Times .+4(Ole10FmtProgID J _1148923941F 0 0Ole KPIC LdPICT N|CompObjXUObjInfoZOlePres000[(16"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 98 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (4) show 13 517 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 355 0 rlineto stroke end d(MATHg  416ubFMathType 5.0 Equation1ELOEquation.DSMT4  416 Equationd`Ole10Native\ Ole10FmtProgID ] _1148923940F 0 0Ole ^PIC _dPICT atCompObjkUObjInfom    t dxpr   " currentpoint ",Times .+2* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 27 517 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 210 0 rlineto stroke end d%MATH  28l FMathType 5.0 Equation1ELOEquation.DSMT4  28OlePres000n(Ole10NativeoOle10FmtProgID p _1148923939F 0 0 Equationd{h    dxpr  " currentpoint " +N(4)N"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 576 div 640 3 -1 roll exch div scale currentpoint translate 64 57 Ole qPIC rdPICT tCompObjUtranslate 114 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (N) show 25 517 moveto 320 /Times-Bold f1 (4) show 202 517 moveto 320 /Times-Bold f1 (N) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 457 0 rlineto stroke end d(MATH  N4NubFMathType 5.0 Equation1ELOEquation.DSMT4  N4N Equationd`|    ObjInfoOlePres000(Ole10Native Ole10FmtProgID  _1148923938F 0 0Ole PIC dPICT tt dxpr   " currentpoint ",Times .+3* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 53 translate 28 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 521 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 208 0 rlineto stroke end d%MATH  34l FMathType 5.0 Equation1ELOEquation.DSMT4  34 EquationCompObjUObjInfoOlePres000(Ole10NativeOle10FmtProgID  _1148923937 F 0 0Ole PIC dd`    t dxpr   " currentpoint ",Times .+6* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 54 translate 24 218 moveto /fs 0 def /sf {exch dup /fs ePICT tCompObjUObjInfoOlePres000(xch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 25 522 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 207 0 rlineto stroke end d%MATH  68l FMathType 5.0 Equation1ELOEquation.DSMT4  68 Equationd,    }dxpr  " currentpoint ",Times .+9(Ole10Native Ole10FmtProgID  _1148923936F 0 0Ole PIC   dPICT }CompObj UObjInfo12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 54 translate 100 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (9) show 13 523 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 356 0 rlineto stroke end d(MATHh  912ubFMathType 5.0 Equation1ELOEquation.DSMT4  912 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51 translate 27 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (30) show 21 526 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 266 moveto 370 0 rlineto stroke end d+MATH   3016neFMathType 5.0 Equation1ELOEquation.DSMT4CompObj"UObjInfoOlePres000!#(Ole10Native$#  3016 Equationd`|t dxpr   " Ole10FmtProgID  _1148923933.)F 0 0Ole PIC &(dPICT tCompObj'+UObjInfoOlePres000*,( currentpoint ",Times .+6* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 54 translate 26 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 27 521 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 210 0 rlineto stroke end d%MATH  62l FMathType 5.0 Equation1ELOEquation.DSMT4  62 EquationOle10Native-Ole10FmtProgID  _11489239322F 0 0Ole PIC /1dPICT ~CompObj04UObjInfod,~dxpr  " currentpoint ",Times .+20* 11"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 27 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfo !"#$%&'()+2456789:;<>EGHIJKLMNOQXZ[\]^_`abcelnopqrstuvxnt dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (20) show 24 525 moveto (11) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 370 0 rlineto stroke end d+MATH  2011neFMathType 5.0 Equation1ELOEquation.DSMT4OlePres00035(Ole10Native6#Ole10FmtProgID   _1148923931I%;F 0 0  2011 Equationd,~dxpr  " currentpoint ",Times .+15* 16"  30 dict begin currentpoint 3 -1 roll sub neg 3 Ole  PIC 8: dPICT  ~CompObj9=U1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 14 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (15) show 13 525 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 355 0 rlineto stroke end d+MATH#  1516neFMathType 5.0 Equation1ELOEquation.DSMT4  1516 Equationd`ObjInfoOlePres000<>(Ole10Native?#Ole10FmtProgID  _1148923930DF 0 0Ole PIC ACdPICT  tt dxpr   " currentpoint ",Times .+6* 5" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 54 translate 23 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 25 520 moveto (5) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 205 0 rlineto stroke end d%MATH  65l FMathType 5.0 Equation1ELOEquation.DSMT4  65 EquationCompObjBF*UObjInfo,OlePres000EG-(Ole10NativeH.Ole10FmtProgID / _1148923929R@MF 0 0Ole 0PIC JL1dd`|t dxpr   " currentpoint ",Times .+6* 7" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 54 translate 24 218 moveto /fs 0 def /sf {exch dup /fs ePICT 3tCompObjKO=UObjInfo?OlePres000NP@(xch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 25 520 moveto (7) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 206 0 rlineto stroke end d%MATH  67l FMathType 5.0 Equation1ELOEquation.DSMT4  67 Equationd`b dxpr   " currentpoint " +7* 6" 30 Ole10NativeQAOle10FmtProgID B _1148923928VF 0 0Ole CPIC SUDdPICT FbCompObjTXPUObjInfoRdict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (7) show 24 515 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 206 0 rlineto stroke end d%MATH  76l FMathType 5.0 Equation1ELOEquation.DSMT4  76 EquationdOlePres000WYS(Ole10NativeZTOle10FmtProgID U _1148923927_F 0 0Ole VPIC \^WdPICT YCompObj]adUdxpr  " currentpoint ",Times .+98(100" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 640 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 99 219 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (98) show 13 524 moveto (100) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 516 0 rlineto stroke end d.MATH"  98100 3FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfofOlePres000`bg(Ole10Nativech&Ole10FmtProgID i "  98100 Equationd,~dxpr  " currentpoint ",Times .+13* 12"  30 dict begin currentpoint 3 -1 roll sub neg 3 _1148923926hF 0 0Ole jPIC egkdPICT m~1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 51 translate 15 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (13) show 13 526 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 266 moveto 356 0 rlineto stroke end d+MATH  1312neFMathType 5.0 Equation1ELOCompObjfjwUObjInfoyOlePres000ikz(Ole10Nativel{##      "!$%B&'()*+,-./021436587:9;<>=@?CAEdDGFIHJKLMNOPQRSTUVXWZY\[^]`_abecgfihkjmlonpqrstuvwxyz{|~}Equation.DSMT4  1312 Equationd,|Ole10FmtProgID | _1148923925vdqF 0 0Ole }PIC np~dPICT ~CompObjosUObjInfoOlePres000rt(~dxpr  " currentpoint ",Times .