поЮ║╠А>ЧЪ =?ЧЪЪЪ<ЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЛ╔а┴@ Ь©у%jbjbq■q■ ╗HЖЖуЪЪЪЪЪЪlТТТТТТТttttt┬$t{ П╦ннннннн8 : : : : : : ,k ▀єf Тнннннf ьТТнн╦ьььн ТнТн8 ь6>6ТТТТн8 ьTь, ТТ, ╛GAJЎttь, , { { , / ь/ , ьцЕMATH 116 ACTIVITY 6: Understanding Relationships between data - scatterplots and correlation WHY: Much of the use of statistics involves relationships between variables. It is important to understand the terms and ideas involved in describing such relationships in the same way that it is important to understand the terms and ideas used in describing distributions of single variables. LEARNING OBJECTIVES: 1. Learn the terminology and ideas for looking at association between two quantitative variables 2. Be able to find and interpret the correlation coefficient for a set of bivariate (two-variable) data. 3. Work as a team, using the team roles. CRITERIA: 1. Success in completing the exercises. 2. Success in working as a team and in filling the team roles. RESOURCES: 1. The Statistics Handbook chapter on Organizing an Describing data - especially p.6 2. The notes on "Association between variables" attached (as pages 4 & 5) 3. Your calculators and the sheet with instructions for your calculator (different for different individuals) 4. The team role desk markers (handed out in class for use during the semester) 5. 40 minutes PLAN: 1. Select roles, if you have not already done so, and decide how you will carry out steps 2 and 3 2. Read through the handout defining the basic terms and work through the examples given there [Note: the examples do not show how to find a general solution.] 3. Complete the exercises given here - be sure all members of the team understand and agree with all the results in the recorder's report. 4. Assess the team's work and roles performances and prepare the Reflector's and Recorder's reports including team grade . EXERCISES: 1. In a study of diet and exercise, data have been collected on the lean body mass (in kilograms- body mass excluding all fat) and metabolic rate (calories burned per 24 hours) of 12 women . The researchers hope to show that lean body mass [which is relatively easy to measure] is useful in predicting metabolic rate [which is harder to measure]. The data are given here: Subject # Mass Rate Subject# Mass Rate 1 40.3 1189 7 41.2 1204 2 33.1 913 8 50.6 1502 3 36.1 995 9 42.0 1256 4 54.6 1425 10 42.4 1124 5 48.5 1396 11 34.5 1052 6 42.0 1418 12 51.1 1347 a.) Which variable (metabolic rate, lean body mass) should be considered the explanatory variable, and which should be considered the response, [or does this distinction not make sense in this situation]?b.) Plot the data. Be sure to label the axes, indicating which variable is on which axis (Mass ranges from about 30 Kg to about 55 Kg. Rate ranges from about 900 calories to about 1600 calories).c.) Describe the association between the variables: Is it positive or negative? What is the form (linear, curved, complicated)? Does the association appear to be strong (a clear pattern, points close to a line or curve) or weak (no clear pattern or lots of scatter away from the pattern)? d.) Find the correlation coefficient r [use your calculator - do not work from the formula]. Does the value seem reasonable for the graph? 