Students Again

Note: All page references are from the book “Thinking Mathematically” by Robert Blitzer

and published by Pearson

Page 47: Chapter 2: Section 2-1 Questions 5, 10,…, 65

5) The set of odd natural numbers less than 100.

10) {e}

15) {101, 102, 103,…}

20) {23, 24, 25, 26, 27, 28, 29}

25) {x | x ÃŽ N and x is less than 6}

30) {x | x ÃŽ N and x is greater than 3}

35) False

40) False

45) False

50) ÃŽ

55) n(A) = 5

60) n(C) = 0

65) False

Page 58-59: Chapter 2: Section 2-2 Questions 5, 10,…, 70

5) A’ = {c, d, e}

10) B’ = {1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

15) C’ = {1, 3, 5, 7,…}

20)

25) Í

30) Í

35) Í or Ì

40) neither

45) True

50) True

55) {} (border collie} {poodle} {border collie, poodle}

60) {}

65) 128 subsets and 127 proper subsets

70) There are 512 different variations for ordering pizza

75) A universal set is a set that contains all elements being considered in a problem or discussion. It is symbolized by an U. For example, if there were two sets: sets A and B.

Set A consist of elements of casino games played with cards:

A = {poker, blackjack, baccarat}

Set B consist of elements of casino games not played with cards:

B = {slots, roulette, craps}

The universal set that contains all elements of sets A and B is the set of casino games (U is the set of casino games).

Page 65-66: Chapter 2: Section 2-3 Questions 5, 10,…, 65

5) A’ = {2, 4, 6}

10) B U C’ = {1, 2, 3, 7}

15) (A U B)’ = {4, 6}

20) C ÇO = O

25) A ÇB = {g, h}

30) B’ = {a, c, d, e, f}

35) (A Ç C)’ = {a, b, c, d, e, f, g, h}

40) (A U C)’ = O

45) A U U = {a, b, c, d, e, f, g, h}

50) B U C = {2, 3, 4, 5, 6, 8}

55) (B ÇC)’ = {1, 3, 5, 6, 7, 8}

60) A U B = {1, 2, 3, 4, 5, 6, 7}

65) (A U B)’ = {8, 9}

Page 72-73: Chapter 2: Section 2-4 Questions 4, 10,…, 65

5) A’ Ç (B U C’) = {2}

10) (A Ç B Ç C)’ = {}

15) (A U B) Ç (A U C) = {a, b, g, h}

20) (C’ Ç A) U (C’ Ç B’) = {a, g, h}

25) II, III, V, VI

30) IV, V

35) A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

40) A Ç C = {6, 7, 8}

45) a) II b) II c) A Ç B = B Ç A

50) Set A is represented by region I, II

Set A’ is represented by region III, IV

Set B is represented by region II, III

Set B’ is represented by region I, IV

A’ Ç B is represented by region III

A U B’ is represented by region I, II, IV

Thus, A’ Ç B and A U B’ are not equal for all sets A and B.

55) a) II, IV, V, VI, VII b) II, IV, V, VI, VII c) (A Ç B) U C = (A U C) Ç ( B U C)

60) Set A is represented by region I, II, IV, V

Set B is represented by region II, III, V, VI

Set C is represented by region IV, VI, VII

A U (B Ç C) is represented by region IV, V, VI, VII

(A U B) Ç C is represented by region IV, V, VI, VII

Therefore, A U (B Ç C) and (A U B) Ç C are not equal for all sets A, B, and C.

65) I

Page 80-82: Chapter 2: Section 2-5 Questions 5, 10,…, 30

5) 37

10) n(A U B) = 43

15) 9 women agreed with the statement

20)

 

25) a) 23 b) 3 c) 32 d) 52 e) 15 f) 6

30) a) 0 b) 30 c) 30

Section 11-1 pg. 564 (5, 10,…, 20)

5) 6 ways the two-part trip can be made.

10) 36 apartment options

Describe two such options:

1) one bedroom, one bathroom, first floor, lake view

2) two bedrooms, one bathroom, second floor, no special view

15) 243 ways you can answer the question

20) 35,152 different four-letter radio station call letters if the first letter must be W or K.

Section 11-2 pg. 571-72 (5, 10,…, 55)

5) 120 different ways to schedule appearances

10) 6 different five-sentence paragraphs can be formed

15) 570,024

20) 700

25) 24

30) 6,720

35) 6,720

40) 1

45) 120 different ways the first three finishers can come in

50) 1,260 different distinct ways

55) 280 different signals can be made

Section 11-3 pg. 579-79 (5, 10,…, 40)

5) Combinations; because order does not matter

10) Combinations; because order does not matter

15) 330

20) 1

25) 7

30) 3,003 different ways

35) 22,957,480 different selections are possible

40) 14,112 ways they can be chosen

Section 11-4 pg. 585-86 (5, 10,…, 60)

5) 1/3

10) 0

15) 3/13

20) 0

25) 1/2

30) 1/4

35) 1/4

40) 1

45) 1/2

50) 3/4

55) 0.16

60) 0.7415

Section 11-5 pg. 591-92 (5, 10, 15)

5) a) 84 b) 10 c) 5/42

10) a) 2/429 all are lawyers b) 7/429 none are lawyers

15) 0.0099547 that all three are picture cards

Section 11-6 pg. 601-604 (5, 10,…, 70)

5) 10/13

10) 648463/649740

15) 2/13

20) 1/26

25) 7/13

30) 7/8

35) 4/5

40) 5/6

45) 15:43 odds in favor; 43:15 odds against

50) 9/2 or 9:2 odds against rolling a number less than five

55) 1:1 odds in favor of drawing a red card

60) 25:1 against drawing a red jack

65) 1:19 in favor of being a victim of a serious crime

70) 193/463 is the probability that a twenty-year-old will still be alive at seventy-yearsold