+10* 22"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 608 3 -1 roll exch div scale currentpoint translate 64 52 translate 20 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (10) show 27 523 moveto (22) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 370 0 rlineto stroke end d+MATH  1022neFMathType 5.0 Equation1ELOEquation.DSMT4  1022 EquationOle10Nativeu#Ole10FmtProgID  _1148923924zF 0 0Ole d,~dxpr  " currentpoint ",Times .+12* 25"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 18 220 moveto /fs 0 def /sf {exch dup /fsPIC wydPICT ~CompObjx|UObjInfo exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (12) show 27 518 moveto (25) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 367 0 rlineto stroke end d+MATH   1225neFMathType 5.0 Equation1ELOEquation.DSMT4OlePres000{}(Ole10Native~#Ole10FmtProgID  _1148923923mF 0 0  1225 Equationd|dxpr  " currentpoint ",Times .+6(Ole PIC dPICT |CompObjU11"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 448 div 640 3 -1 roll exch div scale currentpoint translate 64 54 translate 95 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 13 523 moveto (11) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 348 0 rlineto stroke end d(MATHd  611ubFMathType 5.0 Equation1ELOEquation.DSMT4  611 Equationd,ObjInfoOlePres000(Ole10Native Ole10FmtProgID  _1148923922F 0 0Ole PIC dPICT ||dxpr  " currentpoint ",Times .+1(12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 97 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 13 520 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 356 0 rlineto stroke end d(MATH`  112FMathType 5.0 Equation1ELOEquation.DSMT4  112CompObjUObjInfoOlePres000(Ole10Native Ole10FmtProgID  _1148923921F 0 0Ole PIC d Equationddxpr  " currentpoint ",Times .+6(100" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 640 div 640 3 -1 roll exch div scale currentpoint PICT CompObjUObjInfoOlePres000(translate 64 54 translate 179 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 13 523 moveto (100) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 516 0 rlineto stroke end d+MATH  6100neFMathType 5.0 Equation1ELOEquation.DSMT4  6100 Equationd,Ole10Native#Ole10FmtProgID  _1148923920F 0 0Ole PIC dPICT |CompObjUObjInfo|dxpr  " currentpoint ",Times .+2(17"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 99 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 13 518 moveto (17) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 354 0 rlineto stroke end d(MATHf  217ubFMathType 5.0 Equation1ELOEquation.DSMT4  217 EquationOlePres000(Ole10Native Ole10FmtProgID  _1148923919F 0 0Ole PIC dPICT }CompObjUd,}dxpr  " currentpoint ",Times .+2(20"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 107 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 27 518 moveto (20) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 370 0 rlineto stroke end d(MATH`  220ubFMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoOlePres000(Ole10Native Ole10FmtProgID        !"$+-./0123457>@ABCDEFGHJQSTUVWXYZ[]dfghijklmnpwyz{|}~  220 Equationd,    jdxpr  " currentpoint " +1(16"  _1148923918F 0 0Ole PIC dPICT j30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 96 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 13 520 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 355 0 rlineto stroke end d(MATHd  116ubCompObjUObjInfoOlePres000(Ole10Native FMathType 5.0 Equation1ELOEquation.DSMT4  116 Equationd,Ole10FmtProgID  _1148923917F 0 0Ole PIC d    jdxpr  " currentpoint " +1(10"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 97 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 13 520 mPICT jCompObj#UObjInfo%OlePres000&(oveto (10) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 356 0 rlineto stroke end d(MATH^  110ubFMathType 5.0 Equation1ELOEquation.DSMT4  110Ole10Native' Ole10FmtProgID ( _1148923916F 0 0Ole ) Equationd,    kdxpr  " currentpoint " +4(63"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 60 traPIC *dPICT ,kCompObj6UObjInfo8nslate 102 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (4) show 23 515 moveto (63) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 363 0 rlineto stroke end d(MATHi  463ubFMathType 5.0 Equation1ELOEquation.DSMT4  463 Equationdq    zdxpr  "OlePres0009(Ole10Native: Ole10FmtProgID ; _1148923915F 0 0Ole <PIC =dPICT ?zCompObjIU currentpoint " +10(1228" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 800 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 172 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (10) show 13 525 moveto (1228) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 675 0 rlineto stroke end d1MATH%  1012281 FMathType 5.0 Equation1ELOEquation.DSMT4%  101228 EquationObjInfoKOlePres000L(Ole10NativeM)Ole10FmtProgID N _1148923914F 0 0Ole OPIC PdPICT Rjd,    jdxpr  " currentpoint " +7(15"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 98 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (7) show 13 517 moveto (15) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 353 0 rlineto stroke end d(MATHi  715ubFMathType 5.0 Equation1ELOEquation.DSMT4CompObj\UObjInfo^OlePres000_(Ole10Native`   715 Equationd`    b dxpr   " currentpoint " +5* 9" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 6Ole10FmtProgID a _1148923913F 0 0Ole bPIC cdPICT ebCompObjoUObjInfoqOlePres000r(40 3 -1 roll exch div scale currentpoint translate 64 55 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 24 520 moveto (9) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 205 0 rlineto stroke end d%MATH  59HFMathType 5.0 Equation1ELOEquation.DSMT4  59 Equationd`|    Ole10NativesOle10FmtProgID t _1148923912F 0 0Ole uPIC vdPICT xbCompObjUObjInfo b dxpr   " currentpoint " +4* 7" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 60 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (4) show 26 514 moveto (7) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 208 0 rlineto stroke end d%MATH  47HFMathType 5.0 Equation1ELOEquation.DSMT4  47 EquationOlePres000(Ole10NativeOle10FmtProgID  _11489239113F 0 0Ole PIC dPICT lCompObjUd,    ldxpr  " currentpoint " +10* 21"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 16 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (10) show 27 525 moveto (21) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 362 0 rlineto stroke end d+MATH  1021FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoOlePres000(Ole10Native#Ole10FmtProgID    1021 Equationd`|    b dxpr   " currentpoint " +6* 4" 30 _1148923910F 0 0Ole PIC dPICT