2. On the attached sheet there are 5 scatterplots, labeled a √ f. The correlation coefficients for the plots are 0, -.3, -.65, .8, and .4. Which diagram corresponds to which correlation coefficient? How can you tell? CRITICAL THINKING QUESTIONS:(answer individually in your journal) 1. Give an example of two variables (other than those in the text) that you would expect to show a positive association [increase in one would go with an increase in the other]. Is either of your variables a cause for the change in the other? 2. This scatterplot shows the Percent of High School seniors taking the SAT in each state on the x-axis and the mean SAT Verbal score on the y-axis. The correlation coefficient is r = -.884a.) What characteristic of the graph (answer in terms of visible features of the picture) would tell you that r is close to - 1 (fairly strong negative correlation)?b.) What characteristics of the graph (the picture) does r not describe? SKILL EXERCISES Exercises for Chapter 1, 9-11 Graphs for Correlation exercise a.) b.) c.) d.) e.) Association between variables, correlation Two variables are associated if certain values of one tend to occur more often with some values of the second than with other values. If we wish to use changes or values in one variable to explain changes or values in the other, we refer to them as the response variable - measuring the outcome (think of y in our usual use of function and graphing notation) - and the explanatory variable - measuring the cause or explanation (think of x in our usual function notation). For two quantitative variables, the standard picture is a scatterplot - explanatory variable on the x-axis, response on the y-axis, plot the (x,y) - pairs. [If there isn't an explanatory variable - we aren't explaining one by the other - either variable can go on either axis]. Patterns are described by form (linear, type of curve - general shape of graph), direction (positive - variables increase/decrease together; or negative - when one increases, the other decreases; sometimes there is no fixed direction) and strength (how closely packed around the basic pattern are the data points?). Correlation is a measurement of the amount of linear (y = ax + b) association between two quantitative variables. The correlation coefficient r is given by EMBED "Equation.3" \* mergeformat - but we will calculate using the ⌠Linreg■ command on our calculators, or using computer software. The formula says:1. Convert all values