C Challenge

54. Data Analysis The bar graph below shows the results of 40 responses to a survey.

    
    Image Long Description

    1. Find the number of possible combinations of five people who squeeze toothpaste from the middle of the tube.
    2. Suppose five people are chosen at random from all the people who responded to the survey. How many combinations of five people are possible?
55. 1. In how many ways can you choose three flags from a collection of seven different flags?
    2. In how many different orders can you arrange three flags?
    3. Writing You want to arrange three flags from a group of seven. Explain how you can use   7 C 3 · 3 ! sub 7 , cap c sub 3 , middle dot 3 factorial  to create the permutation formula.

Standardized Test Prep

SAT/ACT

56. What is the value of   7 C 2 ? sub 7 , cap c sub 2 , question mark
    1. 2520
    2. 49
    3. 42
    4. 21
57. What is the complete solution set of 3 x 2 − 1 + 4 x x + 1 = 1.5 x − 1 ? fraction 3 , over x squared , minus 1 end fraction . plus . fraction 4 x , over x plus 1 end fraction . equals . fraction 1.5 , over x minus 1 end fraction . question mark
    6. 1 , − 1 1 comma negative 1
    7. 1, 0.375
    8. 0.375
    9. 0.375, 3
58. Use a calculator to solve − x 2 − 3 x + 7 = 0 . negative , x squared , minus 3 x plus 7 equals 0 .  Round to the nearest hundredth.
    1. − 0.76 , 4.76 negative , 0.76 , comma , 4.76
    2. 0.76, 5.76
    3. − 1.54 , 4.54 negative , 1.54 , comma , 4.54
    4. − 4.54 , 1.54 negative , 4.54 , comma , 1.54
59. What is the center of the circle with equation ( x − 5 ) 2 + ( y + 1 ) 2 = 81 ? open x minus 5 close squared . plus . open y plus 1 close squared . equals 81 question mark
    6. (5, 1)
    7. ( 5 , − 1 ) open 5 comma negative 1 close
    8. ( − 5 , 1 ) open negative 5 comma 1 close
    9. ( − 5 , − 1 ) open negative 5 comma negative 1 close

    Short Response

60. What is the sum of the two infinite series ∑ n = 1 ∞ ( 2 3 ) n − 1 sum , from , n equals 1 , to , infinity , of . open , 2 thirds , close super n minus 1 end super  and ∑ n = 1 ∞ ( 2 3 ) n ? sum , from , n equals 1 , to , infinity , of . open , 2 thirds , close to the n . question mark

Mixed Review

See Lesson 10-6.

Identify the center, vertices, and foci for each ellipse.

61. ( x − 2 ) 2 9 + ( y − 1 ) 2 25 = 1 fraction open x minus 2 close squared , over 9 end fraction . plus . fraction open y minus 1 close squared , over 25 end fraction . equals 1

62. ( x − 1 ) 2 49 + ( y − 1 ) 2 36 = 1 fraction open x minus 1 close squared , over 49 end fraction . plus . fraction open y minus 1 close squared , over 36 end fraction . equals 1

    See Lesson 4-4.

    Factor each expression completely.

63. 4 x 2 − 8 x + 4 4 x squared , minus 8 x plus 4
64. − x 2 − 6 x − 9 negative , x squared , minus 6 x minus 9

65. 3 x 2 − 75 3 x squared , minus 75

    Get Ready! To prepare for Lesson 11-2, do Exercises 66–68.

    See Lesson 11-1.

    Simplify each expression.

66. 10 · 9 · 8 · 7 · 6 10 middle dot 9 middle dot 8 middle dot 7 middle dot 6
67. 8 ⋅ 7 ⋅ 5 ⋅ 6 4 ⋅ 3 ⋅ 2 ⋅ 1 fraction 8 dot 7 dot 5 dot 6 , over 4 dot 3 dot 2 dot 1 end fraction
68. 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 4 ⋅ 3 ⋅ 2 ⋅ 1 fraction 7 dot 6 dot 5 dot 4 dot 3 dot 2 dot 1 , over 4 dot 3 dot 2 dot 1 end fraction

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