bdict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 54 translate 25 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 25 520 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 208 0 rlineto stroke end d%MATH  64l CompObjUObjInfoOlePres000(Ole10NativeFMathType 5.0 Equation1ELOEquation.DSMT4  64 Equationd,|Ole10FmtProgID  _1148923909F 0 0Ole PIC d    idxpr  " currentpoint " +10+ 7"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 608 3 -1 roll exch div scale currentpoint translate 64 52 translate 13 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (10) show 100 522 mPICT iCompObjUObjInfoOlePres000(oveto (7) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 356 0 rlineto stroke end d(MATHd  107ubFMathType 5.0 Equation1ELOEquation.DSMT4  107Ole10Native Ole10FmtProgID  _1148923908 F 0 0Ole  Equationd`    b dxpr   " currentpoint " +9* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 54 translaPIC  dPICT bCompObj UObjInfote 24 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (9) show 23 521 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 205 0 rlineto stroke end d%MATH  96l FMathType 5.0 Equation1ELOEquation.DSMT4  96 Equationd`    b dxpr   " OlePres000  (Ole10NativeOle10FmtProgID  _1148923907!F 0 0Ole PIC dPICT bCompObjU currentpoint " +5* 3" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 26 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 27 520 moveto (3) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 207 0 rlineto stroke end d%MATH  53l FMathType 5.0 Equation1ELOEquation.DSMT4  53 EquationObjInfoOlePres000(Ole10NativeOle10FmtProgID  _1148923906F 0 0Ole PIC dPICT bd`|    b dxpr   " currentpoint " +1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12HFMathType 5.0 Equation1ELOEquation.DSMT4CompObjUObjInfoOlePres000(Ole10Native   12 Equationdmdxpr  " currentpoint " +15(16"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 448 diOle10FmtProgID  _1148923905*%F 0 0Ole PIC "$dPICT mCompObj#' UObjInfo OlePres000&( (                  " $ % & ' ( ) * + , . 5 7 8 9 : ; < = > ? A H J K L M N O P Q R T [ ] ^ _ ` a b c d e g n p q r s t u v w x z v 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 2 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Roman f1 (15) show -3 522 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 338 0 rlineto stroke end d+MATH#  1516neFMathType 5.0 Equation1ELOEquation.DSMT4  1516 Equationd`Ole10Native) #Ole10FmtProgID  _1148923904.F 0 0Ole  PIC +- dPICT  aCompObj,0 UObjInfo a dxpr   " currentpoint " +6* 5" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 21 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Roman f1 (6) show 26 522 moveto (5) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 202 0 rlineto stroke end d%MATH  65l FMathType 5.0 Equation1ELOEquation.DSMT4  65 EquationOlePres000/1 (Ole10Native2 Ole10FmtProgID  _1148923903W7F 0 0Ole  PIC 46! dPICT # aCompObj59- Ud`a dxpr   " currentpoint " +6* 7" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 21 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Roman f1 (6) show 27 519 moveto (7) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 202 0 rlineto stroke end d%MATH  67l FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfo/ OlePres0008:0 (Ole10Native;1 Ole10FmtProgID 2   67 Equationd`a dxpr   " currentpoint " +5* 6" 30 di_1148923902@F 0 0Ole 3 PIC =?4 dPICT 6 act begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 26 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Roman f1 (5) show 21 522 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 202 0 rlineto stroke end d%MATH  56l CompObj>B@ UObjInfoB OlePres000ACC (Ole10NativeDD FMathType 5.0 Equation1ELOEquation.DSMT4  56 Equationd,Ole10FmtProgID E _1148923901N<IF 0 0Ole F PIC FHG d    ~dxpr  " currentpoint ",Times .+12* 20"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 20 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (PICT I ~CompObjGKS UObjInfoU OlePres000JLV (12) show 27 520 moveto (20) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 370 0 rlineto stroke end d+MATH  1220neFMathType 5.0 Equation1ELOEquation.DSMT4  1220Ole10NativeMW #Ole10FmtProgID X _1148923900RF 0 0Ole Y  Equationd,    ~dxpr  " currentpoint ",Times .+15* 25"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint traPIC OQZ dPICT \ ~CompObjPTf UObjInfoh nslate 64 52 translate 20 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (15) show 27 523 moveto (25) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 367 0 rlineto stroke end d+MATH#  1525neFMathType 5.0 Equation1ELOEquation.DSMT4  1525 Equationd,    ~dxpr  "OlePres000SUi (Ole10NativeVj #Ole10FmtProgID k _1148923899iE[F 0 0Ole l PIC XZm dPICT o ~CompObjY]y UW currentpoint ",Times .+18* 30"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 21 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (18) show 27 525 moveto (30) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 370 0 rlineto stroke end d+MATH"  1830neFMathType 5.0 Equation1ELOEquation.DSMT4  1830 EquationObjInfo{ OlePres000\^| (Ole10Native_} #Ole10FmtProgID ~ _1148923898dF 0 0Ole  PIC ac dPICT  ~ d,    ~dxpr  " currentpoint ",Times .+21* 35"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 29 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (21) show 27 518 moveto (35) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 367 0 rlineto stroke end d+MATH! 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y>J}m[=IoFZݿXToiD.zGzzL='Džkס{G˥֜<:L1pTW%iuYezŒ9ir-HOYSE%N6W0A*# QX).G'mQQܤ0ZPp x4ǙNX:s6Rj,l+ d7q SRPȡ߹]x_mQs.>dehLJt/ԁYb-nSvVCT0a8iǠ ffZY=3嚒76yl5ZlHL9xk78+ܿ/;hypuu,Fwq<-;{PcḟZrW X2tؒe {.N8/U/"C+IdH:tMpJv\J]^`qq 5x6/N`t7"U=PnB:ָl O'O"Ǩ,+4b Y'I L4&- Sůe(1ڈ7psm!k\T@b($zu)s6oiwrŲV_qRE^rel':X N1#ICP/wG([Xov܌R 1oTg3ԀӀ@ 1%k hi>1 >X?|cN:suXnv>c6zϜ1|5lԒmOfM(oͽްwsz!V}{tS,HH_ԉ^PICT  ~CompObjko UObjInfo OlePres000np (1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 16 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (12) show 27 520 moveto (21) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 362 0 rlineto stroke end d+MATH  1221neFMathType 5.0 Equation1ELOEquation.DSMT4  1221 Equationd,    Ole10Nativeq #Ole10FmtProgID  _1148923896vF 0 0Ole  PIC su dPICT  ~CompObjtx UObjInfo ~dxpr  " currentpoint ",Times .+16* 28"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 20 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (16) show 27 524 moveto (28) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 369 0 rlineto stroke end d+MATH'  1628neFMathType 5.0 Equation1ELOEquation.DSMT4  1628 EquationOlePres000wy (Ole10Nativez #Ole10FmtProgID  _1148923895[F 0 0Ole  PIC |~ dPICT  ~CompObj} Ud,    ~dxpr  " currentpoint ",Times .