to Standard units (subtract the mean, divide by the standard deviation of the variable)2. Multiply each standardized x by the matching standardized y , 3. Add the results 4. Divide by n-1[to eliminate the effect of more or fewer points being used] . (That is: we multiply the standardized values of x & y for each point, add them, and divide by n-1 to get an average). The value of r will be between -1 and 1.If r is close to 1 , the points are close to making up a line with positive slopeIf r is close to -1 , the points are close to making up a line with negative slopeIf r is close to 0 , the points show no linear association between values of x and values of y [no association, or the association is not linear].See the examples on the other side of this sheet showing sets of points with different levels of r . What happens: If large x-values are with large y-values (and small x's with small y's) then the multiplications will give mostly positive numbers (+ times + or - times - ) and r will be positive - showing a positive association. If large x-values are with small y-values (and small x-values with large y-values) the multiplications will give mostly negative values ( + times - and - times +), so that r will be negative - showing negative association. If there is no such patterns, the signs will be mixed, causing cancellation so that r will be close to 0 - showing no linear association [r does not measure quadratic, cubic, etc correlation or matching to complicated curves]. In practice, r is not calculated directly from this formula, but with a calculator or computer.The calculator work will be the same for calculating the regression line equation [coming up]For TI-82,83: Enter the x-values in one list (using the Stat Edit commands) and then the linreg command [see the instructions for your calculator) - r is displayed as part of the results (TI-83's may require turning this on - see the notes or ask me)For TI-89 √ enter data in two columns with the Data Editor, choose calculation, then choose LinReg command For TI-86 Enter x-values in xstat, y values in ystat (all fstat values are 1), use the linreg command For TI-85 x-values as x1, x2 etc, , y-values as y1, y2,etc use the linreg command. For Casios- use 2-variable data entry, linreg command. Some scatter Plots, showing the corresponding values of the correlation coefficient r `dС Т с/T%*".7Vcfghjkmz{|}┌┐└┤ЁфпКЗЁд)=лв╘╠цгЗ :B≥║ХС,7`|▀▄╟╠╡Ё.R²╔ЦФЬЩЩШЫЩЫЫТЩЩОЙЩЕЮЩшЩЩыЩЩЩЩЩЩЩЩЩЩЩЩЩТжндТЩЩЩj▄уB EHЮЪUVj▄уB UVEHЮЪ6│ jJ%U jdU j▓U jхU jД U jU>*<│5│M_`┴┼═no≤≥ёкл n p ╪ Ґ - . ─ ▐ ░ ЭЭЫНКЭЭЭЭЭЭКЭЭЭЭКЭЭЭЭЭЭЭЭЭЭ1$└═└`З1$^└═`└`З1$1$_`┴┼═no≤≥ёкл n p ╪ Ґ - . ─ ▐ ░ √ З Ш ²·+,╗╘ЄR╗67UHI6WXglm{~┐┘├ЁЄ<▒▓╗╘ГХ\ъТGюа ⌡V"W"│$Г$;%s%t%н%о%п%т%у%ЩШШШШШШШШШ^░ √ З Ш ²·+,╗╘ЄR╗67UHIЭЫЫЫЫЫЫЫЭЭт╞єЫЫЭЭЫЫ└h└≤Ч1$^└h`└≤Ч$└h└≤Ч1$^└h`└≤Ч ф0п═p@Ю╟─P П└єь дДT<$└h└≤Ч1$^└h`└≤Ч ф0п═p@Ю╟─P П└єь дДT┬1$1$I6WXglm{~┐┘├ЁЄ<▒▓╗╘ГЭЭЭЭЭЫВЯЭЙЭЭЙЭЭЭЭЭЕВВВВВВВ$a$1$ фД$1$a$1$1$ГХ\ъТGюа ⌡V"W"│$Г$;%s%t%н%о%п%т%у%ЩЩЩЩЩЩЩЩЩЩЩЩЩЩЩЩЩЬЬЬЩЩ$a$ЬЧап2≥⌡╘И!