C Challenge

50. Reasoning Without listing each subset of a set, how can you determine the number of subsets that the set has?

Use your answer from Exercise 50. Determine how many subsets each set has.

51. R = {positive even numbers less than 20}
52. Q = {0}

Standardized Test Prep

SAT/ACT

53. Let the universal set be U = {x | x is a natural number}, and let set E = {2, 4, 6, 8, …}. What is E '?
    1. {1, 3, 5, 7, …}
    2. {0, 2, 4, 6, 8, …}
    3. {all positive integers}
    4. {2, 4, 6, 8, c}
54. Which set represents the solutions of − 9 x + 17 ≥ − 64 ? negative 9 x plus 17 greater than or equal to negative 64 question mark
    6. { x | x ≤ 9 } the set of all x such that x less than or equal to 9
    7. { x | x ≥ 9 } the set of all x such that x greater than or equal to 9
    8. { x | x ≤ − 47 9 } the set of all . x such that x less than or equal to negative , 47 over 9
    9. { x | x ≥ − 47 9 } the set of all . x such that x greater than or equal to negative , 47 over 9
55. In the diagram below, △ A B C ~ △ E F G . white up pointing triangle eh b c tilde white up pointing triangle e f g .  What is FG?

    

    1. 3 8 9 3 , and 8 ninths
    2. 6 3 7 6 , and 3 sevenths
    3. 11
    4. 12 3 5 12 , and 3 fifths
56. What is the least whole-number solution of − 10 n ≤ 5 ? negative 10 n less than or equal to 5 question mark
    6. − 1 negative 1
    7. 0
    8. 1
    9. 2

Short Response

57. Mum's Florist sells two dozen roses for $24.60. First Flowers Florist sells 6 roses for $7.50. Which florist has the lower cost per rose? Explain.

Mixed Review

See Lesson 3-4.

Solve each inequality.

58. 3 b + 2 > 26 3 b plus 2 greater than 26
59. 2 ( t + 2 ) − 3 t ≥ − 1 2 open t plus 2 close minus 3 t greater than or equal to negative 1
60. 6 z − 15 < 4 z + 11 6 z minus 15 less than 4 z plus 11

See Lesson 1-2.

Evaluate each expression for the given value of the variable.

61. 3 n − 6 ; n = 4 3 n minus 6 semicolon n equals 4
62. 7 − 2 b ; b = 5 7 minus 2 b semicolon b equals 5
63. 2 d − 3 5 ; d = 9 fraction 2 d minus 3 , over 5 end fraction . semicolon d equals 9

Get Ready! To prepare for Lesson 3-6, do Exercises 64–66.

See Lesson 3-1.

Graph each pair of inequalities on one number line.

64. c < 8 ; c ≥ 10 c less than 8 semicolon c greater than or equal to 10
65. t ≥ − 2 ; t ≤ − 5 t greater than or equal to negative 2 semicolon t less than or equal to negative 5
66. m ≤ 7 ; m > 12 m less than or equal to 7 semicolon m greater than 12

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