+20* 35"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 27 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (20) show 29 523 moveto (35) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 370 0 rlineto stroke end d+MATH   2035neFMathType 5.0 Equation1ELOEquation.DSMT4ObjInfo OlePres000 (Ole10Native #Ole10FmtProgID    2035 Equationd,|    ~dxpr  " currentpoint ",Times .+24* 42_1148923894F 0 0Ole  PIC  dPICT  ~"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 608 3 -1 roll exch div scale currentpoint translate 64 59 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (24) show 26 516 moveto (42) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 370 0 rlineto stroke end d+MATH"  2442neCompObj UObjInfo OlePres000 (Ole10Native #FMathType 5.0 Equation1ELOEquation.DSMT4  2442 Equationd,Ole10FmtProgID  _1148923893F 0 0Ole  PIC  d    ~dxpr  " currentpoint ",Times .+28* 49"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 27 219 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (PICT  ~CompObj UObjInfo OlePres000 (28) show 26 522 moveto (49) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 369 0 rlineto stroke end d+MATH-  2849neFMathType 5.0 Equation1ELOEquation.DSMT4  2849Ole10Native #Ole10FmtProgID  _1148923892F 0 0Ole   Equationd,    ~dxpr  " currentpoint ",Times .+21* 35"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint traPIC  dPICT  ~CompObj UObjInfo nslate 64 57 translate 29 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (21) show 27 518 moveto (35) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 367 0 rlineto stroke end d+MATH!  2135neFMathType 5.0 Equation1ELOEquation.DSMT4            ! " # $ % & ' ) 0 2 3 4 5 6 7 8 9 : < C E F G H I J K L M N P W Y Z [ \ ] ^ _ ` a c j l m n o p q r s t v }    2135 Equationd,    ~dxpr  "OlePres000 (Ole10Native #Ole10FmtProgID  _1148923891F 0 0Ole  PIC  dPICT  ~CompObj U currentpoint ",Times .+20* 35"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 27 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (20) show 29 523 moveto (35) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 370 0 rlineto stroke end d+MATH   2035neFMathType 5.0 Equation1ELOEquation.DSMT4  2035 EquationObjInfo OlePres000 (Ole10Native #Ole10FmtProgID  _1148923890F 0 0Ole  PIC  dPICT  Xd    X"dxpr  """ currentpoint ",Times .+3* 4" , Symbol ( = (12* 16"  E30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 28 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 521 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 208 0 rlineto stroke 316 363 moveto 384 /Symbol f1 (=) show 647 224 moveto 320 /Times-Bold f1 (12) show 648 524 moveto (16) show 634 264 moveto 356 0 rlineto stroke end dEMATH9  34 = 121664CompObj( UObjInfo* OlePres000+ (Ole10Native, =FMathType 5.0 Equation1ELOEquation.DSMT49  34 = 1216 Equationd`|Ole10FmtProgID - _1148923889F 0 0Ole . PIC / d    t dxpr   " currentpoint ",Times .+3* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 53 translate 28 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3)PICT 1 tCompObj; UObjInfo= OlePres000> ( show 25 521 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 208 0 rlineto stroke end d%MATH  34l FMathType 5.0 Equation1ELOEquation.DSMT4  34Ole10Native? Ole10FmtProgID @ _1148923888F 0 0Ole A  Equationd{h|    dxpr  " currentpoint " + 2 ( 1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 576 div 608 3 -1 roll exch div scale currentpoint translate 64 PIC B dPICT D CompObjO UObjInfoQ 57 translate -6 359 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Bold f1 (2) show 263 220 moveto 320 ns (1) show 266 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 239 260 moveto 210 0 rlineto stroke end d(MATHa 2 12ubFMathType 5.0 Equation1ELOEquation.DSMT4 2 12 Equationd`    OlePres000R (Ole10NativeS Ole10FmtProgID T _1148923887F 0 0Ole U PIC V dPICT X tCompObjb Ut dxpr   " currentpoint ",Times .+1* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18NFMathType 5.0 Equation1ELOEquation.DSMT4  18 EquationObjInfod OlePres000e (Ole10Nativef Ole10FmtProgID g _1148923886F 0 0Ole h PIC i dPICT k td`|    t dxpr   " currentpoint ",Times .+1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs e &     "!$#'%)E(*+-,/.1032456789:<;>=?@ABCDGFIHKJMLONPQSRUTXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~xch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4CompObju UObjInfow OlePres000x (Ole10Nativey   12 Equationd`|    t dxpr   " currentpoint ",Times .+1* 4Ole10FmtProgID z _1148923884F 0 0Ole { PIC | dPICT ~ tCompObj UObjInfo OlePres000 ( " 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 23 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 208 0 rlineto stroke end d%MATH  14l FMathType 5.0 Equation1ELOEquation.DSMT4  14 Equationd`|Ole10Native Ole10FmtProgID  _1148923883F 0 0Ole  PIC  dPICT  tCompObj UObjInfo     t dxpr   " currentpoint ",Times .+1* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 23 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 208 0 rlineto stroke end d%MATH  14l FMathType 5.0 Equation1ELOEquation.DSMT4  14OlePres000 (Ole10Native Ole10FmtProgID  _1148923882F 0 0 Equationd,    |dxpr  " currentpoint ",Times .+1(12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint tOle  PIC  dPICT  |CompObj Uranslate 64 57 translate 97 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 13 520 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 356 0 rlineto stroke end d(MATH`  112ubFMathType 5.0 Equation1ELOEquation.DSMT4ObjInfo OlePres000 (Ole10Native Ole10FmtProgID    112 Equationd`|    t dxpr   " _1148923881F 0 0Ole  PIC  dPICT  t currentpoint ",Times .+1* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 23 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 208 0 rlineto stroke end d%MATH  14l FMathType 5.0 Equation1ELOEquation.DSMT4  14 EquationCompObj UObjInfo OlePres000 (Ole10Native Ole10FmtProgID  _1148923880F 0 0Ole  PIC  dd`    t dxpr   " currentpoint ",Times .+1* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfontPICT  tCompObj UObjInfo OlePres000 ( dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18NFMathType 5.0 Equation1ELOEquation.DSMT4Ole10Native Ole10FmtProgID  _1148923879F 0 0Ole    18 Equationd`    b dxpr   " currentpoint " +1* 3" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 6PIC  dPICT  bCompObj UObjInfo 40 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (3) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  13l FMathType 5.0 Equation1ELOEquation.DSMT4  13 Equationd`    OlePres000  (Ole10Native  Ole10FmtProgID  _1148923878SF 0 0Ole  PIC   dPICT  tCompObj  Ut dxpr   " currentpoint ",Times .