College Algebra Essentials
College Algebra Essentials
1st Edition
ISBN: 9780078035616
Author: Julie Miller
Publisher: MCG
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Concept explainers

Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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Chapter R.2, Problem 4PE

For Exercises 3-4, write an absolute value expression to represent the distance between the two points on the number line. Then simplify the expression without absolute value bars.

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Chapter R Solutions

College Algebra Essentials

Ch. R.1 - Practice Exercises Concept Connections A ________...Ch. R.1 - Practice Exercises Concept Connections = {0, 1, 2,...Ch. R.1 - Practice Exercises Concept Connections N = {1, 2,...Ch. R.1 - Practice Exercises Concept Connections Z = {...,...Ch. R.1 - Practice Exercises Concept Connections A set can...Ch. R.1 - Prob. 6PECh. R.1 - Prob. 7PECh. R.1 - Prob. 8PECh. R.1 - Practice Exercises Concept Connections The...Ch. R.1 - Practice Exercises Concept Connections The...
Ch. R.1 - Prob. 11PECh. R.1 - Prob. 12PECh. R.1 - Practice Exercises Concept Connections The symbol...Ch. R.1 - Practice Exercises Concept Connections The...Ch. R.1 - Prob. 15PECh. R.1 - Prob. 16PECh. R.1 - Objective 1: Identify Subsets of the Set of Real...Ch. R.1 - Objective 1: Identify Subsets of the Set of Real...Ch. R.1 - Prob. 19PECh. R.1 - Prob. 20PECh. R.1 - Prob. 21PECh. R.1 - Prob. 22PECh. R.1 - Prob. 23PECh. R.1 - Prob. 24PECh. R.1 - Prob. 25PECh. R.1 - Prob. 26PECh. R.1 - Prob. 27PECh. R.1 - Prob. 28PECh. R.1 - Prob. 29PECh. R.1 - Prob. 30PECh. R.1 - Prob. 31PECh. R.1 - Prob. 32PECh. R.1 - Prob. 33PECh. R.1 - Prob. 34PECh. R.1 - Prob. 35PECh. R.1 - Prob. 36PECh. R.1 - Prob. 37PECh. R.1 - Prob. 38PECh. R.1 - Prob. 39PECh. R.1 - Prob. 40PECh. R.1 - Prob. 41PECh. R.1 - Prob. 42PECh. R.1 - Prob. 43PECh. R.1 - Prob. 44PECh. R.1 - Objective 2: Use Inequality Symbols and Interval...Ch. R.1 - Prob. 46PECh. R.1 - Prob. 47PECh. R.1 - Prob. 48PECh. R.1 - Prob. 49PECh. 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R.1 - Prob. 142PECh. R.1 - Prob. 143PECh. R.1 - Prob. 144PECh. R.1 - Prob. 145PECh. R.2 - For Exercises 1-2, write the interval notation and...Ch. R.2 - For Exercises 1-2, write the interval notation and...Ch. R.2 - For Exercises 3-4, write an absolute value...Ch. R.2 - For Exercises 3-4, write an absolute value...Ch. R.2 - For Exercises 5-8, determine whether the statement...Ch. R.2 - For Exercises 5-8, determine whether the statement...Ch. R.2 - For Exercises 5-8, determine whether the statement...Ch. R.2 - For Exercises 5-8, determine whether the statement...Ch. R.2 - For Exercises 9-10, simplify. 12(99)2(2)37+1Ch. R.2 - For Exercises 9-10, simplify. 