О!W"╧"t%н%р%с%у%ЩЩЩЩШЩЩЖ j,U>*5│* 00░hP╟п/ ╟Т=!╟п"╟п#░`$░`%╟|HHТ@ЪЭЪНR)Э,,P `,-═^Л&'Д Dd`hХХП<╡ П CПA│©ЪП─BПT `=;Яфз{j9Prkmй√Ъ0 D TП( `=;Яфз{j9Prkmй√ЄЬр 0Ь╠(ЖЧx°щXАkгЁёН·ґУМ²T+╚JhЕ°B═щКQУBT²RвЫZЗИ└Аэ÷©yU╧┘ёЖGзрЧ)Щ■+T$■╨5v|i└}┼┼l▄М°-E^KїSъ⌡ы²Ґ⌠Мж╔│п╨шВ~Ш~ofч╪y3ё·?}ўAimв└]Э@Т дЫШ∙ґ!єWы╨Ж|ЧЧЬ·а╞ҐzаЧюЙйкЯПб┌▒пЫЬх/$Рм)│▀v╠eіX╠▐k╒╙mmЧе÷▌ІНGЪМёsЎф<ъ█dc╣D╡YлT"ы6Ёz$gЧЭщ╙KЫ{╣╒▓┤3▒M.;c*Ыєўd{ґ'ижуУz$КЮ} цЫ┼b4сqДч≤┴#Г Y5ЗvOGґwfc╧ZR6У╧P=▓┬Д╠ы╒иygQDнB╧ъ`>╦;┘k╟÷╨┐bЩt▓ьф┌v92 з╛_b▄/АШyМ╪°СЇьпЧі<[ч╣6Ы─■╧ЕAЫ:tQhнЫаhб╚H╒═G1UЇ∙~й г4▌У3Г7╔·╩И}ю.@a╘G1АU1Q яpЕ_┬▒.Єyф.╞Ає5─Я├─ь°uФК2А ОOр"dЫь╪бG▀нҐP7HgюЇDl╣Вўц╛4[*жdlгс╟Wo≥Ч$6Дo+Ф~ █≤▐є°яHKlк╔ў⌠ймP²юa#ї"Ґs,■ ┴└МяHJmHкє┘>эХЩt┬хФи╚5█▄TтЄ╣(ыўJ─]┴─С│ Ц| ╩┬v>pЪ&tEщ ║ ─Є └8цїU z┼S \аnyn┴┴н▀уCЛ>╦иC∙V╙0hr]Bь╠░g?Е⌠rnБс0ГRa▌~g\╩Єэё▓кB5л>Vvo@Jж┤°й7╗9'─╪E╘├пDЦ╔(B NuС▒(√c1wCL~ '÷▓Gєді·В╠┬ф▐CщР┘н▐ОягшuЖA]┐ґR▄yqІу■╗∙БІМЖІy"р╔oїяч√ЄХ²Al⌡▄√▌░ъ═#VпнъуЗ▒Z2ЩСу0Lц;BME┐ьmn┼Є╛+`DзДoB7f┼яQW`ц└╔E]p|*\ью┬D╟ы\E ┴⌡pСї└х╪ь┘QцuФ ▓┤4З▀г" j`▐ov└√░8╣iFZ╘Яc▒├<в?іvdг;*Ж╙ :Pі╛/АxoкE▀uПІдt`/aР6єєІb R!"дW√i╒²@мy$Нc`oҐP┼vL╒°╒BЛ┘ШJ┬S╚?-_у4&д'fUта┴P╗┼б`┤jЎ│о[rЄ║:qKXЬ- ╔К▒ ║ш^АГvРtk░┴т┴'■≈В(g3"ївє▌╚6]>Г≈└Ыр[gqsЦh!fм┌ґс╧╠2a≤1FMЁ└AЦ.tс|жче3И⌡ЩК/╛I╛▄ь┬дЛCбW└ua}9╛ЇAd√*ЙЖ^л^rfo┬Ґ1КЭzM═╧╩4┐\мe(МYЧа3Б·⌠@Є╚Л5вЧ▀гc┐÷фEf8smўqBьeBЙT`П^zL╞F≤▐XПz#в{ шхАСїП Є~╩УMп(Ц&ҐКmя+v©УU#╞Э-Х▀▓щЦ╧÷7JЕА&hБ]W Р X·э│6╗9┌·═sUЙ√qx⌠mЗДП$ц0⌠┼3╒р}вЙ:ML─1EI├хПzX#РГVbМё├EюлV└Фm┬-н┐╛ы█f≥$ ЁІ╚ W╔]+└h_╛еювё█КИm└п#╛┼ІB5cчЪ^AЬТЛBNаэX\Я6·гсv+ЎZш■▒┼║;╔%└aнГ#Д.-$Т└;С&▒├АЦYсэ╒>mB╙ x╟хг@и╗╠║┼-У3а}н╠v Ы╛@.~Н║'ж┘кЪTG²йъҐ\TХЯБ}%╣Шр▒░я▒U≈┐uФx▐юЩюYп╦┤It[td1╛╧─r!НDФ 3╨їt&Ф;D@лBОЁ╗║НH=⌡▓z^Й'╚tч┴УЁБpшu)cd─╘-ч╩═n╠э║ТЬ╙o┘_чщ▓СЬniї/╘;їиу]я╡5u÷ЛК]SrЖ∙!u+?+н░║эъ3╧=єН√э╪SR╡Я©г>Рыь┤┌su≈5Аuэ√Т╙ctEф╞┴_▌эгїКZЧ╞m÷Щрw▒m ;∙k┌aa│гЁ+┼lЇ#6` хҐ т╘т⌠xК@ё!,⌡Ї┴нyaя@Ґ4ы└tсA7tКk²ЖЇ ▐Є╪ЕZ▌hї░√╧└=ргfхЯ|lъУЯПpлфЦ╒√C7cЁAsD⌡Fзь╛п╠Р3тъ#}иеqЙ┴&(&╟Шvio]√ЄA╒╔yLvilВ]Ik░√]"зрXцGз|H+▄"ґ[C АБк▀HЦtc╛М[Ц┼І@ЄS{iZрl┌ч┤гgЩ,рЛИ▌ґ^Т?И}ЪПInЎ5╒к3kK'ҐУ3О>еssZ ^╛Эф>╪xХMVВЧТO╠ГВдЦ╟|▄эШВ┌щ{ЯДDdєєХХП<╡ П CПA│©ЪП─BПTіфу`ЁL в%R#Б*HЪ0( TП(іфу`ЁL в%R#Б*H≤─╞UDлF)лъЖЧx°М√wXVeфoх▓лHи▄╛hОA{ь╒ҐМ=lОA;h(≤ё║&M(m─⌡д Q+╠RCя╗4Z▌J+жв}?ъYх╔Щш{]ГЭнyчъyчГ}оЫнw┤a╡bрc2░Й▄╡Fаbрn=┐N·⌡≈UМ╩МgБХфИ═c╞й▀дў+Ю>коbЄ÷5╠b^І{ВF1- [ l%▀GEЗq"ЩґEЗ²DЗшX6═Ё╡яъVd$^є©²H©▀H?аF5*Щў"Щ$▒=щDЗи"ЩМґ:═╩╙ё©┐H©┤HG▒F┼H'⌡W-dsфн"Щ]DЗ╩┼ТSE ╩ыl│щ5[О!ръSє©≈Ho▒Ч>І*юЎZМ7кЖв·Ч"ЩEЗY/p╟zИ"2r╗H?Mє≤HЪpк║,Т▐И%╡Гh▒Ч1"Щcm4Ю8█FЪx▒~/▒Ч "█EЗ'YUюи╙┼Ч)"Їt▒Ч╘"ЩсD ї[У|ЎT=Щ3EфнИ÷-р?Gєўм8OЁДяЫ"ЩDЗ┼Т/И_l╚\╒у═÷!2ri·5\і=ЩкEЗWX╦RQЗW┴Т╞ыs█HЪZ▒Чuv5pҐўі┐HЪF▒ЧM"█⌡EЗЇь(\█BЪV▒Чm"ЇшEЗw┬4ОЄj─╩T Щ╩EЗВ┬Л╩Wє÷HЪ~╚x@UСХA▒ЧC"Щ┤EЗ▐┬Т3mvюё ЩгDFИ?!рRєЪ■ґПЄV│Ч3"Щ,▒=ыҐґАYМИ?ggюС:ёЪ┌H©▐H©╞H#Gє÷kWЩtЩEЗЩEЗDnE ┐,;П▓╡сYєЪ┼HЪU▒н`▒Ч╚╙*xТ HX ЩR`w▐ЧК"Щ7╛ZЮMUKЪ-▒▒ЇEЗО┬ТСEЗ6+Ю]м┼Ч{"ЩА"{F┬ТъИ`Ё>тЛИ$р/И┴4FіYц(шё╣ї?Fє?Vє?Nє?^ДVl6ПqЬ █ "Щ▒ЧD▒Ч'"щO-+П≥╡Р╗Tє?Iє_&р÷,р÷bёS5:ЩоEFЎИ)р÷&р/Ї*│И╙▓ЧW"Щ╞EЖ|#р÷aЁf┼╪нчТ©И'р╞iV┼Тfш╛│9 4Щ*▒Ч\▒ЧВ"Щj▒Ф╪у╚m}ФвжkJK█ █sr▄?dfk3бЪ▀?