+1* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 21 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 23 518 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 205 0 rlineto stroke end d%MATH  16NFMathType 5.0 Equation1ELOEquation.DSMT4  16 EquationObjInfo OlePres000 (Ole10Native Ole10FmtProgID  _1148923877F 0 0Ole  PIC  dPICT  b                 ! ( * + , - . / 0 1 2 4 ; = > ? @ A B C D E G N P Q R S T U V W X Z a c d e f g h i j k m t v w x y z { | } ~ d`|    b dxpr   " currentpoint " +1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4CompObj UObjInfo OlePres000 (Ole10Native   12 Equationd,    jdxpr  " currentpoint " +1(12"  Ole10FmtProgID  _1148923876&!F 0 0Ole  PIC   dPICT  jCompObj# UObjInfo" OlePres000"$# (30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 97 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 13 520 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 356 0 rlineto stroke end d(MATH`  112ubFMathType 5.0 Equation1ELOEquation.DSMT4  112 Equationd`|Ole10Native%$ Ole10FmtProgID % _1148923875*F 0 0Ole & PIC ')' dPICT ) tCompObj(,3 UObjInfo5     t dxpr   " currentpoint ",Times .+3* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 53 translate 28 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 521 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 208 0 rlineto stroke end d%MATH  34NFMathType 5.0 Equation1ELOEquation.DSMT4  34OlePres000+-6 (Ole10Native.7 Ole10FmtProgID 8 _1148923874A3F 0 0 Equationd`    t dxpr   " currentpoint ",Times .+1* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint transOle 9 PIC 02: dPICT < tCompObj15F Ulate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18NFMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoH OlePres00046I (Ole10Native7J Ole10FmtProgID K   18 Equationd`|    b dxpr   " _1148923873<F 0 0Ole L PIC 9;M dPICT O b currentpoint " +1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4  12 EquationCompObj:>Y UObjInfo[ OlePres000=?\ (Ole10Native@] Ole10FmtProgID ^ _1148923872J8EF 0 0Ole _ PIC BD` dd`k dxpr   " currentpoint " +3* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def PICT b kCompObjCGl UObjInfon OlePres000FHo (sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 523 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 207 0 rlineto stroke end d.MATH"  Times|3|8 :FMathType 5.0 Equation1ELOEquation.DSMT4Ole10NativeIp &Ole10FmtProgID q _1148923871NF 0 0Ole r "  Times|3|8 Equationdidxpr  " currentpoint " +7(16"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 448 divPIC KMs dPICT u iCompObjLP UObjInfo  640 3 -1 roll exch div scale currentpoint translate 64 56 translate 95 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Roman f1 (7) show -3 519 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 261 moveto 338 0 rlineto stroke end d(MATHj  716ubFMathType 5.0 Equation1ELO Equation.DSMT4  716 Equationd`OlePres000OQ (Ole10NativeR Ole10FmtProgID  _1148923870w/WF 0 0Ole  PIC TV dPICT  aCompObjUY Ua dxpr   " currentpoint " +3* 5" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 56 translate 22 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Roman f1 (3) show 22 521 moveto (5) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 261 moveto 194 0 rlineto stroke end d%MATH  35l FMathType 5.0 Equation1ELOEquation.DSMT4  35 EquationObjInfo OlePres000XZ (Ole10Native[ Ole10FmtProgID  _1148923869`F 0 0Ole  PIC ]_ dPICT  bd`b dxpr   " currentpoint " +4+ 7" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 29 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Roman f1 (4) show 32 514 moveto (7) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 212 0 rlineto stroke end d%MATH  47l FMathType 5.0 Equation1ELOEquation.DSMT4CompObj^b UObjInfo OlePres000ac (Ole10Natived   47 Equationd`a dxpr   " currentpoint " +3* 7" 30 diOle10FmtProgID  _1148923868n\iF 0 0Ole  PIC fh dPICT  aCompObjgk UObjInfo OlePres000jl (ct begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 56 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Roman f1 (3) show 26 518 moveto (7) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 261 moveto 201 0 rlineto stroke end d%MATH  37$rFMathType 5.0 Equation1ELOEquation.DSMT4  37 Equationd`Ole10Nativem Ole10FmtProgID  _1148923867rF 0 0Ole  vb:Tհ 1tHeЊwoAk^4(muݳ%r䪖zD:HgҘxzG; |;Vao[lNV>EGq3 f041gڧdSps pQ|jT&!Ef=v0sˏx8|^н##Hv*ܯۦI( y?YsSq]s ;aibӈA/VМ(z~wV}! eVt`.ͤИKƓCm)@zNUV3?6.vHۖ{3 uzinŰ-9pVLv) Љkl0ZY_7 o^z0Ĝ0C_JtۥA2&8G9#_8AVfj:Ϥs/٨әBR ˅[{Z[xeK=зx?{.L|a>^;T}^Vh)3z _Ґ^z4niCr|ھIV3x,5.C3?ա+ #\cO[ZC[R%R6 PV-KݜLTC1>/ `/r,76%cϖ? ;Q?h!P&hHkL#~~ R'pSd3$qTzܨ\@\X(Z(Κ*e': ! ]ut$`ꒉWxέ]9b?SR)68 ϗ, ~fh E!$[Na+Av\(A˧cGvo5q\P뮈}wnD!Y x2|X'I]Jxg,)+bšlgOGm Z>nn@c9U=s hH>(ɋϿidL<}Wz)ƕ3 U@A 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Uranslate 64 53 translate 100 219 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (8) show 13 524 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 356 0 rlineto stroke end d(MATHg  812ubFMathType 5.0 Equation1ELOEquation.DSMT4ObjInfo0 OlePres0001 (Ole10Native2 Ole10FmtProgID 3   812 Equationd`|b dxpr   " _1148923861F 0 0Ole 4 PIC 5 dPICT 7 b currentpoint " +n* n" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 63 translate 24 214 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (n) show 24 508 moveto (n) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 254 moveto 223 0 rlineto stroke end d%MATH4  nnl FMathType 5.0 Equation1ELOEquation.DSMT4  nn EquationCompObjA UObjInfoC OlePres000D (Ole10NativeE Ole10FmtProgID F _1148923860F 0 0Ole G PIC H ddp    ,dxpr  ,", currentpoint " +3* 4"  (  (2* 2"  ( = ($6* 8" $30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1408 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 28 218 moveto /fs 0 def /sf {exch dup /fs exch defPICT J CompObjZ UObjInfo\ OlePres000] ( dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 521 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 208 0 rlineto stroke 294 363 moveto 384 /Symbol f1 (\327) show 481 224 moveto 320 /Times-Bold f1 (2) show 481 522 moveto (2) show 454 264 moveto 210 0 rlineto stroke 772 363 moveto 384 /Symbol f1 (=) show 1114 219 moveto 320 /Times-Bold f1 (6) show 1115 523 moveto (8) show 1090 264 moveto 207 0 rlineto stroke end dSMATHGU  34  22 = 68FMathType 5.0 Equation1ELOEquation.DSMT4G  34  22 = 68Ole10Native^ KOle10FmtProgID ` _1148923859F 0 0Ole a  Equationd`    t dxpr   " currentpoint ",Times .