10282(164)2Ch. R.2 - One type of mathematical model is a formula that...Ch. R.2 - Model _______ is a term used to describe a...Ch. R.2 - A _____ is a product of factors that may include...Ch. R.2 - The numerical _________ of a term is the constant...Ch. R.2 - The _______ properties of addition and...Ch. R.2 - The sum of a number and its additive inverse is...Ch. R.2 - The number _______ is the identity element of...Ch. R.2 - Zero is the _______ element of addition.Ch. R.2 - The additive inverse of a real number x is ______.Ch. R.2 - The statement a(b + c) = ab + ac represents the...Ch. R.2 - The multiplicative inverse of a nonzero real...Ch. R.2 - The ________ property of addition indicates that a...Ch. R.2 - The associative property of multiplication...Ch. R.2 - The number _________ is the only real number that...Ch. R.2 - Gas mileage depends in part on the speed of the...Ch. R.2 - The bacterium Pseudomonas aeruginosa is cultured...Ch. R.2 - Data from the Bureau of Labor Statistics Consumer...Ch. R.2 - Selena started a new diet and exercise program,...Ch. R.2 - The temperature at noon in Orlando, Florida, in...Ch. R.2 - Scientists often use the Kelvin scale to measure...Ch. R.2 - The retail price P for a sofa is the sum of the...Ch. R.2 - The sale price S for a tractor is the difference...Ch. R.2 - Jake is 1 yr younger than Charlotte. a. Write a...Ch. R.2 - For a recent NFL season, Aaron Rogers had 9 more...Ch. R.2 - At the end of the summer, a home store discounts...Ch. R.2 - When Ms. Tibbets has excellent service at a...Ch. R.2 - Suppose that an object is dropped from a height h....Ch. R.2 - The height of a sunflower plant can be determined...Ch. R.2 - A power company charges one household $0.12 per...Ch. R.2 - A utility company charges a base rate for water...Ch. R.2 - The cost C (in $) to rent an apartment is $640 per...Ch. R.2 - For a certain college, the cost C (in $) for...Ch. R.2 - A hotel charges $159 per night plus an 11% nightly...Ch. R.2 - A hotel charges $149 per night plus a 16% nightly...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 45-50, list the terms and...Ch. R.2 - For Exercises 51-56, apply the commutative...Ch. R.2 - For Exercises 51-56, apply the commutative...Ch. R.2 - For Exercises 51-56, apply the commutative...Ch. R.2 - For Exercises 51-56, apply the commutative...Ch. R.2 - For Exercises 51-56, apply the commutative...Ch. R.2 - For Exercises 5156, apply the commutative property...Ch. R.2 - For Exercises 5760, apply the associative property...Ch. R.2 - For Exercises 5760, apply the associative property...Ch. R.2 - For Exercises 5760, apply the associative property...Ch. R.2 - For Exercises 5760, apply the associative property...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6168, (a) identify the additive...