Algebra 1 Common Core Student Edition, Grade 8-9

17. random; good sample 19. not biased; respondent is
    not influenced by question 21. During the day many
    people are at work so your sample is not representative of
    the population. 23. Because each sample is random, it
    would not be expected to be exactly the same.
    25a. People at an airport are more likely to be travelers,
    b. Your question is influencing the result. Respondents
    might prefer "neither." c. The sample is biased as it
    includes mostly people who might prefer France.


18. people who are customers at the store; every fifteenth
    customer; systematic 29. attendees at the game; random
    attendees; random 31. quantitative; univariate


19. qualitative; bivariate 35a. Responses are voluntary
    and there are sports that are not listed, b. no for the
    reasons listed in part (a) 37. Response is voluntary and
    only those who like the scent are probably going to return
    the card. 39a. Answers may vary. Sample: Does your
    family have a pet? If so, w hat kind of pet is it?; qualitative
    b. Check students' work. c. Check students' work.


20. D 43. B 45. 40 46.60 47. a > 1 48. x>-3


21. b > 0.2 5 0 .2 0 5 1 .4 2 5 2 .6

Lesson 12-6 pp. 762-768

Go t I t? 1a. 48 b. No; t h e t r e e d i a g ra m w o u ld b e very
large, so using the Multiplication Counting Principle
would be easier. 2. 40,320 ways 3. 20,160 4. 455 ways
Lesso n Ch eck 1. 5040 2. 6,227,020,800 3. 120

4. 5040 5. 10 6. 35 7. 24 outfits 8. permutations


5. Permutations are used to count in situations where
   order is important. Combinations are used to count in
   situations where selection, not order, is important.


6. There is only one way to take n things, n at a time.
   Also, rCn n(n-n)_h!__ 0! _J_x 1 i’•
   Ex e r c i se s 1 1 a. 8 , 1 0 b. 8 x 10 6 or 8,000,000


7. 3,628,800 15. 1680 17. 5040 19. 42 21. 6


8. 90 25. 5040 ways 27. 1 29. 9 31. 56 33. 28


9. 10 37. 220 ways 39. 142,506 groups 41. gP 7


10. 9 P 6 45. 8 C 5 47a. 24 ways b. No; there is a limited
    number of ways that you can arrange the letters so
    someone can figure it out. 49. 60 51. 210


11. Combination; the order of the books does not
    matter. 55a. 35,152 call signs b. 913,952 call signs


12. 2 59. 4 61. 1 63. sometimes 65a. 15 b. 4; 3 c. 3
    d. 60 67. 0.073 70. qualitative 71. quantitative


13. quantitative 73. qualitative 74. 0.81, -6.81


14. 6.70, 0.30 76. 1.46, - 5 .4 6 77.-1, -1.67


15. 32% 79. 9% 80. 22.5% 81. 18%

Lesson 12-7

Go t It? 1. | 2. It will be 1 -
number of other samples added. The probability will
increase. 3. 3 : 1 4. 98% 5. about 34,995 light bulbs

20

50 + x

pp. 769-774

, w h e r e x is the

Lesso n Ch eck 1. g 2. g 3. | 4. | 5. 1 : 5 6. 16%

7. Theoretical probability is based on the number of
   favorable outcomes when all of the outcomes are equally
   likely. Experimental probability is based on the results of
   an experiment. 8. There are only two outcomes that are
   favorable, getting a 1 or a 2 , therefore the probability is
   4 or b
   Ex e r c i se s 1 1. 0 13. | 15. \ 17. | 19. | 21. g


8. 5 : 1 25. 5 : 1 27. 1 : 5 29. 43% 31. 85%


9. about 201 trees 35. 98.4% 39. 40%


10. 25% 43. 45. | 47. B 49. Since order does
    not make a different group, this is a combination
    problem. 11 C 5 =-5!(1111! _ 5)! ■ = 462. There are 462
    different groups the coach can choose. 50. 840


11. 6 52. 30 53. 9 54. 5 55. {1,4, 5, 6 , 7, 10}


12. {4, 6 } 57. {0, 2, 4, 5, 6 , 7, 8 , 10} 58. {4, 10}


13. (0, 1, 2, 4, 6 , 7, 8 , 10}

Lesson 12-8

Go t It? 1a. § b.

pp. 776-782

g b. 3 2. 225 3. Tg 4 -1 0 5 5a- 33 N<

the numerators and the denominators are the same, so

the product is the same

Lesso n Ch eck l a .I b. § c. 1 d. § JL 20 25^3 A.

4. Answers may vary. Sample: find the probability of
   spinning a number less than 5 th at is even. 5. Mutually
   exclusive; answers may vary. Sample: The complement of
   being even on a number cube is being odd, and even and
   odd are mutually exclusive. 7. Because a tile can be both
   yellow and a letter, the formula should be
   P(yellow or letter) = P(yellow) + P(letter) -
   P(yellow and letter) = \ + =
   Ex e r c i se s 9. f 1 1. \ 13. § 15. ^ 17. |


5. £ 23. 1 25. A 27. £ 29. ± 31. £


6. ^2 37. Dependent; the outcome of the first event
   affects the outcom e of the second. 39. For i n d e p e n d e n t
   events, the outcome of the first event does not affect the
   outcome of the second event, while for dependent
   events, the outcome is affected. An example of two
   independent events is the rolling of two number cubes.
   An example of two dependent events is picking two cards
   from a deck without replacing the first one. 41. about
   4.7% 43a-c. Check students' work. 45a. 4c b.
   19.^1 6
   33. 0

36

Chapter Review pp. 786-790

1. element 2. frequency 3. outlier 4. quartile


2. '-12 7 6. '4.4 4 .5 '
   4 6. 9.5 -10.2
   .3.4 - 2. 6.

c

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