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48. True Chapter 1 Real Numbers and Expressions 4. A finite set has a finite (countable) number of elements; an infinite set does not. ^` 52. False 54. True Exercise Set 1.1 2. 50. True is not empty because the set contains one 56. False 58. False 60. True element, the symbol . 62. False because 0 is neither positive nor negative. 6. Because the absolute value of 0 is 0, and 0 is neither positive nor negative. 64. 2.8 8. {a, e, i, o, u} 66. 1 1 4 10. {April, June, September, November} 68. 0 12. {Washington, Wyoming, West Virginia, Wisconsin} 70. 18 14. {2, 3, 5, 7} 16. {5, 10, 15,…} 18. ^ 2, 1, 0,1, 2` 22. ^ x x is a natural number` 24. ^ x x is a vowel of the English alphabet` 26. 28. 20. { } or ^ x x is a month` ^ x x is a natural-number multiple of 4` 30. 72. < 74. < 76. > 78. = 80. = 82. > 84. 4.7, 2.56, 5.4, 7 1 , 8.3 2 86. 1.3, 1, 0.05 , 0.4, π , 4 2 3 88. {2002, 2004, 2007} 32. 90. {2000, 2002, 2003, 2004, 2007} 92. {Musical, Anime, Westerns} 94. { } or 34. 96. {413, 497} 98. {Canada, Mexico, Saudi Arabia} 36. 38. True 40. False Exercise Set 1.2 2. The sum of 0 and a number is itself; the product of 1 and a number is itself. 4. Multiplicative inverses are two numbers that have a product of 1. 6. To add two numbers that have different signs, subtract the smaller absolute value from the greater 42. True 44. False 46. True 2 8. Chapter 1 Real Numbers and Expressions absolute value and keep the sign of the number with the greater absolute value. 64. When multiplying or dividing two numbers with different signs, the product or quotient is negative. 66. 13 10. Multiplicative inverse 12. Additive inverse 14. Multiplicative inverse 16. Additive identity 68. 9 70. 15 72. 4 74. 18. Additive identity 20. Multiplicative identity 22. 12 , 1 12 24. 9 , 26. 1 9 7 2 , 2 7 28. , 2.5 2 5 7 8 1 6 76. 0 78. 3.34 80. 4.8 82. 10 84. 5 86. 2 3 88. 7 9 5 30. Commutative property of multiplication 90. 32. Commutative property of addition 92. 20 34. Associative property of addition 94. 24 36. Distributive property 96. 4.5 38. Commutative property of multiplication 98. 120 40. Associative property of multiplication 100. 42. 6 44. 20 46. 7 48. 16 50. 7 12 52. 23 20 54. 3.47 56. 16.96 58. 3 60. 4.2 62. 23 48 102. 256.5 273.15 16.65D C 104. $2197.75 106. 20 lb. 108. $1.365 million 110. a) Earth: 8726.2 lb. The Moon: 1490.5 lb. b) Mars: 3333.3 lb. 112. 1.875: Puzzle Problem When two books are placed back to back on a shelf, the first page of one book and the last page of the other are separated only by two covers, so the worm only travels 1 of an inch. 4 Collaborative Exercises Instructor’s Solutions Manual 2. 40° at 35 mph; 35° at 20 mph 4. 2 – (–12) = 14; the answer is positive because it “feels” like the temperature increases when the wind speed drops. 6. Between 10 and 15 mph Exercise Set 1.3 2. 4. 6. 8. A number’s square is a product resulting from multiplying the number by itself. A number’s square root is a number whose square is the given number. Work from the inside out: parentheses, then brackets, and then braces. Because a negative number raised to an odd power is negative. 46. 1 2 48. not a real number 50. 5 52. 18 54. 54 56. 10 58. 63 60. 8 62. 15 64. 25.1 66. 11.999 2 5 base = 5; exponent = 2; five to the second power, or five squared 10. 28 base = 2; exponent = 8; the additive inverse of two raised to the eighth power. 12. 128 14. 49 16. 32 18. 81 20. 1 22. 3 1 81 24. 8 27 68. 21 70. 4 5 72. 2 74. undefined 76. The distributive property was applied instead of adding 2 5 within the parentheses. 78. The commutative property of addition was used to exchange –2 and 8 instead of adding –11 + 8 from left to right. 80. Mistake: Subtracted before multiplied. Correct: 246 82. Mistake: Raised the wrong base to the power 4. Correct: 10 26. 0.0001 84. a) $201.5 b) Yes, as long as his usage remains the same in 2010. 28. 2.744 86. 167, 742 30. s9 88. 1360.024 32. s11 90. 2.69 5 34. s 6 92. 49 0.05 1258 1000 0.15 72 $72.70 36. No real-number roots exist. 94. 0.30 127 21.26 2 112.80 131.08 38. 10 96. «2 10.98 2 12.98 4 1.68¼º z 8 40. 3 98. 1500 499 4 12 0.20 68, 000 60, 000 = 42. 0.1 44. 4 $27,052. $416.04 $6.83 4 Chapter 1 Real Numbers and Expressions 100. 216 58. 102. 3125 17 4 60. 132 104. 30, 000, 000 62. 14 64. a) 40 b) 12 Exercise Set 1.4 2. from and less than 4. To rewrite an expression, we apply mathematical rules to write an expression that is equivalent to the original. To evaluate an expression, we replace all of the variables with numbers and then simplify so that the result is a number. 6. 8. To combine like terms, add or subtract the coefficients and keep the variables and their exponents the same. 8n 12. m – 7 16. 2n – m 10. 5n – 4 14. y2 9 3 66. a) 13 b) 10 68. 0 70. 2 72. 2, 1 74. 3 5 76. 24 x 8 78. 16 x 56 80. 8k 18. x y 1 14 82. 8.82 x 21 20. m 2 n 3 22. 4 7 n 9 84. 3 p 24. y 6 4 26. 12 + 0.7n 86. 28. c d a b 1 y 3 88. 9n 10m 7 30. Mistake: incorrect order Correct: m 4 90. 0.6t 2 6.8 32. Mistake: incorrect order. Correct: 7 z 2r 92. 34. 2l 38. 1 d 2 36. 4l 5 40. $ 2500 n ¨ 1· 42. © t ¸ hr. ª 4¹ 44. bh 46. 2π r r h 48. 50. 54. 1 2 at 2 52. mc 2 x2 x1 2 y2 y1 2 56. 4 4 3 πr 3 5 2 t 1.2t 8 12 94. 15 x 30 96. 6t 9 98. a) 5n 8 2n b) 7 n 8 c) 6.6