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 6974, combine like terms. (See...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 7582, apply the distributive...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 8390, simplify each expression. (See...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - For Exercises 9196, evaluate each expression for...Ch. R.2 - The width of a rectangle is 3 ft less than twice...Ch. R.2 - The longest side of a triangle is 5 ft less than...Ch. 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R.4 - Prob. 88PECh. R.4 - Prob. 89PECh. R.4 - Prob. 90PECh. R.4 - Prob. 91PECh. R.4 - Prob. 92PECh. R.4 - Prob. 93PECh. R.4 - Prob. 94PECh. R.4 - Prob. 95PECh. R.4 - Prob. 96PECh. R.4 - Prob. 97PECh. R.4 - Prob. 98PECh. R.4 - Prob. 99PECh. R.4 - Prob. 100PECh. R.4 - Prob. 101PECh. R.4 - Prob. 102PECh. R.4 - Prob. 103PECh. R.4 - Prob. 104PECh. R.4 - Prob. 105PECh. R.4 - Prob. 106PECh. R.4 - Prob. 107PECh. R.4 - Prob. 108PECh. R.4 - Prob. 109PECh. R.4 - Prob. 110PECh. R.4 - The size of a television is identified by the...Ch. R.4 - If the span of a roof is 36 ft and the rise is 12...Ch. R.4 - Prob. 113PECh. R.4 - Prob. 114PECh. R.4 - Prob. 115PECh. R.4 - Prob. 116PECh. R.4 - Prob. 117PECh. R.4 - Prob. 118PECh. R.4 - Prob. 119PECh. R.4 - Prob. 120PECh. R.4 - Prob. 121PECh. R.4 - Prob. 122PECh. R.4 - Prob. 123PECh. R.4 - Prob. 124PECh. R.4 - Prob. 125PECh. R.4 - Prob. 126PECh. R.4 - Prob. 127PECh. R.4 - Prob. 128PECh. R.5 - Prob. 1PECh. R.5 - Prob. 2PECh. R.5 - Prob. 3PECh. 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R.5 - Prob. 54PECh. R.5 - Prob. 55PECh. R.5 - Prob. 56PECh. R.5 - The total national expenditure for health care has...Ch. R.5 - Prob. 58PECh. R.5 - Prob. 59PECh. R.5 - Prob. 60PECh. R.5 - Prob. 61PECh. R.5 - Prob. 62PECh. R.5 - Prob. 63PECh. R.5 - Prob. 64PECh. R.5 - Prob. 65PECh. R.5 - Prob. 66PECh. R.5 - Prob. 67PECh. R.5 - Prob. 68PECh. R.5 - Suppose that x represents the smaller of two...Ch. R.5 - Prob. 70PECh. R.5 - Prob. 71PECh. R.5 - Prob. 72PECh. R.5 - Prob. 73PECh. R.5 - Prob. 74PECh. R.5 - Prob. 75PECh. R.5 - Prob. 76PECh. R.5 - Prob. 77PECh. R.5 - Prob. 78PECh. R.5 - Prob. 79PECh. R.5 - Prob. 80PECh. R.5 - Prob. 81PECh. R.5 - Prob. 82PECh. R.5 - Prob. 83PECh. R.5 - Prob. 84PECh. R.5 - Prob. 85PECh. R.5 - Prob. 86PECh. R.5 - Prob. 87PECh. R.5 - Prob. 88PECh. R.5 - Prob. 89PECh. R.5 - Prob. 90PECh. R.5 - Prob. 91PECh. R.5 - Prob. 92PECh. R.5 - Prob. 93PECh. R.5 - Prob. 94PECh. R.5 - Prob. 95PECh. R.5 - Prob. 96PECh. R.5 - Prob. 97PECh. R.5 - Prob. 98PECh. R.5 - Prob. 99PECh. R.5 - Prob. 100PECh. R.5 - Prob. 101PECh. R.5 - Prob. 102PECh. R.5 - Prob. 103PECh. R.5 - Prob. 104PECh. R.5 - Prob. 105PECh. R.5 - Prob. 106PECh. R.5 - Prob. 107PECh. R.5 - Prob. 108PECh. R.5 - Prob. 109PECh. R.5 - Prob. 110PECh. R.5 - Prob. 111PECh. R.5 - Prob. 