+8* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint transPIC b dPICT d tCompObjn UObjInfop       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~late 64 53 translate 25 219 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (8) show 25 523 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 207 0 rlineto stroke end d%MATH  88l FMathType 5.0 Equation1ELOEquation.DSMT4  88 Equationd`    t dxpr   " OlePres000q (Ole10Nativer Ole10FmtProgID s _1148923858F 0 0Ole t PIC u dPICT w tCompObj U currentpoint ",Times .+3* 3" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 27 522 moveto (3) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 207 0 rlineto stroke end d%MATH  33l FMathType 5.0 Equation1ELOEquation.DSMT4  33 EquationObjInfo OlePres000 (Ole10Native Ole10FmtProgID  _1148923857F 0 0Ole  PIC  dPICT  td`    t dxpr   " currentpoint ",Times .+6* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 54 translate 23 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (6) show 23 521 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 263 moveto 205 0 rlineto stroke end d%MATH  66l FMathType 5.0 Equation1ELOEquation.DSMT4CompObj UObjInfo OlePres000 (Ole10Native   66 Equationd_ b'dxpr  '"' currentpoint ",Times .+21* 35"  , Symbol ( > (20* 35"  Ole10FmtProgID  _1148923856F 0 0Ole  PIC  dPICT  bCompObj UObjInfo OlePres000 (G30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1248 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 29 225 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (21) show 27 523 moveto (35) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 367 0 rlineto stroke 470 364 moveto 384 /Symbol f1 (>) show 809 220 moveto 320 /Times-Bold f1 (20) show 811 523 moveto (35) show 782 265 moveto 370 0 rlineto stroke end dKMATH?>  2135 > 2035-1FMathType 5.0 Equation1ELOEquation.DSMT4? 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_1148923848"F 0 0Ole < PIC = dPICT ? tCompObjI UObjInfoK OlePres000 L ( currentpoint ",Times .+1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4  12 EquationOle10Native!M Ole10FmtProgID N _1148923847&F 0 0Ole O PIC #%P dPICT R tCompObj$(\ UObjInfo^ d`    t dxpr   " currentpoint ",Times .+1* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18l FMathType 5.0 Equation1ELOEquation.DSMT4OlePres000')_ (Ole10Native*` Ole10FmtProgID a _1148923846s/F 00  18 Equationd,    }dxpr  " currentpoint ",Times .+5(12"  30 dict begin currentpoint 3 -1 roll sub neg     (                    ! " # $ & % ) ' + * m l - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k x o n p q r s t v u y z { | } ~  Ole b PIC ,.c dPICT e }CompObj-1o U3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 101 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 13 522 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 356 0 rlineto stroke end d(MATHd  512ubFMathType 5.0 Equation1ELOEquation.DSMT4  512 Equationd    ObjInfoq OlePres00002r (Ole10Native3s Ole10FmtProgID t _11489238458F00Ole u PIC 57v dPICT x u udxpr  " currentpoint " +75(100" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 640 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 101 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (75) show 13 522 moveto (100) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 516 0 rlineto stroke end d.MATH"  75100 3FMathType 5.0 Equation1ELOEquation.DSMT4"  75100 EquationCompObj6: UObjInfo OlePres0009; (Ole10Native< &Ole10FmtProgID  _1148923844F4AF00Ole  PIC >@ dd,    ldxpr  " currentpoint " +12* 16"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 13 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg PICT  lCompObj?C UObjInfo OlePres000BD (matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (12) show 14 520 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 356 0 rlineto stroke end d+MATH   1216neFMathType 5.0 Equation1ELOEquation.DSMT4  1216 Equationd    dxpr  " currentpoint ",Times .+40(Ole10NativeE #Ole10FmtProgID  _1148923843JF00Ole  PIC GI dPICT  CompObjHL UObjInfo 100" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 640 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 99 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (40) show 13 525 moveto (100) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 516 0 rlineto stroke end d.MATH"  40100 3FMathType 5.0 Equation1ELOEquation.DSMT4"  40100 EquationOlePres000KM (Ole10NativeN &Ole10FmtProgID  _1148923842a=SF00Ole  PIC PR dPICT  tCompObjQU Ud`    t dxpr   " currentpoint ",Times .+2* 5" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 28 515 moveto (5) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 210 0 rlineto stroke end d%MATH  25l FMathType 5.0 Equation1ELOEquation.DSMT4ObjInfo OlePres000TV (Ole10NativeW Ole10FmtProgID    25 Equationd    dxpr  " currentpoint ",Times .+40(100" 30 dict begin currentpoint 3 -1 roll sub ne_1148923841\F00Ole  PIC Y[ dPICT  g 3 1 roll sub 640 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 99 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (40) show 13 525 moveto (100) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 516 0 rlineto stroke end d.MATH"  40100 3CompObjZ^ UObjInfo OlePres000]_ (Ole10Native` &FMathType 5.0 Equation1ELOEquation.DSMT4"  40100 Equationd,Ole10FmtProgID  _1148923840jXeF00Ole  PIC bd d    |dxpr  " currentpoint ",Times .+4(10"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 99 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1PICT  |CompObjcg UObjInfo OlePres000fh ( (4) show 13 517 moveto (10) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 356 0 rlineto stroke end d(MATHa  410ubFMathType 5.0 Equation1ELOEquation.DSMT4  410Ole10Nativei Ole10FmtProgID  _1148923839nF00Ole   Equationd|    v dxpr   " currentpoint " +D+ 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 384 div 608 3 -1 roll exch div scale currentpoint translate 64 60 translPIC km dPICT  vCompObjlp UObjInfo ate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (D) show 59 515 moveto 320 /Times-Bold f1 (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 275 0 rlineto stroke end d%MATH  D2FMathType 5.0 Equation1ELOEquation.DSMT4  D2 Equationd`    b dxpr   " OlePres000oq (Ole10Nativer Ole10FmtProgID  _1148923838OwF00Ole  PIC tv dPICT  bCompObjuy U !