C Challenge

36. Assume that an event is neither certain nor impossible. Then the odds in favor of the event are the ratio of the number of favorable outcomes to the number of unfavorable outcomes.
    1. If the odds in favor of the event are a to b, or a b , eh over b , comma  what is the probability of the event?
    2. If the probability of the event is a b , eh over b , comma  what are the odds in favor of the event?
    3. Would you rather play a game in which your odds of winning are 1 2 , 1 half , comma  or a game in which your probability of winning is 1 2 ? 1 half , question mark  Explain.

Standardized Test Prep

SAT/ACT

37. What is the theoretical probability of getting a 2 or a 3 when rolling a standard number cube?
    1. 1 2 1 half
    2. 1 3 1 third
    3. 1 4 1 fourth
    4. 1 6 1 sixth
38. Which expression is equivalent to ( n 3 2 ÷ n − 1 6 ) − 3 ? open . n super 3 halves end super , divides . n super negative , 1 sixth end super . close super negative 3 end super . question mark
    6. n 27 n to the twenty seventh
    7. n − 27 n super negative 27 end super
    8. n − 4 n super negative 4 end super
    9. n − 5 n super negative 5 end super
39. How can you rewrite the equation x 2 + 12 x + 5 = 3 x squared , plus 12 x plus 5 equals 3  so the left side of the equation is in the form ( x + a ) 2 ? open x plus eh close squared . question mark
    1. ( x − 6 ) 2 = 28 open x minus 6 close squared . equals 28
    2. ( x + 6 ) 2 = 34 open x plus 6 close squared . equals 34
    3. ( x + 6 ) 2 = 39 open x plus 6 close squared . equals 39
    4. ( x + 12 ) 2 = − 2 open x plus 12 close squared . equals negative 2
40. How many ways are there to select 25 books from a collection of 27 books?
    6. 702
    7. 5.4 × 1027 5.4 times , 1027
    8. 351
    9. 675

Short Response

41. Use the center and radius to graph the circle with equation ( x + 4 ) 2 + ( y − 2 ) 2 = 16 . open x plus 4 close squared . plus . open y minus 2 close squared . equals 16 .

Mixed Review

See Lesson 11-1.

Evaluate each expression.

42.   5 P 2 sub 5 , cap p sub 2
43.   7 P 4 sub 7 , cap p sub 4
44.   5 C 3 sub 5 , cap c sub 3

45.   10 C 8 sub 10 , cap c sub 8

    See Lesson 8-5.

    Add or subtract. Simplify where possible.

46. 5 a 2 b − 7 a 5 b 2 fraction 5 , over eh squared , b end fraction . minus . fraction 7 eh , over 5 , b squared end fraction
47. 3 p + 7 q 3 over p , plus , 7 over q

48. x x − 5 + x 5 − x fraction x , over x minus 5 end fraction . plus . fraction x , over 5 minus x end fraction

    Get Ready! To prepare for Lesson 11-3, do Exercises 49–51.

    See Lesson 11-2.

    A bag contains 24 green marbles, 22 blue marbles, 14 yellow marbles, and 12 red marbles. Suppose you pick one marble at random. What is each probability?

49. P(yellow)
50. P(not blue)
51. P(green or red)

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