і┤Ъ?JM5Ч°░`\XфеT∙Яю2.,ЦRю2.,Цrю2ў,c`W√q∙▓2Ц╞6x-~≥я╙fф5"3ў≥q²х▄©▀лЬ┤х▄┼л╦~╣5l╗╣├©JґАОBkЬ'гЙ3ґ║!цсґ║)у ╛!ЭОО⌡аЪvПЎ):dёЧ.ўы║БP#:7Сeш╧ы']б'MhM╡@R8═ҐІ╡(┐ґР╣ї╗ЪO6~≈qUГв~╠ЁЖ5Q[Ешл:u╡─W█БVb║ -t╡▐q8Я?tmd▄x┘rx:н7r²▀ф[(!jе╦▒ў┼ТсГ╠^[АX7е&п╙Аg╣≈нj)qр-pНJvу═!TlА·аП<┤LXГwk≤jї╚рАJ╪ЎМ╡ЯЗПй┼┬╟s╩*Ґ╒{lжП╨а┤aґ⌠}fшA╚є┼ЄоuB▒yщpІчаm╩╦yЁУфчtУсL]О',Вnh;≤√0е4Е∙qU`┴кЩў▒-nй&╩▓┐]ч8Ж╪Яt`4wk+Qo+1е÷t┐7И╘~1n0÷Жp©|7Лчм~≈РФ;А%<Lz╗^Йp╨ъ5дYеі┬ўВМ6Gtv▐ЛlРфJ┼Л≤|vi∙╣{АZэ┬дЮМEhЁo╗SУ ╙Ё┐s╚sрмi;hЇo▓СVj.┐ШV┼хК├цб-\Ґ/К#3Г8] а*іFмKwpК╟[ь`/sb0э╞ґP╪⌡3Їщ72 ШґЪ█Ч~-ё²ZDR·Bnк┌╚ЕЎо√Gt▄*/_{іГ}ИЫЩ√зюйDdТТХХП<╡ П CПA│©ЪП─BП:U┴⌠4yЁCрY╗ <&I0Ъ TПU┴⌠4yЁCрY╗ <&I0ІўXG< *<іэЧx°щ≈wXUuг©░%≥░│ёhОA{ь╒hoйЖі=lяжkjTZ"іQj≥%IeCеqSшYX)xM⌡@P├&фУШ}О9w─└ВСyЗ=о9÷ъyъоyЦpоҐ$гLеюьл≤ЧH┬Угцо├│ё`╠≥Є>┬AЇ═[0╗2ьwш)ндя█Sїk©█┴m хЁV÷#дХ\R┌X╠═⌡┴ыыХ"іїcsЁ─-d╠вUє'ръRєъMє©∙UБU█Чж"#щEЗш┬Т{┬ТlT QёръVєъSdf;▒~▓H{⌡░╛ыяъAє÷"рOiТИВІUpвЭІfТИО(ръIє÷&рэыVЛ╒у╡©╚H7▒ЧН"Щ=DЗ{зў{iWьш╩дЖя≥ЧЎ"ЩЩDЗШ[8@YЗ┼▄$рOИ,р?д╙┤╙ ЩцDЗ┤▀л!р?Rє■█ґяХ#рО'р?Vєq°HЪx⌡p┌fEЪD▒G├HЪ$▒Чи"мL⌡=ЪЎ4{Зї┼▄²&р?]є├HЪL[%p√Vичы"ЩsDЗГ┼ТоИ÷o╩\═щ═÷%2ra│5\є3ЩЧ"Щ▀- \╒(ЩKEЗ≈┴л\.р©Bє╔щ \╔╩И_-р©FєґHЦ:▒ЧУ6 Ї@ёп©AєёхЦ&▒Чм"м[l6юґ ЩшDЗЇ▀лщ!р©Sє?юf э╔YЁwЇHЪ▒ЧҐ"ЩШDЗ9І:Ю~ґ▌Ч"#┼ТИ?,рдvxT╩═7┼H░х▄'шКLЪ1╩├Х┼ЧP▒Ч0▒ЧЦ"█\▒ЧvПєН╒Ъ■H╦H└хЦi▒Ф3V╘ЙТСDЗёDЗЫ"²я"Щgmюм┌Ґ╠"ЩГрМ⌠{zТ÷И©`ЁфiІТг▀▄LИ©(рIє?яV╪╛Uя÷$рEdФU▒Чd▒~║ґxM╚ї?Eє_$р]єЯF╨5╪ig`╙нТъИ©-рGєЪўхc ыюТю3DЗе"Щ≥"ЩY"щыV≤ё╙ЛyEЗО┴ТГ┼ТГ┴ТГшХюШ²Ч"#┼Т?И,рЪдf |╙YрЪLє©@dФs▒ЧІ ЮK▒Выш┌~╘H©Lє©PєЫ∙HОk[5PўEс╞И/И#рЪVєЫ]C┐Моb÷о╦дК5V╚rs█Ksr▄Ў╛,Ц╡▄ЦВiiфЕ фjю*жPUе╚XXе─UЭ╟┼?VЯgю*ЧXе_╚Ь⌡┼╡b² НCҐх┼6kVЭ]dEШ6fе&▒ЪYЯO▒W┼╛ЬW┐54Ш╛a∙вVYцъ╧ж╟&гZ╡╛am├5Э⌠f ґ жЬv┐Ш⌡!ЛЇCП7E :е╣бЦ÷Ф_█ЬV>!▐ЩEЧшE▐юе|ЄЗвX═g ю©8©z-QшушюyЭъ.°}╗Ф>,ъґgЇ√DlW╞Ц║╩Кb$е)v≥╗к<їXQ║6u:p<еqv≥єк N╘Z├ГZ8%<╪бА╪нRInМз┬╟Ёk┐у²@╔А╩XОэV╙6└Nd╦▐╨3.wб МсЁ°P┘цЗЮH)КK┤фsSЕ╪#lц4чЮ6s:sCCоe├SaXЄ!уЯР(ъ▓:г[ ╒▐N~Dь╣л █n┤⌡йV▐kпи▒УҐN╙0.f╦&"Л<┴@╗≥Иі▌с╚6гJY_:?r╪Ф┬pb═v╚мpv(Дq╛9я├Tї0X+5|O*▌Oц-в7@·Ъж TПd▒]UЎ=ҐьТ^э4>@·ЄF/ гь>*═tДЧx°М≈ TUU├п■▄х)5 к╡╒y╟┴l·ё╡yЄyhN $+mр╒yп,т┌@╛╣-╔╔R),ЄRУҐвЪО{ъҐ·╛┌V╚уZжҐъҐШ|g÷sЖ}IЫ┬а≤с┴╠║x└ьxFа0NК┐tРэ╛aчu╦К@щ8]tT9ю"╠К├П┌ЕГ1:≈√"VлйB;qХPЄSR╟≥Y@Y╪Й(р▐Иo.рО$ръб╡ЯйFK▒▒н"ЩґDЗ "ЩD⌡Hр╛ТЇИwысUєъMєъщVТпЙХo#рО)рО%рХ-ръжvа╙┘lоХ+рО'рО/рOing╩ІвnyҐ┐HG▒ЧN"Щ²EЗ╩XU─]U^МVj tі©╩H▒Ч@КЖT/ЩҐDFЖИї┬ТВИОkY─Щ■┘ЧЧ"ЩDЖ(р?Hє╟м╒ыХ*р$р?Lєq╦HЪ[pєVEЪ(▒G╙HЪh▒Ч`▒Ф1ІzЎЎЄzЗг┴▄/р?Aє╒HЪ$ш%p╡vи╚SDЗї┼ТOИ÷.р?ц╙°╘jпO9+кнж≥Ч9"Щ!нU■Чy"ЩСEЖ\ р©Pє▒█.жhЗ≈┬Т/И_&р╦\є┘мбhЗW┼Т╞y\-р©Fєyґґ╦N╚║ҐHЪ▒}7┼ТoИъl╚nя╙yu╚HЪ6▒ЧМ"Щ;DЗИІ;ЮNМ▌Ч]"#w▀ТОИъ+р©о╙э╞*п@є?LdOфPkxPgЗыП╟НХ?"рTє?\є▒)рлF#4┼ЧЦ"Щ'DЗO┼=щX∙√f\■ j\°°l\▓≤h╛,ЦR╙йXXфкЬ#`≈√╠╟▄ккXXфzю2ўPRfЭи&╞бо"3з╙≥q╔х▄╚DfЭEdф_EfЭMdфу"3ўi╟├╣UжП{║5╛кІ├фLkX÷n р╛ac╙5▓ґ!≤h нЇ╪ъЧoО7EШ▄GЁS\║╪P#Б|LЖ╡Эк7 ╨Y▐ с-пE│ <┌fмhe0*_ТlЙ рЯr8c┐nІжёР╣╔ЪъЭ┤nэ'>≈O╪.РuQФЎ.ЙЪ48÷Cё┌Еf6кYН╞m9≤ЮГ\Ж/╔бчt▀Щ╣V"Эж\рй`TЎ©Яє╙≥fAd≈╨⌠-l[p9С Г╛sмyґ&)╗┤≈еёлВб9╣ґ&└3fЮ÷xA╦E]и fGnk∙╩▄9-╩;ауЁ┴Ь⌠cBм3╞q⌠лl9hU°й│:J|╞х╚M╟-аbfшh∙Ьао\kаn▒а"зEН·AЇ╚ь5┐pчВежукы]ю┌МBn©ЁёАЎ─;(эя;Ю-<Рp:Ш╗s'╗v©╒тП&LVВD7\Ъ╚-Х╔Щё{HA╚Ї▄Ў⌡2Лf┼_"g #б]▌▌нЪчАh▓u╙RЮ▐÷дшEНЫ~'ш╩я /Бu·ъUЮ#√И┐║▒~╣Эў!