(*+,-./01234568?ABCDEFGHIKRTUVWXYZ[\^eghijklmnoqxz{|}~ currentpoint " +2* 3" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (2) show 29 516 moveto (3) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 210 0 rlineto stroke end d%MATH  23l FMathType 5.0 Equation1ELOEquation.DSMT4  23 EquationObjInfo OlePres000xz (Ole10Native{ Ole10FmtProgID  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+1* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18l FMathType 5.0 Equation1ELOEquation.DSMT4  18 EquationOlePres000M(Ole10NativeNOle10FmtProgID O _1148923834F00Ole PPIC QdPICT SkCompObj]Ud,kdxpr  " currentpoint " +3(16"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 101 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 13 524 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 355 0 rlineto stroke end d(MATHf  316ubFMathType 5.0 Equation1ELOEquation.DSMT4ObjInfo_OlePres000`(Ole10Nativea Ole10FmtProgID b       )                   " ! # $ % ' & * ( , H + . - / 0 2 1 4 3 6 5 8 7 : 9 ; < = > ? @ A B C D E F G J I M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~    316 Equationd`|b dxpr   " currentpoint " +1* 4" 30 _1148923833F00Ole cPIC ddPICT fbdict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 23 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 208 0 rlineto stroke end d%MATH  14l CompObjpUObjInforOlePres000s(Ole10NativetFMathType 5.0 Equation1ELOEquation.DSMT4  14 Equationd`Ole10FmtProgID u _1148923832F00Ole vPIC wdb dxpr   " currentpoint " +3* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 523 movetPICT ybCompObjUObjInfoOlePres000(o (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 207 0 rlineto stroke end d%MATH  38l FMathType 5.0 Equation1ELOEquation.DSMT4  38Ole10NativeOle10FmtProgID  _1148923831F00Ole  Equationd    sdxpr  " currentpoint ",Times .+5*8"30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 256 div 448 3 -1 roll exch div scale currentpoint translaPIC dPICT sCompObjUObjInfote 64 32 translate 25 154 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 224 /Times-Roman f1 (5) show 22 373 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 189 moveto 155 0 rlineto stroke end d%MATH  58l FMathType 5.0 Equation1ELOEquation.DSMT4  58 Equationd`|b dxpr   " OlePres000(Ole10NativeOle10FmtProgID  _1148923830K+F00Ole PIC dPICT bCompObjU currentpoint " +3* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 53 translate 28 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 521 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 208 0 rlineto stroke end d%MATH  34l FMathType 5.0 Equation1ELOEquation.DSMT4  34 EquationObjInfoOlePres000(Ole10NativeOle10FmtProgID  _1148923829F00Ole PIC dPICT bd`b dxpr   " currentpoint " +7* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate 25 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (7) show 25 516 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 257 moveto 207 0 rlineto stroke end d%MATH  78l FMathType 5.0 Equation1ELOEquation.DSMT4CompObjUObjInfoOlePres000(Ole10Native  78 Equationd,ldxpr  " currentpoint " +16* 16"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 divOle10FmtProgID  _1148923828F00Ole PIC dPICT lCompObjUObjInfoOlePres000( 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 13 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (16) show 13 525 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 355 0 rlineto stroke end d+MATH$  1616neFMathType 5.0 Equation1ELOEquation.DSMT4  1616 EquationdOle10Native#Ole10FmtProgID  _1148923827F00Ole PIC dPICT CompObjUObjInfodxpr  " currentpoint ",Times .+ 5 ( 9( 16" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 704 div 640 3 -1 roll exch div scale currentpoint translate 64 54 translate -8 362 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Bold f1 (5) show 333 218 moveto 320 ns (9) show 247 523 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 234 263 moveto 355 0 rlineto stroke end d+MATH+ 5 916neFMathType 5.0 Equation1ELOEquation.DSMT4 5 916OlePres000(Ole10Native#Ole10FmtProgID  _1148923826F00 EquationdWT|dxpr  " currentpoint ",Times .+ 2 ( 1* 4" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 544 div 608 3 -1 roll exch div scale currentpOle PIC dPICT CompObjUoint translate 64 57 translate -6 359 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Bold f1 (2) show 262 220 moveto 320 ns (1) show 264 517 moveto (4) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 239 260 moveto 208 0 rlineto stroke end d(MATHc 2 14ubFMathType 5.0 Equation1ELOEquation.DSMT4 2 14 EquationdObjInfoOlePres000(Ole10Native Ole10FmtProgID  _1148923824F00Ole PIC dPICT     ')*+,-./013:<=>?@ABCDFMOPQRSTUVWY`bcdefghijlsuvwxyz{|}~dxpr  " currentpoint ",Times .+ 4 ( 7( 16" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 704 div 640 3 -1 roll exch div scale currentpoint translate 64 60 translate -8 356 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Bold f1 (4) show 336 217 moveto 320 ns (7) show 250 517 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 237 257 moveto 355 0 rlineto stroke end d+MATH( 4 716egFMathType 5.0 Equation1ELOEquation.DSMT4 4 716CompObj UObjInfo OlePres000(Ole10Native#Ole10FmtProgID  _1148923823F00Ole PIC d Equationddxpr  " currentpoint ",Times .+ 7 ( 13* 16" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 704 div 640 3 -1 roll exch div scale currenPICT CompObjUObjInfo!OlePres000"(tpoint translate 64 51 translate -8 365 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Bold f1 (7) show 249 220 moveto 320 ns (13) show 248 526 moveto (16) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 235 266 moveto 355 0 rlineto stroke end d.MATH" 7 1316 3FMathType 5.0 Equation1ELOEquation.DSMT4" 7 1316 Equationd`|    Ole10Native#&Ole10FmtProgID $ _1148923822F00Ole %PIC &dPICT (tCompObj2UObjInfo4t dxpr   " currentpoint ",Times .+1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12nFMathType 5.0 Equation1ELOEquation.DSMT4  12 EquationOlePres0005(Ole10Native6Ole10FmtProgID 7 _1148923821'F00Ole 8PIC 9dPICT ;}CompObj EUd,    }dxpr  " currentpoint ",Times .+5(12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 55 translate 101 217 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (5) show 13 522 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 262 moveto 356 0 rlineto stroke end d(MATHd  512ubFMathType 5.0 Equation1ELOEquation.DSMT4ObjInfoGOlePres000 H(Ole10Native I Ole10FmtProgID J   512 Equationd`    t dxpr   " currentpoint ",Times .+1* 8_1148923820F00Ole KPIC  LdPICT Nt" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 22 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 25 519 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 207 0 rlineto stroke end d%MATH  18NCompObjXUObjInfoZOlePres000[(Ole10Native\FMathType 5.0 Equation1ELOEquation.DSMT4  18 Equationd,Ole10FmtProgID ] _1148923819 F00Ole ^PIC _d    ~dxpr  " currentpoint ",Times .+10* 12"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 13 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (PICT a~CompObjkUObjInfomOlePres000n(10) show 13 525 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 356 0 rlineto stroke end d+MATH  1012neFMathType 5.0 Equation1ELOEquation.DSMT4  1012Ole10Nativeo#Ole10FmtProgID p _1148923818"F00Ole q EquationdWT|    dxpr  " currentpoint ",Times .