A-1 Chapter 1 RECREATIONAL MATH, PAGE 24 The boatman crosses with the goat first. Then he can take the herbs across the river. But he must return the goat temporarily so that the goat doesn’t eat the herbs. He then takes the wolf across the river. Then he returns for the goat. He will make seven crossings—four forward and three back. The answer to the St. Ives riddle is 1. SECTION 1.1, PAGE 6 1. Natural 3. Counterexample 5. Inductive 7. Deductive 9. × = 5 5 25 11. 1 5 10 10 5 1 13. 15. 17. 9, 11, 13 19. 16, 32, 64 − 21. , , 1 5 1 6 1 7 23. 34, 55, 89 25. The product of two odd numbers is an odd number. 27. The sum of two even numbers is an even number. 29. a) Answers will vary. b) Products involving 10 and natural numbers will have a one’s digit of 0. 31. a) 36, 49, 64 b) square 6, 7, 8, 9, and 10 c) No, 72 is between 82 and 9 ,2 so it is not a square number. 33. Blue: 1, 5, 7, 10, 12; Purple: 2, 4, 6, 9, 11; Yellow: 3, 8 35. a) $3700 b) We are using specific cases to make a prediction. 37. a) You should obtain the original number. b) You should obtain the original number. c) The result is the original number. 39. a) 5 b) You should obtain the number 5. c) The result is always the number 5. 41. n n n n n n , 3 , 3 6, 2, 2 2 n3 6 3 + = + + − = + 43. n n n n n n n n n n , 1, 1 2 1,2 19 2 10, 5, 5 5 n2 10 2 ( ) + + + = + + + = + = + + − = + 45. × = 3 5 15, which is not divisible by 2. 47. + = (3 2)/2 5/2, which is not an even number. 49. − = − 1 2 1, which is not a counting number. 51. a) The sum of the measures of the interior angles should be 180°. b) Yes, the sum of the measures of the interior angles should be 180°. c) The sum of the measures of the interior angles of a triangle is 180°. 53. Inductive reasoning; a general conclusion is obtained from observation of specific cases. 55. 129, the numbers in positions are determined as follows: + + a b c a b c 57. (c) SECTION 1.2, PAGE 15 1. Estimation 3. 120 5. 50,000 7. 18 9. 17 11. 1800 13. $30 15. $600 17. $53 19. 400 lb 21. $10 23. 20 miles per gallon 25. $400 27. $1500 29. $1300 31. 45 minutes 33. $30 35. $3100 37. 90 mi 39. a) 175 b) 70 c) 140 41. a) 5 million b) 98 million c) 65 million d) 280 million 43. a) 85% b) 15% c) 59,500,000 acres d) No, since we are not given the area of each state 45. 20 47. 120 bananas 49. 150° 51. 10% 53. 9 square units 55. 160 feet 57. a) Answers will vary. b) Answers will vary. c) Answers will vary. 58. $1.40 59. There are 118 ridges around the edge. 60. a) Answers will vary. b) 11.6 days SECTION 1.3, PAGE 28 1. 51 mi 3. 38.4 ft 5. $493.81 7. a) 14 bags b) $55.58 c) $59.47 9. a) $106.60 b) $689.00 11. a) 108 golf balls b) $98 13. $90 15. $46,470.60 17. 92 19. a) 18.4 min b) 31 min c) 40 min d) 27.5 min 21. a) 30.5 mpg b) 7.54 gal c) $24.81 23. $82.08 25. a) $60.50 b) $11.26 c) $61.76 27. a) 4106.25 gal b) $45.99 29. a) ≈35.61 gal b) $106.83 c) ≈4,985,400,000 gal 31. $4.73 33. $420 35. a) 1 box of 20 and 1 box of 12 b) $420 37. 144 square inches 39. The area is 4 times as large. 41. The volume is 8 times as large. 43. a) 2 tsp chili powder and 1 6 tsp cayenne pepper b) 10 servings 47. a) refresh b) workout 49. 4 3 2 5 1 6 51. 8 18 6 2 16 10 4 14 12 53. The sum of the four corners is 4 times the number in the center. Answers
RkJQdWJsaXNoZXIy NjM5ODQ=