ьъ╗Хq╙R, tiІpujx²сtАФЗ;я$dfNдN"б╧╩х┴в3<ж_I8╪бЕ╦іЫК⌡└m%c └:+4зкы√▐Оgъі~"ТUш!ФDdєЮХХП<╡ П CПA│©ЪП─BПV│эuКЎ7Ё2х~YDВЪ2╗ TП*│эuКЎ7Ё2х~YDВ╙U,*длF)═tЬЧx°е√XUeгЪ-ях─░тт┼Іыє=lяч┐йЖЄҐmҐ▌є╡0█R fKqbE╔з4M╞╘-BD+5EАТЪ©Вэ{К┴⌡ЫТ=о9©СҐОО{©qgrA═2╔│НH┼sЮ╟!`▄!P┼pК├зEщЭЎСёо▒v╙{ЯtЦУпіГ╒▀дґОе╩╚о╨≈∙!NлоG+╠woЄсс╠∙Yюж╡ЬтFє/рo+рo'ръф╙ ╙F[▒▒Ж"ЩМDЗ┴"Щ$⌡Hж╛ТЇИї┬лtИї┼Тw╟у╣:З²DЗ²EЗ;┼4╨┬Т╩з.xj▌М;┴ТwИО"рOiНj╩vсnЫ╪╩H▒Ч·"ЩҐDЗ{ш╘щu*|зїлzХN_▒Ч~"ЩЩ-═,ЩEFИї▀ТИbU─CU┘Чa"ЩцEf▌И)р?йf▌жlТ▐ИВИ+р8Nє╪ґ 8A╚╒╒х+Cє▓HЪd▒Ф)ІzЎ©ЄzЗї┴▄².р?CєіHЪ,ш%pІvиїsDЗГ┼ТоИ÷/р©юN╦Pї║O─ххEЫжp╠НТ/ИВ╡(p╘╒Т/И_.2s┘HЪJ▒ЧU6╦ZёИ_#р©Vє²HЦz▒Ч 6▐@Ёп©Qє⌠хКf▒Ч-"м[m5юmZ ЩшEЗw┬лщ)р©KєЇґ╦G╚ФсҐ"ЩШDЗВ▀ТИgыН─╣;З┴▄<,рDєЪ╗HЪ1;Юq²Щ>"ЩЎ"3ачжпOwЗЩґP▐Ч@▒Ч"ЩA"█l▒Ч⌠6 xJёХ?-р,рFДУ╛HС9╚QuЗ9"Щ\▒~·Hg╗HЪy[0L╚Юсp▒ЧИЖI│ҐzТ_И©d╚Fh╣ТG┼▄▄И©,рEєЪ╙М xM╩╒?Zє?FdФu▒ЧX▒Ч8ш=0^╩їЪ├H©@є?AєЯf╨5LЄ;П√НТъИ©#рWєЪ·хk▓ыюДП74 EЗSDЗSEЗсD╨сґ*0CUЫT$р_є_,р÷)р/╠ы│Y ²Ч"#┼Т?И≈┼Т?ІU÷h∙Т?Ио≥≥#рЪлv|.r°}[п/ИоИоi~!рШрv |╔MсЪZєЪ█HЪ[▒Ч|▒Фwууv>B!Цб╒"ЦВфEыыфеYYфPfіqIFЬВО┤Є4Црє$Ц2ю*.ї╙┼?VЯ'ю*ЧXе_╚Ь+`+╚Ь`+╚╦BEY╠й&a╔х┼ІjV\%╡Бj▒YЯ▒ЪYq█х┼k╚ґa]хЧ*╡├Уж╟!шj╡╛acі5lй╟├з4k╗K╡├П╞"Ъ|Ъ╒Ъ)Z1чґm:⌠°█H┬ЦKЄЇd▀;┴АN Й°є└|Ъ9u┬-ь╗ч©YтЛ╦К╚БЗйЩ╩XИНbn▄аFУ mЁеЧ╣n█≥м;жV╡дB5+щДB≥ЕЪt≈╣,Zs3Nr▀т;÷*w╙y1ушЛв╨Ґ:y╛7ж╨иЙuГв\(уZга┘^X╣ж╧╘)^xцЙ┘;+°Ц├j▐┬є6DК'Шц^H╣вП Н┘┌ў5ё╧░M1▓┐*┤G╧║┼З5#А▒м┘зGj▌hи║Oі8п⌡Єп-UгП`wЯбґCюa2г▓щ HзЬ\/ґЙ╪°█Ф²ЩDvЎ▒ц-уA╘Я▒T$j╩х61:Zр▄bvkyУЇP'┘fЗвg@3≥Zg░e╨61FWІЇНыЖVрD╣ Ss\{uҐQ╘Чт*▌O∙БУКЫ└i├═~жbЭMЕ╦~чiLskВ▐!т═▌uг╠⌡КМє▄щ╔Н═EЧЪЪЪABCDFGPYIJKLMNOЧЪЪЪQRSTUVWXЧЪЪЪЧЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪRoot EntryЪЪЪЪЪЪЪЪ юF─uґaMе@юData ЪЪЪЪЪЪЪЪЪЪЪЪ%Ї<WordDocument ЪЪЪЪЪЪЪЪ╗HObjectPoolЪЪЪЪ─uґaMе─uґaMе_1108268428ЪЪЪЪЪЪЪЪнюF─uґaMе─uґaMеOle ЪЪЪЪЪЪЪЪЪЪЪЪPIC ЪЪЪЪTPICTЪЪЪЪЪЪЪЪЪЪЪЪлЧЪЪЪЧЪЪЪ !"#$%&ЧЪЪЪ(ЧЪЪЪЧЪЪЪЧЪЪЪ,-ЧЪЪЪЧЪЪЪ0123456ЧЪЪЪ89:;ЧЪЪЪ=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopЧЪЪЪrЧЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪTm<ЬХХЖЪЪЪЖЪЪЪл&█║dЇxpr═▄ &█"&█═Ў║ю currentpoint ═©"═Ў +r)=(1(n)-) 1"(Bx +i (M-) x"V(Js +x"@ ( :Ф *Х (:Г ( ]Ж *Ь (]В (ky +i (u-) y"(ss +y"i (cФ *Х (cГ (├Ж *Ь (├В (,Е║юZ30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4512 div 1216 3 -1 roll exch div scale currentpoint translate 64 39 translate -9 665 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-Italic f1 (r) show 249 665 moveto 384 /Symbol f1 (=) show 840 426 moveto 384 /Times-Roman f1 (1) show 591 958 moveto 384 /Times-Italic f1 (n) show 863 958 moveto 384 /Symbol f1 (-) show 1122 958 moveto 384 /Times-Roman f1 (1) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 567 566 moveto 738 0 rlineto stroke 2052 426 moveto 384 /Times-Italic f1 (x) show 2225 522 moveto 224 ns (i) show 2407 426 moveto 384 /Symbol f1 (-) show 2719 426 moveto 384 /Times-Italic f1 (x) show 2708 109 moveto 183 0 rlineto stroke 2319 958 moveto (s) show 2475 1054 moveto 224 ns (x) show 2009 566 moveto 914 0 rlineto stroke 1810 399 moveto 384 /Symbol f1 (\346) show 1810 976 moveto (\350) show 1810 757 moveto (\347) show 