+ 5 ( 1* 2" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 544 div 608 3 -1 roll exch div scale currentpPIC !rdPICT tCompObj $UObjInfooint translate 64 57 translate -8 359 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Bold f1 (5) show 258 220 moveto 320 ns (1) show 261 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 234 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3gU>SpO-e: P56pHѹc8sL8~Cr)d$48t 6Y;˴槑!.e1TfgJBYOg(}o!-bUOoS>VeG%tD 7Bz BbQq<A6tMwH_hMwjg o"'cm3Zn~7A?&U1}O(7 kE~o|o5!eY&R |MTf_>Ixh; >KeŬ aMFۖ*u!6GXt<@~yC bAoמ=y"7T~8R~cP?UE>h& fGnp?Nk9s-FtyvO3G:w8~+>iҝ2\>y$>\yݷ5)wGP>pE_{~N{A]Y5&`p6c i\5yq7 TF^VR8XiԸLll68",jPQ[cTзU5XϬR勻ct)o`eU﫯D; 'JHEgXb<+Z/X !BT?0)iHz \V(to 8ߡм4'Ole PIC (*dPICT lCompObj)-Uldxpr  " currentpoint " +24* 30"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 59 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (24) show 27 518 moveto (30) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 258 moveto 370 0 rlineto stroke end d+MATH  2430NFMathType 5.0 Equation1ELOEquation.DSMT4  2430 EquationObjInfoOlePres000,.(Ole10Native/#Ole10FmtProgID  _11489238164F00Ole PIC 13dPICT ~d,~dxpr  " currentpoint ",Times .+18* 30"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 52 translate 21 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (18) show 27 525 moveto (30) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 265 moveto 370 0 rlineto stroke end d+MATH"  1830neFMathType 5.0 Equation1ELOEquation.DSMT4CompObj26UObjInfoOlePres00057(Ole10Native8#  1830 Equationd`|b dxpr   " currentpoint " +3* 2" 30 Ole10FmtProgID  _1148923815B0=F00Ole PIC :<d"P?!X} ⇞+?pUoi`owϮ{-sKM u}^!duI#&b*8i?"A/%}/O;*cᐣX[mcs,G_ekgU&TMz_G8v\CDL*m ~|XP&_ Წ+]ptZ84 kV9V,; shKk}0 fJLL1L3ISbSrlO~bec`Y*r=U]ƾϯP/:QTUQ[hTE7x|ӵ--}{c%U8.]S40[69_«#a?reVDO5F RnΙ,ShT iߦd `3`2OnLqVqX8٠8LWF0pZ{=5giQ}pP:j +u330b/W\W;eC}]e[>pc[1?0E FDEW qH:7\C-H(mWH7 R2Daj8} |J;1"~@{C㽀SJ[~/=#"ރzfP8ӡH*Ytmr\2hn7d_ HI+q\+E#/Wy} P[9t1+<~{{4y>;'h[ TfXxdiݠU1>UH.|~Pt#BUí*.tت ٚ+* *T{ݮ<^)=rX[A"T'jwAUW%g(}+ T+ӎ7YП3 jU۲/73P_;[ xUfėֆ8ٌ.49"JF .}nO@p_HY-ν;b#TN(qnqc>2zWB Ddhɒ뾸0T@ujiߗM >bO݊^NmP[(,/d*]fA9E%P*%Eu-RمA _lw^ÕK9L0@EpeZOHƯQP# 8Jh)wÁ@pҠjs|pNxI@LѺda"aLdnOp`\deZK  @ߝY&lgI&‘ك|`%\8.&)6&ѫ %WNBOp=!a>7ffZo|r7Əb{̓SN G`PP7X'baJ0Q"&FF j a'l !^(ğ Pk62eaga 0Pi+eYc4chtC砫6:o|[ 6kL/FO1D e١xGFI3 :a4{ %^W688π)H=IӅ`4arS797ۀ>r/fR7/K.8y9?݋Λ u8,)zgzA $ ՟cO&]3;(N:*!߉p;V΅q2kX V+3◖X7q>t."s/W7S-={i#9C.D{ch "8h^beH|@_AsGvC A{ƜETf}^З'^w Mˮ?kIi_43GvS[P?\,33. ̣W`\ّNR!>(큺HKaXBa)+G Xer@/iQ21!{q8] K岾QZi5@{HuXCiXg{EL?Laņ5[Y57tVbx>8Gje%^Ak矠9s?=I*Ve[Ɓ{ 91>4 r &VIS>x*.k༤WsTgPΌ5}M7K]foLzT#}S.~ _@Q<Njᘥ+46a*6'x;u?(VN .pϬl5(}w Py)DQ;$uh1 .T7Yl֝ڿ{*^(_y-J/`Җ?]oP{A<,Gr8Ѻ`2{wЪy )qoS?=&Rϼxr1~ WmJvOKʔLr^kggL3ԊA/Ӎxbus>Fvri>E=+7r1 xR&yW=M ަԙϱQXa_+ۚɟxzV:ttex;Z9ϑ#o~-2X)M51Y~EݨAaA>M)gFZVEE&WtaB:z?eE$ XNN_BW-;>/ʛhtoo_k¸MzVcΰ0pl27UЯCxEpŇǟi>q}XJOX--{^,h.ίtt!oiF1`q ?f)cUf0+T* E Ls7I 6 nNyF7u_ڹ /LQ@JL||[9Eyx&+/դ\`ȳVE_;nt1p.sP1 >x(f`2%4Ŭ|(H1J~'W%6eӽ0mEB*WZ,+i]o7탮dl {i8`U/<f۞eܩԫ@_4e‚c D?˾2 RLĆ1ʶM E9k`7ӻU?ڛڜ΅Xbό ҪO0as62pU40X1}uP3"?W~N?]1fdZГ]5=|l_a&Z=t|t(}U *J";@/Zpv[ĭ:f!C8V/L^] /uE{{CzD[T*Ӧ͝upqpS(3מi[tpsCP .n߽ f5qk;q74ꫯJ?iq!oW,KoqZS0QO;lpF X p^BT6=SaJ;>&?/>몧NLEʍ܏Xqc; &̬^qqs*y=#?xLՔX;?I4*%?f n9p^aߘB+1:;rz Xvqfn!ub+1'"m\HLwxh~s /u2bJ4+ޭUw=xPCX՘r&KeDخ0+ zFN2+rBf5Wl7VWC:[)vZr('sn4,P ϊW) pQ?Xm=[(p941MF2o@:w@;ot sPc"4\X'Jz%CSߚZ2]p61ؕxƑq؁" ]'aRؗUYt?I ! c\sVq)@V݃I8 PYf>c`U8 %|evF?F( ^PD_ēC@Cpp }p@L,rfNm{jxxx Lĝ}BL`:s\Cyx5^`:99YBp$F7CRnPj4o`zZ`Dr! 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H`.x3YFdLoPj@mvP>r`uVR![ε5u*Srנom/ViwhCЬ%h(<6~gV/gV`[\A7P9~X9Q6-1 PVi9?;KH*APbC <#b&wF{zhEDr A{ 471f6`v߃ ^ʰV3n M2#(>mUHQ9ggCGsaPKp"c_1148923796F00Ole *PIC +dPICT -|3 1 roll sub 480 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 97 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 13 520 moveto (12) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 356 0 rlineto stroke end d(MATH`  112ubFMathType 5.0 Equation1ELOCompObj7UObjInfo9OlePres000:(Ole10Native; Equation.DSMT4  112 Equationd`    Ole10FmtProgID < _1148923795F00Ole =PIC >dPICT @tCompObjJUObjInfoLOlePres000M(t dxpr   " currentpoint ",Times .+1* 6" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 57 translate 21 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 23 518 moveto (6) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 205 0 rlineto stroke end d%MATH  16l FMathType 5.0 Equation1ELOEquation.DSMT4  16 EquationOle10NativeNOle10FmtProgID O _1148923794F00Ole Pd`    t dxpr   " currentpoint ",Times .+3* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 27 218 moveto /fs 0 def /sf {exch dup /fs e O PIC QdPICT StCompObj]UObjInfo_xch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 523 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 207 0 rlineto stroke end d%MATH  38l FMathType 5.0 Equation1ELOEquation.DSMT4OlePres000`(Ole10NativeaOle10FmtProgID b _1148923793F00  38 Equationd`|    t dxpr   " currentpoint ",Times .+1* 2Ole cPIC ddPICT ftCompObjpU" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 608 3 -1 roll exch div scale currentpoint translate 64 57 translate 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (1) show 27 518 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 210 0 rlineto stroke end d%MATH  12l FMathType 5.0 Equation1ELOEquation.DSMT4  12 Equationd`ObjInforOlePres000s(Ole10NativetOle10FmtProgID u _1148923792 F00Ole vPIC   wdPICT yt    t dxpr   " currentpoint ",Times .+3* 8" 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 320 div 640 3 -1 roll exch div scale currentpoint translate 64 53 translate 27 218 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (3) show 25 523 moveto (8) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 264 moveto 207 0 rlineto stroke end d%MATH  38l FMathType 5.0 Equation1ELOEquation.DSMT4  38CompObj UObjInfoOlePres000 (Ole10NativeOle10FmtProgID  _1148923791F00Ole PIC d Equationd,|    ldxpr  " currentpoint " +11* 24"  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 480 div 608 3 -1 roll exch div scale currentpoint translate 64 57 transPICT lCompObjUObjInfoOlePres000(late 24 220 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 320 /Times-Bold f1 (11) show 27 518 moveto (24) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 260 moveto 370 0 rlineto stroke end d+MATH  1124neFMathType 5.0 Equation1ELOEquation.DSMT4  1124 Equation Oh+'0|  8 D P\dlt'YR 1 CH 5 6/15/01Division of EducOle10Native#Ole10FmtProgID  1Table SummaryInformation( bKV`叼"lńA}ϽZp!i Qcwߕ J\Dt. 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