The sum of a number times three and 16 is at most
[PDF File]2.1 Sample Space - University of Minnesota Duluth
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Any probability is a number between 0 and 1. For any event A, 0 P(A) 1 It is trivial to see that P(f)=0 and P(S)=1 Ways to assign the probabilities If the sample space S consists of a nite (or countable in nite) number of outcomes, assign a probability to each outcome. The sum of all probabilities equals to 1. X. Li 2015 Fall STAT-3611 Lecture ...
Math 20 { Inequalities of Markov and Chebyshev
ipped 100 times. Find a bound on the probability that the number of times the coin lands on heads is at least 60 or at most 40. Let Xbe the number of times the coin lands on heads. We know Xhas a binomial distri-bution with expected value 50 and variance 100 0:5 0:5 = 25. By Chebyshev, we have P(X60) = P(jX j 10) 25 102 = 1 4:
[PDF File]Translating English Words Into Algebraic Expressions
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Five is three more than a number 5 = x + 3 The product of 2 times a number is 10 2x = 10 One half a number is 10 x/2 = 10 Five times the sum of x and 2 5(x + 2) Seven is greater than x 7 > x Five times the difference of a number and 4 5(x - 4) Ten subtracted from 10 times a number is that number plus 5 10x - 10 = x + 5 The sum of 5x and 10 is ...
[PDF File]Lesson 5: Writing and Solving Linear Equations
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1. A pair of congruent angles are described as follows: the measure of one angle is three more than twice a number and the other angle’s measure is . less than three times the number. Determine the size of the angles. Let š be the number.
[PDF File]Unit-3 Data Handling - NCERT
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In Questions 1 to 16, there are four options, out of which only one is correct. Write the correct answer. 1. Let x, y, z be three observations. The mean of these observations is (a) ×× 3 x yz (b) ++ 3 x yz (c) −− 3 x yz (d) ×+ 3 xy z 2. The number of trees in different parks of a city are 33, 38, 48, 33, 34, 34, 33 and 24. The mode of ...
[PDF File]Mid-Chapter Quiz Translate each sentence into an equation.
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The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. three times a number a plus four equals five times a number a 3a + 4 = 5a The equation is 3a + 4 = 5a. One fourth of m minus six is equal to two times the sum of m and 9. 62/87,21
[PDF File]Individual Contest Solution
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total is 4×16 = 64. 3. The sum of ļ¬ve consecutive positive integers is the cube of an integer and the sum of the middle three numbers is the square of an integer. Find the smallest possible value of the middle number. Solution: The sum of ļ¬ve consecutive numbers is equal to 5 times the middle number and the sum of three consecutive numbers ...
[PDF File]1 Translating to algebra - City University of New York
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(d) Three times the sum of a number and six equals the diļ¬erence of the number and eight. Answer. 3x+18 = x−8, where xstands for the unknown number. (e) The sum of twice a number and twenty is smaller than three times the number plus seven. Answer. 2x+20
[PDF File]2%2D1 Writing Equations
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Three times r less than 15 equals 6 is the same as 15 minus 3 times r equals 6 . The equation is 15 ± 3r = 6. 15 minus 3 times r equals 6 15 ± 3 r = 6 The sum of q and four times t is equal to 29. 62/87,21 Rewrite the verbal sentence so it is easier to translate. T he sum of q and four times t is equal to 29 is the same as
[PDF File]Multiple Choice Questions forReview
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4. The number of four letter words that can be formed from the letters in BUBBLE (each letter occurring at most as many times as it occurs in BUBBLE) is (a) 72 (b) 74 (c) 76 (d) 78 (e) 80 5. The number of ways to seat 3 boys and 2 girls in a row if each boy must sit next to at least one girl is (a) 36 (b) 48 (c) 148 (d) 184 (e) 248 6.
[PDF File]1. The sum of a certain number and a second number is 42 ...
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The sum of a certain number and a second number is 42. The first ... She invested three times as much money in an account that paid 8% interest as in an account that paid ... Because he enjoys roller coasters the most, the number of times he rode the roller coasters was the sum of the times he rode the other two rides. If ...
[PDF File]A Collection of Dice Problems - mad and moonly
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16.How many dice must be rolled to have at least a 95% chance of rolling a one and a two? What about a one, a two, and a three? What about a one, a two, a three, a four, a ļ¬ve and a six? 17.How many dice should be rolled to maximize the probability of rolling exactly one six? two sixes? n sixes? 18.Suppose we roll a fair die 100 times.
[PDF File]TRANSLATING KEY WORDS AND PHRASES INTO ALGEBRAIC EXPRESSIONS
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“x” is used to represent the unknown. In translation problems, the words sum, total, difference, product and quotient imply at least two parts – use parentheses when a sum or difference is multiplied. For example, the phrase "the sum of three times a number and five" translates to "3x + 5," while the phrase "three times the sum of a ...
[PDF File]TRANSLATE WORD SENTENCES INTO ALGEBRAIC EXPRESSIONS
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9) The product of two numbers, if one number is one less than x(2x - 1) twice the other number. 10) If seven times a number is reduced by nine, the result is ten 7x - 9 = x -10 less than the number. 11) The product of the sum and difference of two numbers. (x + y)(x - y) 12) The sum of three consecutive integers is 126.
[PDF File]Math Definitions: Introduction to Numbers
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To cube a number is to multiply it by itself three times. A number x cubed is written x3. Cubing a number means to raise it to the third power. 2 cubed is 8, since 2•2•2 = 8. Root rd: The root of x is a number that when multiplied by itself a number of times will result in x. The number of times is the degree of the root.
[PDF File]Name: Unit3 #2 Writing Expressions and Equations
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2 multiplied by a number 2 times a number 2n The quotient of z and 3 A number divided by 3 The ratio of z and 3 Practice: Underline key words. Write each phrase as an algebraic expression or equation. 11. Seven less than a number is 15 n – 7 = 15 12. The total of 5 and c 5 + c 13. 7 less than m m – 7 14. The sum of a number and 16 is 23 n ...
[PDF File]3 Sums and Integrals - University of Pennsylvania
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Series you can explicitly sum We will learn to sum three kinds of series: arithmetic (accent on the third syllable) ... pair sums to twice the average and therefore that the sum is the number of terms times the average term. Here is an example in a particular case and then the general ... partition of the x-axis into 16 equal strips.
[PDF File]Write an algebraic expression to represent
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$16:(5 The sum of five times a number and 7 equals 18. $16:(5 The difference between the square of a number and 9 is 27. $16:(5 The difference between five times a number and the cube of that number is 12. $16:(5 Eight more than the quotient of a number and four is ±16. Name the property illustrated by each statement. $16:(5 Reflexive Property
[PDF File]PERFECT NUMBERS: AN ELEMENTARY INTRODUCTION
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The number 6 is unique in that 6 = 1+2+3, where 1, 2, and 3 are all of the proper divisors of 6. The number 28 also shares this property, for 28 = 1+2+4+7+14. These “perfect” numbers have seen a great deal of mathematical study—indeed, many of the basic theorems of number theory stem from the investigation of the
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