2935 399 moveto (\366) show 2935 976 moveto (\370) show 2935 757 moveto (\367) show 3365 426 moveto 384 /Times-Italic f1 (y) show 3527 522 moveto 224 ns (i) show 3709 426 moveto 384 /Symbol f1 (-) show 4020 426 moveto 384 /Times-Italic f1 (y) show 4010 109 moveto 171 0 rlineto stroke 3624 958 moveto (s) show 3780 1054 moveto 224 ns (y) show 3323 566 moveto 890 0 rlineto stroke 3124 355 moveto 384 /Symbol f1 (\346) show 3124 1020 moveto (\350) show 3124 801 moveto (\347) show 4225 355 moveto (\366) show 4225 1020 moveto (\370) show 4225 801 moveto (\367) show 1361 752 moveto 576 ns (\345) show end ═©║dдMATH╦Я ┐r├=┬1┐n├-┬1┐x┐i ├-┐x┐s┐x √(√)┐y┐i ├-┐y┐s┐y √(√) ├Е m═█ЪЧЪЪЪЪЪнюFMicrosoft Equation 3.0ЧЪЪЪ1ELOCompObj ЪЪЪЪ'RObjInfoЪЪЪЪЪЪЪЪЪЪЪЪ)OlePres000 ЪЪЪЪ*(Ole10NativeЪЪЪЪЪЪЪЪ+╪Equation.3ЧЪЪЪЪЪЪЪ╦ ┐r├=┬1┐n├-┬1┐x┐i ├-┐x┐s┐x √(√)┐y┐i ├-┐y┐s┐y √(√) ├ЕEquation.3ЧЪ Ю┘÷РЫOh╚▒+'Ёы0■░Ole10FmtProgID ЪЪЪЪЪЪЪЪЪЪЪЪ.1TableЪЪЪЪ</ SummaryInformation(ЪЪЪЪ/дDocumentSummaryInformation8ЪЪЪЪЪЪЪЪЪЪЪЪ7@uш÷K║)▀╦√pWп▒Е═іт╩мМTКщ╙p Ч&X╒еРН╟Л√ю°ZPъc┴+ЬщхO[=iт≤ЮhP╣\q╔.│KьU0U╦юсEPc┬ZЕ"QїЫ╚╣У0Ly╙олг█y╨(┴└HЯЄV©ЦB-ф Ш1раъШ=iт≤K7╟8_2z©ЦHщ⌠Єfи,Eц{▒╦│Ю≈\k_ЮSPк╡Н┴,≥hxf%їWy╦4K`аuН└W`mIS═ы[Nуw╦р╗Яї0Т╟╣²┌Ж╠ao`W▓зW~√$Е═з?бпм%╦DЮIЗЙ┘QX =j┌0v┌*═Бtжf;Б}r⌠vмsб&w≈ВRn%р┴У~Р┘0╚Ё6р┴╧Хж%|╪)▐÷fаб9Д6Ы╙п~НєHRЛк║нn╞s╡!ўzxt░НT╧╘╩ЄнТ╟lsKЯЫ┴УЁф$oА╘п▌,≥Mh╦┼Xі©'pрхd'Lк┌ы▄STUрRА╪ёЮ┴═ч╛*≥k≤яюU▐▐▐YЭ@╛*°╠чЭ0▓Ї╧├ґзФюЄВФ^"ь╘ъL#У┬К╧3'2КAҐІW┐gм°і╨x65ўОд░ЬХlГО7ітЕ╛\юг~Ц╙ЁgёЫ©рэі8)zДЭ║╔<▀^Р·E╞╨╩╙┌M$■╟3{⌠╧е7cб!╟Ёе┐\j╙ІнЫпҐч$Н7]aЛёz█2с⌠4_М7цNсг┤дгЕт|⌡бCїvє1░м©AЩВгшмҐгу~>"≤тtJЙ⌡$O╟²[И╦ot5╗WJ⌠╟▐`⌡о'▄ff≈┼кЕqлэ&гЇlх┼┤КВWJXФcкЎg<·╦[≈ЯіЫv WwИn░5ЖЛ ь╡sX.·`КэЭ║≤еГефRўД=i÷я+▄╔▒rяД│╚{t ┘udПЎmqZ╟ЖHйWsпЙ╪Жь)яnё≈║╚Ys`ҐуIРтх;╧Я┘bЧіиДG+.bК╔щn÷`1нш║╣▐1ЦПZ3"у8o7≤&░Г■c▓ры,X z-Kк≈c▌[Лv!Q|j╠Ю'▓лОЖ║Й└b═У°╠зИJАўeбШzif╦nT+╗h╣²Pf{╡2М3VчОi▀їа╦(:}Ч> Х╡Ю;М╡н┼≤kCr}р┐Ть▄╔²▄шьцв,Я_[7=]Я#А:╘≈:^≤>мД6l6W6│fW e'ж&yuЗ°РєQcLґG!*q╒╞u■смВ▒GKaХr7п║! ╔оEїO3╪ыХ.RИK{ЁlbЄ?+w!*y─дУЄвоъИ·7╠°l_j≤W⌠Жыё╚▌ЮыАЦ≈ю╗┬R╧Шp4Ў?▀╗Hдp⌡<хЩ"▌⌡g┬(кw%QЭ█У0za~4рlЛ8┬+ЦД{`t}Ўй╞їMТпEp5ЪoL*і┼bя8ТБnъН2Х┘яs.C▒bk9ддГґыJY╘├г┼█ёы1[.з ╞Ц╧·╡`+Ї]WH≈VК├╪h$&іr-┼и╞┤╪≤┼е°нп·T5▐Єx▄RjR■ЙМIIc^чZЄGя}Ь$пF<ўРpфпY▌-л'ё╧бgQ_>╘kК▒╘ґGvб╨░┘&_'f≈ШGЬ╣■`э8Y┐┘DШш!`"s%▒└ЗA┼≤─g≤▐Цe║и^pФзАГКFpo°в≈\в9вЭHЇ2Е0Чwц{┘ВE.┘╡х^ЇЇя#╧zр╣ЩГ0хі╣Рxщч╔7J~╟2P⌠бпгэ(Тi╧Е·4ЙЭщХtюоЫЮЩШ▐RФЕ│П2Ґ╠=NдЇv┬\t!кt▀е╞;У}я∙.Цp╒ЬЛkжЮЕЄTгґbФHаЯPМ/VМм╘═ўХИJB≥юRnkAЦ+O:іw1Q╞ч²8┌Ш1o&Хс≤РT▓≥?и▌┴F)`yрк@ЩMК<фQ°ы∙ЛV≈─W│zq═║ЎAбИт°I<NРЙх&E{-ЪЬ*щщ(лpгv╟сi╘╔аds╨гM#?Т ОcU■ьsєівBfХўм▓5CЗЄTООk╡`я═]ф╧ё3А╩,RМIёфй²DДqЄ$ўКЦ╛'RЙ÷ax62Ы╧9В┬YЪ▄ЁЇ[+@┌└╨ҐИT▀#<^ЕxWDjAH**n,█╨з⌡І°Ш&Ц⌡▓Юа÷ЮFPЁ²Ьё>Ц>O?ъsбшЁБАy█R┬ї∙╦а≥ы=$ЧJt(6┘▀Iл0╛ ?`oжх-ъмNГE╨q"█Ь@PЁ═Neщ}▐x░╦│/│┐JАж╨$Ь>kўч┤.д:>NПOфc⌠+┘⌡ЦиKUx2╗4▐Ну╠ЇN0▐╞щщцGQ8≥5m©и°эVЇЦзЫПЧўt-╚╧░ыЙmNґOF|·>dщ'вU╨еi▓[ш÷3╘У═іs znш▐⌠щM·╠ЬF╚п7И)O1F╘_х┬`зДю©6²^VLn$]~#Я+1p╟3Т╣х7ь▄⌡%╒К'a& EЯf^ір┘Ї]ф╒Ы■;█O|Ц═^ZФбрш_ЬбpМР*щ:М╣(їp┐иshl:Кe√0:$╩о7З O╨ ╒Їu·4╨Ц)|-А;│кю.]