112PECh. R.5 - Prob. 113PECh. R.5 - Prob. 114PECh. R.5 - Prob. 115PECh. R.5 - Prob. 116PECh. R.5 - Prob. 1PRECh. R.5 - Prob. 2PRECh. R.5 - Prob. 3PRECh. R.5 - Prob. 4PRECh. R.5 - Prob. 5PRECh. R.5 - Prob. 6PRECh. R.5 - Prob. 7PRECh. R.5 - Prob. 8PRECh. R.5 - Prob. 9PRECh. R.5 - Prob. 10PRECh. R.5 - Prob. 11PRECh. R.5 - Prob. 12PRECh. R.5 - Prob. 13PRECh. R.5 - Prob. 14PRECh. R.6 - Prob. 1PECh. R.6 - Prob. 2PECh. R.6 - Prob. 3PECh. R.6 - Prob. 4PECh. R.6 - Prob. 5PECh. R.6 - Prob. 6PECh. R.6 - Prob. 7PECh. R.6 - Prob. 8PECh. R.6 - Prob. 9PECh. R.6 - Prob. 10PECh. R.6 - Prob. 11PECh. R.6 - Prob. 12PECh. R.6 - Prob. 13PECh. R.6 - Prob. 14PECh. R.6 - Prob. 15PECh. R.6 - Prob. 16PECh. R.6 - Prob. 17PECh. R.6 - Prob. 18PECh. R.6 - Prob. 19PECh. R.6 - Prob. 20PECh. R.6 - Prob. 21PECh. R.6 - Prob. 22PECh. R.6 - Prob. 23PECh. R.6 - Prob. 24PECh. R.6 - Prob. 25PECh. R.6 - Prob. 26PECh. R.6 - Prob. 27PECh. R.6 - Prob. 28PECh. R.6 - Prob. 29PECh. R.6 - Prob. 30PECh. R.6 - Prob. 31PECh. R.6 - Prob. 32PECh. R.6 - Prob. 33PECh. R.6 - Prob. 34PECh. R.6 - Prob. 35PECh. R.6 - Prob. 36PECh. R.6 - Prob. 37PECh. R.6 - Prob. 38PECh. R.6 - Prob. 39PECh. R.6 - Prob. 40PECh. R.6 - Prob. 41PECh. R.6 - Prob. 42PECh. R.6 - Prob. 43PECh. R.6 - For Exercises 3144, factor the trinomials. (See...Ch. R.6 - Prob. 45PECh. R.6 - Prob. 46PECh. R.6 - Prob. 47PECh. R.6 - Prob. 48PECh. R.6 - Prob. 49PECh. R.6 - Prob. 50PECh. R.6 - Prob. 51PECh. R.6 - Prob. 52PECh. R.6 - Prob. 53PECh. R.6 - Prob. 54PECh. R.6 - Prob. 55PECh. R.6 - Prob. 56PECh. R.6 - Prob. 57PECh. R.6 - Prob. 58PECh. R.6 - Prob. 59PECh. R.6 - Prob. 60PECh. R.6 - Prob. 61PECh. R.6 - Prob. 62PECh. R.6 - Prob. 63PECh. R.6 - Prob. 64PECh. R.6 - Prob. 65PECh. R.6 - Prob. 66PECh. R.6 - Prob. 67PECh. R.6 - Prob. 68PECh. R.6 - Prob. 69PECh. R.6 - Prob. 70PECh. R.6 - Prob. 71PECh. R.6 - Prob. 72PECh. R.6 - Prob. 73PECh. R.6 - Prob. 74PECh. R.6 - Prob. 75PECh. R.6 - Prob. 76PECh. R.6 - Prob. 77PECh. R.6 - Prob. 78PECh. R.6 - Prob. 79PECh. R.6 - Prob. 80PECh. R.6 - Prob. 81PECh. R.6 - Prob. 82PECh. R.6 - Prob. 83PECh. R.6 - Prob. 84PECh. R.6 - Prob. 85PECh. R.6 - Prob. 86PECh. R.6 - Prob. 87PECh. R.6 - Prob. 88PECh. R.6 - Prob. 89PECh. R.6 - Prob. 90PECh. R.6 - Prob. 91PECh. R.6 - Prob. 92PECh. R.6 - Prob. 93PECh. R.6 - Prob. 94PECh. R.6 - Prob. 95PECh. R.6 - Prob. 96PECh. R.6 - Prob. 97PECh. R.6 - Prob. 98PECh. R.6 - Prob. 99PECh. R.6 - Prob. 100PECh. R.6 - Prob. 101PECh. R.6 - Prob. 102PECh. R.6 - Prob. 103PECh. R.6 - Prob. 104PECh. R.6 - Prob. 105PECh. R.6 - Prob. 106PECh. R.6 - Prob. 107PECh. R.6 - Prob. 108PECh. R.6 - Prob. 109PECh. R.6 - Prob. 110PECh. R.6 - Prob. 111PECh. R.6 - Prob. 112PECh. R.6 - Prob. 113PECh. R.6 - Prob. 114PECh. R.6 - Prob. 115PECh. R.6 - Prob. 116PECh. R.6 - Prob. 117PECh. R.6 - Prob. 118PECh. R.6 - Prob. 119PECh. R.6 - Prob. 120PECh. R.7 - For Exercises 18, factor completely. 