Find the value of each expression.

56.   5 P 3   5 P 2 fraction sub 5 , cap p sub 3 , over sub 5 , cap p sub 2 end fraction
57.   4 P 3   4 P 2 fraction sub 4 , cap p sub 3 , over sub 4 , cap p sub 2 end fraction
58.   7 P 3   7 P 2 fraction sub 7 , cap p sub 3 , over sub 7 , cap p sub 2 end fraction
59.   2 C 2 +   2 C 1 +   2 C 0 sub 2 , cap c sub 2 , plus , sub 2 , cap c sub 1 , plus , sub 2 , cap c sub 0
60.   3 C 3 +   3 C 2 +   3 C 1 +   3 C 0 sub 3 , cap c sub 3 , plus , sub 3 , cap c sub 2 , plus , sub 3 , cap c sub 1 , plus , sub 3 , cap c sub 0
61.   90 C 90 sub 90 . cap c sub 90

C Challenge

Determine whether each statement is always, sometimes, or never true. Assume n ≠ 0 . n not equal to 0 .

62.   n C 1 = n sub n , cap c sub 1 , equals n
63.   3 C x > x sub 3 , cap c sub x , greater than x
64.   n C ( n − 1 ) = n sub n . cap c sub open n minus 1 close end sub . equals n
65. A test has 10 questions. You must answer a total of 7 questions, including exactly 4 of the first 6 questions.
    1. In how many ways can you choose 4 of the first 6 questions?
    2. How many questions are left after you have answered 4 of the first 6 questions? How many must you still answer?
    3. In how many ways can you choose questions to finish the test?
    4. How many different ways are there of completing the test (meeting all of its requirements)?

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

66. The school cafeteria serves lunches consisting of 1 main dish, 1 vegetable, 1 salad, and 1 dessert. The menu has choices of 2 main dishes, 3 vegetables, 3 salads, and 4 desserts. How many different lunches are possible?
67. What is 7.3 × 10 − 2 7.3 times , 10 super negative 2 end super  written in standard form?
68. How many elements are in the union of the two sets M = {4, 5, − 6 negative 6 , 7, 8} and N = { − 4 , negative 4 comma  5, 6, 7, − 8 negative 8 }?
69. You deposit $500 in an account earning 5.25% annual interest. You make no further deposits to the account and the interest is compounded annually. What is the balance in dollars after 10 yr? Round to the nearest dollar.

Mixed Review

See Lesson 12-5.

Determine whether each data set is qualitative or quantitative.

70. ZIP codes
71. race times
72. heights of people
73. emotions

See Lesson 9-6.

Use the quadratic formula to solve each equation. If necessary, round answers to the nearest hundredth.

74. 2 x 2 + 12 x − 11 = 0 2 , x squared , plus 12 x minus 11 equals 0
75. x 2 − 7 x + 2 = 0 x squared , minus 7 x plus 2 equals 0
76. x 2 + 4 x − 8 = 0 x squared , plus 4 x minus 8 equals 0
77. 3 x 2 + 8 x + 5 = 0 3 , x squared , plus 8 x plus 5 equals 0

Get Ready! To prepare for Lesson 12-7, do Exercises 78–81.

See p. 793

Rewrite each decimal or fraction as a percent.

78. 0.32
79. 0.09
80. 45 200 45 over 200
81. 9 50 9 fiftieths

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