Section 11-7 pg. 612-13 (5, 10,…, 60)

5) 1/4

10) 1/27

15) 3/52

20) 1/4

25) a) 1/256 b) 1/4096 c) 0.524 d) 0.476

30) 3/29

35) 4/35

40) 14/285

45) 1/5

50) 1/3

55) 9/10; 0.9

60) 67/100

Section 11-8 pg. 620-21 (5, 10, 15)

5) $0; on average there will be no gain or loss

10) 1/6; since the expected value is 1/6 there is an expected gain for guessing

15) $ -0.17; the expected loss is approximately $0.17 per game

Chapter 12 : Section 3 pgs. 641-43 Questions 5,10,…,25

5) 7;31 – 7 is the stress rating with the greatest number of students. 31 is the number of

students that responded with this rating.

10)

15)13 students had at least 30 social interactions for the week.

20)

25) B

Chapter 12 : Section 2 pgs. 655-56 Questions 5, 10,…, 50

5) 62

10) 4.1290322

15) 95

20) 1.95

25) 3

30) 5 and 8 (bimodal)

35) 6

40) 65

45) 4.5

50) a) 43.933 b) 46 c) 46 d) 41

Chapter 12 : Section 3 pgs. 663-64 Questions 5, 10,…, 25

5) 2

10) a) -5, -5, -5, 0, 0, 0, 1, 2, 5, 5 b) 0

15) a) 2.7 b) -0.8, -0.45, 0.05, 0.4, 0.8 c) 0

20) 2.24

25) 2.14

Chapter 12 : Section 4 Pgs. 680-81 Questions 5, 10,…, 95

5) 150

10) 50

15) 47.5%

20) 2.5%

25) 47.5%

30) 16%

35) 3

40) 0

45) -1.5

50) 1.75

55) -1.5

60) 550

65) 275

70) a) 91.92% b) 8.08%

75) 33.99%

80) 76.98%

85) 27.43%

90) 4.66%

95) 24.17%

Chapter 8: Section 1 Pgs. 413-14 Questions 5, 10,…, 65

5) 37.5%

10) 16.25%

15) 287%

20) 95%

25) 1.3

30) 0.75

35) A = 6

40) B = 20

45) P = 12%

50) B = 680,000 jail capacity in 2001.

55) $9

60) a) $6.60 is the discount amount b) $9.90 is the sale price.

65) 15% decrease of the sale price from the regular price.

Chapter 8: Section 2 Pgs. 419-20 Questions 5, 10,…, 35

5) $318.75

10) A = $2,360

15) r = 7.5%

20) r = 14.12%

25) P = $4,507.59

30) a) $5,100 b) $14,900 c) r = 11.41%

35) P = $2,654.87

Chapter 8: Section 3 Pgs. 425-26 Questions 5, 10,…, 35

5) a) $12,795.12 b) $3,295.12

10) a) $1,623.66 b) 423.66

15) $7,528.59

20) 6.1%

25) The investments are virtually equal. (0.0820 vs. 0.0825; both round to 0.083)

30) A = $150,307,000,000 is the amount asked in the lawsuit.

35) $94,460.79

Chapter 8: Section 4 Pgs. 435-37 Questions 5, 10,…, 20

5) 12.5%

10) 16%

15) a) $11.05 b) $1,013.05 c) $28

20) a) $35.20 b) $44 c) $36.62

Chapter 8: Section 5 Pgs. 444-45 Questions 5, 10

5) The 20-year mortgage at 7.5% is more economical.

10) a) $600.46 b) $94,999.30 c) $5,000.70

Chapter 10: Section 1 – Pg. 497-498 Questions 5, 10,…,25

5) 20° ; acute

10) 90° ; right

15) Complement = 42° ; Supplement = 132°

20) Complement = 72 2/3° ; Supplement = 164 2/3°

25) Ð1 = 108° ; Ð2 = 72° ; Ð3 = 108°

Chapter 10: Section 2 – Pg. 506-509 Questions 5, 10,…, 35

5) Ð1 = 50° ; Ð2; 130° ; Ð3 = 50° ; Ð4 = 130° ; Ð5 = 50°

10) Ð1 = 65° ; Ð2 = 70° ; Ð3 = 45° ;Ð4 = 45° ; Ð5 = 70° ; Ð6 = 45° ; Ð7 = 45°

; Ð8 = 135° ; Ð9 = 65° ; Ð10 = 65°

15) c = 16 in.

20) ÐEDA and ÐCBA have corresponding sides and angles. The corresponding

angles have the same measure and the ratios of the lengths of the corresponding

sides are equal.

25) a = 12cm

30) 12.81 ft. is the length of the ladder.

35) The new road will cost $750,000.

Chapter 10: Section 3 – Pg. 513-515 Questions 5, 10,…, 40

5) a – square ; b – rhombus ; d – rectangle ; e – parallelogram

10) a – square

15) R = 1,000in.

20) R = 24mm

25) 540°

30) mÐA = 120° ; mÐB = 60°

35) Stop, yield, and deer crossing.

40) Stop

Chapter 10: Section 4 – Pg. 523-525 Questions 5, 10,…, 35

5) A = 2100cm2

10) A = 24yd2

15) C = 25.1cm ; A = 50.3cm2

20) 45ft2

25) $556.50 for carpet.

30) $698.18 is deductible.

35) 125.7m of fencing.

Chapter 10: Section 5 – Pg. 531-533 Questions 5, 10,…, 35

5) V = 175yd3

10) V = 150.8cm3

15) V = 47yd3

20) V = 7,238.23in3

25) V = 1,018cm3

30) V = 9,000yd3 of water used in a three month period.

35) $27 to fill the pool.