30x365x225xCh. R.7 - Prob. 2PECh. R.7 - Prob. 3PECh. R.7 - Prob. 4PECh. R.7 - Prob. 5PECh. R.7 - Prob. 6PECh. R.7 - Prob. 7PECh. R.7 - Prob. 8PECh. R.7 - Prob. 9PECh. R.7 - Prob. 10PECh. R.7 - Prob. 11PECh. R.7 - Prob. 12PECh. R.7 - Prob. 13PECh. R.7 - Prob. 14PECh. R.7 - Prob. 15PECh. R.7 - Prob. 16PECh. R.7 - Prob. 17PECh. R.7 - Prob. 18PECh. R.7 - Prob. 19PECh. R.7 - Prob. 20PECh. R.7 - Prob. 21PECh. R.7 - Prob. 22PECh. R.7 - Prob. 23PECh. R.7 - Prob. 24PECh. R.7 - Prob. 25PECh. R.7 - Prob. 26PECh. R.7 - Prob. 27PECh. R.7 - Prob. 28PECh. R.7 - Prob. 29PECh. R.7 - Prob. 30PECh. R.7 - Prob. 31PECh. R.7 - Prob. 32PECh. R.7 - Prob. 33PECh. R.7 - Prob. 34PECh. R.7 - Prob. 35PECh. R.7 - Prob. 36PECh. R.7 - Prob. 37PECh. R.7 - Prob. 38PECh. R.7 - Prob. 39PECh. R.7 - Prob. 40PECh. R.7 - Prob. 41PECh. R.7 - Prob. 42PECh. R.7 - Prob. 43PECh. R.7 - Prob. 44PECh. R.7 - Prob. 45PECh. R.7 - Prob. 46PECh. R.7 - Prob. 47PECh. R.7 - Prob. 48PECh. R.7 - Prob. 49PECh. R.7 - Prob. 50PECh. R.7 - Prob. 51PECh. R.7 - Prob. 52PECh. R.7 - Prob. 53PECh. R.7 - Prob. 54PECh. R.7 - Prob. 55PECh. R.7 - Prob. 56PECh. R.7 - Prob. 57PECh. R.7 - Prob. 58PECh. R.7 - Prob. 59PECh. R.7 - Prob. 60PECh. R.7 - Prob. 61PECh. R.7 - Prob. 62PECh. R.7 - Prob. 63PECh. R.7 - Prob. 64PECh. R.7 - Prob. 65PECh. R.7 - Prob. 66PECh. R.7 - Prob. 67PECh. R.7 - Prob. 68PECh. R.7 - Prob. 69PECh. R.7 - Prob. 70PECh. R.7 - Prob. 71PECh. R.7 - Prob. 72PECh. R.7 - Prob. 73PECh. R.7 - Prob. 74PECh. R.7 - Prob. 75PECh. R.7 - Prob. 76PECh. R.7 - Prob. 77PECh. R.7 - Prob. 78PECh. R.7 - Prob. 79PECh. R.7 - Prob. 80PECh. R.7 - Prob. 81PECh. R.7 - Prob. 82PECh. R.7 - Prob. 83PECh. R.7 - Prob. 84PECh. R.7 - Prob. 85PECh. R.7 - Prob. 86PECh. R.7 - Prob. 87PECh. R.7 - Prob. 88PECh. R.7 - Prob. 89PECh. R.7 - Prob. 90PECh. R.7 - Prob. 91PECh. R.7 - Prob. 92PECh. R.7 - The concentration C (in ng/mL) of a drug in the...Ch. R.7 - An object that is originally 35C is placed in a...Ch. R.7 - Prob. 95PECh. R.7 - Prob. 96PECh. R.7 - Prob. 97PECh. R.7 - Prob. 98PECh. R.7 - Prob. 99PECh. R.7 - Prob. 100PECh. R.7 - Prob. 101PECh. R.7 - Prob. 102PECh. R.7 - Prob. 103PECh. R.7 - Prob. 104PECh. R.7 - Prob. 105PECh. R.7 - Prob. 106PECh. R.7 - Prob. 107PECh. R.7 - Prob. 108PECh. R.7 - Prob. 109PECh. R.7 - Prob. 110PECh. R.7 - Prob. 111PECh. R.7 - Prob. 112PECh. R.7 - Prob. 113PECh. R.7 - Prob. 114PECh. R.7 - Prob. 115PECh. R.7 - Prob. 116PECh. R.7 - Prob. 117PECh. R.7 - Prob. 118PECh. R.7 - Prob. 119PECh. R.7 - Prob. 120PECh. R.7 - Prob. 121PECh. R.7 - Prob. 122PECh. R.7 - Prob. 123PECh. R.7 - Prob. 124PECh. R.7 - Prob. 125PECh. R.7 - Prob. 126PECh. R.7 - Prob. 127PECh. R.7 - Prob. 128PECh. R.7 - Prob. 129PECh. R.7 - Prob. 130PECh. R.7 - Prob. 131PECh. R.7 - Prob. 132PECh. R.7 - Prob. 133PECh. R.7 - Prob. 134PECh. R - Prob. 1RECh. R - Prob. 2RECh. R - Prob. 3RECh. R - Prob. 4RECh. R - Prob. 5RECh. R - Prob. 6RECh. R - Prob. 7RECh. R - Prob. 8RECh. R - Prob. 9RECh. R - Prob. 10RECh. R - Prob. 11RECh. R - Prob. 12RECh. R - Prob. 13RECh. R - Prob. 14RECh. R - Prob. 15RECh. R - Prob. 16RECh. R - Prob. 17RECh. R - Prob. 18RECh. R - Prob. 19RECh. R - Prob. 20RECh. R - Prob. 21RECh. R - Prob. 22RECh. R - Prob. 23RECh. R - Prob. 24RECh. R - Prob. 25RECh. R - Prob. 26RECh. R - Prob. 27RECh. R - Prob. 28RECh. R - Prob. 29RECh. R - Prob. 30RECh. R - Prob. 31RECh. R - Prob. 32RECh. R - Prob. 33RECh. R - Prob. 34RECh. R - Prob. 35RECh. R - Prob. 36RECh. R - Prob. 37RECh. R - Prob. 38RECh. R - Prob. 39RECh. R - Prob. 40RECh. R - Prob. 41RECh. R - Prob. 42RECh. R - Prob. 43RECh. R - Prob. 44RECh. R - Prob. 45RECh. R - Prob. 46RECh. R - Prob. 47RECh. R - Prob. 48RECh. R - Prob. 49RECh. R - Prob. 50RECh. R - Prob. 51RECh. R - Prob. 52RECh. R - Prob. 53RECh. R - Prob. 54RECh. R - Prob. 55RECh. R - Prob. 56RECh. R - Prob. 57RECh. R - Prob. 58RECh. R - Prob. 59RECh. R - Prob. 60RECh. R - Prob. 61RECh. R - Prob. 62RECh. R - Prob. 63RECh. R - Prob. 64RECh. R - Prob. 65RECh. R - Prob. 66RECh. R - Prob. 67RECh. R - Prob. 68RECh. R - Prob. 69RECh. R - Prob. 70RECh. R - Prob. 71RECh. R - Prob. 72RECh. R - Prob. 73RECh. R - Prob. 74RECh. R - Prob. 75RECh. R - Prob. 76RECh. R - Prob. 77RECh. R - Prob. 78RECh. R - Prob. 79RECh. R - Prob. 80RECh. R - Prob. 81RECh. R - Prob. 82RECh. R - Prob. 83RECh. R - Prob. 84RECh. R - Prob. 85RECh. R - Prob. 86RECh. R - Prob. 87RECh. R - Prob. 88RECh. R - Prob. 89RECh. R - Prob. 90RECh. R - Prob. 91RECh. R - Prob. 92RECh. R - Prob. 93RECh. R - Prob. 94RECh. R - Prob. 95RECh. R - Prob. 96RECh. R - Prob. 97RECh. R - Prob. 98RECh. R - Prob. 99RECh. R - Prob. 100RECh. R - Prob. 101RECh. R - Prob. 102RECh. R - Prob. 103RECh. R - Prob. 104RECh. R - Prob. 105RECh. R - Prob. 106RECh. R - Prob. 107RECh. R - Prob. 108RECh. R - Prob. 109RECh. R - Prob. 110RECh. R - Prob. 111RECh. R - Prob. 112RECh. R - Prob. 1TCh. R - Prob. 2TCh. R - Prob. 3TCh. R - Prob. 4TCh. R - Prob. 5TCh. R - Prob. 6TCh. R - Prob. 7TCh. R - Prob. 8TCh. R - Prob. 9TCh. R - Prob. 10TCh. R - Prob. 11TCh. R - Prob. 12TCh. R - Prob. 13TCh. R - Prob. 14TCh. R - Prob. 15TCh. R - Prob. 16TCh. R - Prob. 17TCh. R - Prob. 18TCh. R - Prob. 19TCh. R - Prob. 20TCh. R - Prob. 21TCh. R - Prob. 22TCh. R - Prob. 23TCh. R - Prob. 24TCh. R - Prob. 25TCh. R - Prob. 26TCh. R - Prob. 27TCh. R - Prob. 28TCh. R - Prob. 29TCh. R - Prob. 30TCh. R - Prob. 31TCh. R - Prob. 32TCh. R - Prob. 33TCh. R - Prob. 34TCh. R - Prob. 35TCh. R - Prob. 36TCh. R - Prob. 37TCh. R - Prob. 38TCh. R - Prob. 39TCh. R - Prob. 40TCh. R - Prob. 41TCh. R - Prob. 42T
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