=°4^Б⌡▌ъ⌡Vzдrв}a╒²░╚²}▌+<Гш┼ЁМ0Ї┤Хsй∙з─[╣╣ІHжdьF╛ут⌠+©Э5.iв2ъ=>xW ╚╗ю+√╚╞{3⌡█▓,f#▌▄─JSjґ▐Cs▌eD6e▌pті▌ю6▓nM╞Р0в░≥?n╣сkр²BуЕJдУM┼-ч╙╦║ЁуёeЎL~©┐~≈╨⌡EЇ1╠ф`zусИIёф≤▐rЮэ:ўф╩К├ъyМ.ЬтR мТ┌╨lN╣Z}@÷╒S/3║6tж▒9"xлЖ┴hK,я9+ИCМy "╧}0:_Ео╧,:_gмеиЙУ├4Аз-RУbЮй╟Р═ЄаZ\╡FСm, √≤4▌?╡zЕwЙa@xV╒┼6Ь▄zEQ1∙+1LІ╗AcSB┼3"[8#)4█⌡ІXY}2бP╔tР√ ?>K╡яq*A,]■:Є0FЖ÷╛fj>u┌hзХtХ╡НЖъdи^ёмМ░├F&e┴>в╡пДlc2% щ▀ Й1~50w■Сє$ЬЭ╛с· L5b2■ ЇBWB▓bо!fФ_6╙аXцоw?∙xО≈ўКИoЄдвеаuъ²ў]Ў%:\sЗS├кuМ^к≈ш╧ЗcТяМu²гДMP *Еw╨т])° fпфВ9Ы`&·xу7z▀kС÷8яїiпS⌡ ,(oІ╠Z<хс\Pзш8┤]╘с╪УуЇЦO≥jЎМIЦйejьНфґP╞╗≈_uK≤╩А)┌≥╠^Ў)╞язр4і%Б╨#┘n[Йт'G╒гVcЙS©√h╠а╒C·Бэ8RбV⌠О┤d?г█┌yeм╪ЛХ┘(²≥fвЎ╒╦А┴mc▄T#И)cО░╚/P<t0√ўьВ;│▀|ёк@ҐLЕ6GлI/ЭЫK@ҐмО4хДl⌠;о≥к┴ДL ЁЩ*]9ХжcE©kтй5Ґ2 c1─zs\БD wB~:╞≈Er&┘xc╧~}IrGЫЬ лМй┬`Ш~ K29a%gvM`н╡[Р²Нц2Ўr_пщ║ўd ъ╠БзVэ┐Жх[mw╧ы╟тЬbї√╩J╣│┌╣ЮFС├r∙'Ґтґ║о╙\)■-╛%гїРі3Ї│DЇ┌r0ЇС╚ЯВА ·Y╩├ю.5╧ W░▄в┐ X{╔N}╛3ЕF║Лxyyє\п:ВaSы╗>йу/ЎlУи%Ч{lKк╩∙З:сF╘с╣щ^╠╛╡Бz4 ©ы┘╛,>Ё▄▓╒ *пtПь ² └Ї─ [ёҐH?Nґrё║чIЇ1K&f╠╟ф,ЗyрўJUфA{⌠Ыo╚хє-ЇNZ2ь с⌠■J°ЎЩъХFcC©*TbҐОQъ(ҐЁY·jV▐їFъh╗)УТ`Ъйи|·╘5█фчm0У]avЗКь@HБRф%лМП nEeN%/ЦИ²≤┤|┌≤┐иЗ&цb0ДцT÷єєЪ8Fї═рж'эДAnжсI╧Y╘╚Ё-ЗНW9≤І,eсQ╩PІJ;╧u╔HІZ[╦цxт∙з≥"шїДЙSzj▐.о2Х╣n&ЫиП▀]VЇх÷PЧч9╚&;f▐К^≈{жтҐZ√n┼ИEЙPЦпTw≤Нpл[(?Ь─Аи╙і▐ ■Ьq]│МРV-Ж%Б╨├:Х╠~73;в.щzgмЁ8зj╛≤WOо≥и╒8 3+цМ k╦Асйm8%ЇОс╣ЗqЛо╛pB*)Ом²└ё╔p┘^1tGr ё┬)IО}╒@уn▐qчнЁыЧ∙ьцЫoюKfO^СЬяІ4²є╨э≥Z^чЦ┬ыЖї╛┬≥ґЫ°╦╡#Є╘k▀■^шSRбіі└▒╨!▐_ыkKжHс┼mЪW}И┘J┼<д╣ t─)1╘є╦vз÷╡"fv3Мzo╔4Рx■·─│╘├~mІЩ)╙a6ъ"≈tjpD'·b²>]9╙╣@Л║эЖК<сГї!IT©ИgаЩЮ Ч%!,≤╦дЮЛЭ ( DP\ ht|└▄'MATH 115 ACTIVITY 1:1ATHCharles F. Peltier1harNormal Information Technology13foMicrosoft Word 10.1@▄├G@bБU÷Цб@°4Бvе@(╩)wе▀ХЧЪ уму°.⌠≈+,Ыў0hp░≤═╗╟╦юх пР'Saint Mary's CollegeVI7 п MATH 115 ACTIVITY 1:Title if@ЯЪfNormal; ф&п═p@Ю╟─P Пю!└п└0Щ^└п`└0ЩOJQJmH <A@РЪ║<Default Paragraph Font*ЧР*toa heading.Ч.def└h└^└h`└CJ6Ч6discuss└h└^└h`└CJ&ЧO"&section5│6Ч26 form title$a$5│CJ$*ЧOB*why└═└`З^└═`└`ЗуH,HЪЪ<╛≥ЪЪ<╛≥ЪЪ<╛≥ЪЪ<╛≥ЪЪ<╛≥77┤uуш ,YЬу%#░ IГу% !"у%▀╟╡у:■Ъ∙─вЪЪCharles Peltier8Macintosh HD:Documents:M116S03:Activities:116ACT6S03.doc c peltierSMacintosh HD:Users:charlesp:Current semester docs:M116S03:Activities:116ACT6S03.docInformation TechnologyXMacintosh HD:Users:cpeltier:Documents:Current Semester:M251S04:Activities:116ACT6S04.docInformation Technology;Macintosh HD:Users:cpeltier:AutoRecovery save of 116ACT6S04Information Technology`Macintosh HD:Users:cpeltier:Documents:Course Archives:M115-116:M116S04:Activities:116ACT6S04.docInformation TechnologyMMacintosh HD:Users:cpeltier:Documents:Current Semester:M116S05:116ACT6S04.docInformation TechnologyXMacintosh HD:Users:cpeltier:Documents:Current Semester:M116S05:Activities:116ACT6S05.docInformation TechnologyXMacintosh HD:Users:cpeltier:Documents:Current Semester:M116S05:Activities:116ACT6S05.docвЪ@─┬<Хhуp@G░Times New Roman5░─Symbol3░Arial9░New York а─УпІ ⌠F╦ ⌠F0s├▀Х ┐7!─У;└пуФ─У;└ъЪЪMATH 115 ACTIVITY 1:Charles F. PeltierInformation TechnologyЧЪЪЪЪЪ юFMicrosoft Word DocumentЧЪЪЪNB6WWord.Document.8CompObjЪЪЪЪЪЪЪЪЪЪЪЪqXЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪЪ