C Challenge

43. Two standard number cubes are rolled. What is the probability that the sum is greater than 9 or less than 6?
44. Reasoning Tatyana has x + 2 pens in the pocket of her backpack. Samuel has 2 x − 1 2 x minus 1  pens in the pocket of his backpack.
    1. Tatyana has 2 blue pens. Find the probability that she pulls out a blue pen at random.
    2. Samuel has x − 3 x minus 3  blue pens. Find the probability that he pulls out a blue pen at random.
    3. Find the probability that either Tatyana or Samuel pulls out a blue pen at random.

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

45. A bag contains 5 red marbles, 1 blue marble, 3 yellow marbles, and 2 green marbles. One marble is drawn from the bag. What is the probability that the marble is red or yellow?
46. What is the theoretical probability of getting a 1 or 6 when rolling a standard number cube?
47. The first term of an arithmetic series is 123. The common difference is 12 and the sum 1320. How many terms are in the series?
48. What is the slope of the graph of the equation 6 x − 18 y = − 24 ? 6 x minus 18 y equals negative 24 question mark
49. What is the radius of the circle with equation x 2 − 4 x + y 2 − 21 = 0 ? x squared , minus 4 x plus , y squared , minus 21 equals 0 question mark
50. How many five-letter permutations can you form from the letters of the word COMPUTER?

Mixed Review

See Lesson 11-2.

Find the theoretical probability of each event when rolling a standard number cube.

51. P(5)
52. P(an even number)
53. P(less than 4)

See Lesson 8-6.

Solve each equation. Check each solution.

54. 1 2 − x = x 6 1 half , minus x equals , x over 6
55. 2 2 x − 1 = x 3 fraction 2 , over 2 x minus 1 end fraction . equals , x over 3
56. 3 2 x − 2 3 x = 5 fraction 3 , over 2 x end fraction , minus , fraction 2 , over 3 x end fraction , equals 5

See Lesson 7-6.

Solve each equation. Check your answers.

57. l n 2 x = 3 l n 2 x equals 3
58. l n x + l n 2 = 6 l n x plus l n 2 equals 6
59. l n x 2 + 1 = 5 l n , x squared , plus 1 equals 5

Get Ready! To prepare for Lesson 11-4, do Exercises 60–62.

See Lesson 11-3.

A spinner has four equal sections that are red, blue, green, and yellow. Find each probability for two spins.

60. P(blue, then blue)
61. P(red, then yellow)
62. P(not yellow, then green)

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