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Thinking Mathematically MATH1101 Comprehensive Mathematics Homework Solutions Chapter 1 Problems Chapter 1, Section 1 In Exercises 1-30, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) 1. 8, 12, 16, 20, 24, ____ 2. 19, 24, 29, 34, 39, _____ 3. 37, 32, 27, 22, 17, _____ 4. 33, 29, 25, 21, 17, _____ 1. Answer: 28 (keep adding 4 to the previous.) 2. Answer: 44 (keep adding 5 to the previous.) 3. Answer: 12 (keep subtracting 5 from the previous.) 4. Answer: 13 (keep subtracting 4 from the previous.) Chapter 1, Section 1 square, triangle, circle... rotate 90º counterclockwise d d d alphabetical: a, b, c, d, ... and d d add an additional letter each time. Alternate triangles and squares. Add little line going down from bottom each time. Chapter 1, Section 1 35. 5 12 100 2 n 20 48 400 8 4n 28 56 408 16 4n+8 14 28 204 8 2n+4 10 24 200 4 2n four examples : algebraic solution: By inductive reasoning: By deductive reasoning: twice the number twice the number Chapter 1, Section 1 36. 5 12 100 2 n 15 36 300 6 3n 21 42 306 12 3n+6 7 14 102 4 n+2 2 2 2 2 n+2 – n = 2 four examples : by algebraic solution: by inductive reasoning: 2 deductive reasoning: 2 Chapter 1, Section 1 37. 5 12 100 2 n 10 17 105 7 n+5 20 34 210 14 2n+10 16 30 206 10 n+3 8 15 103 5 n+3 – n = 3 3 3 3 3 four examples : by algebraic solution: by inductive reasoning: 3 deductive reasoning: 3 Chapter 1, Section 1 38. 5 12 100 2 n 8 15 103 5 n+3 16 30 206 10 2n+6 20 34 210 14 2n+10 10 17 105 7 n+5 5 5 5 5 5 four examples : by algebraic solution: by inductive reasoning: 5 deductive reasoning: 5 Chapter 1, Section 1 51. The problem states that in general, the sum of the numbers from 1 to n is equal to n( n 1) . So if n is 100 and the 2 formula holds, the sum up to 100(101) 100 would be . 2 This is deductive reasoning. 52. The HMO studied only 200 patients . The conclusion drawn generalizes for the public in general on the basis of these 200 patients. Therefore this is inductive reasoning. Chapter 1, Section 1 53. We are generalizing about all college students on the basis of a sample of 1200 of them. This is inductive reasoning. Chapter 1, Section 1 54. We are reasoning that because the policy exists and because I did turn my report in a day late, that my grade will be reduced by one letter grade. This is deductive reasoning. Chapter 1, Section 2 The key here is to NOT use a calculator. By rounding off, the six items cost about $3, $6, $20, $2, $12 and $0. Adding these numbers together in your highly mathematical brain, you get $43. So these items cost around $43. If you whip out your calculator, they come to exactly $43.45. Not bad for a quick guess. Chapter 1, Section 2 24. $4 + $8 + $29 + $4 + $13 + $1 = $59. Calculator: $59.22 25. Estimate 40 hours per week, $20 and 50 weeks per year. That gives us around $40,000 per year. Calculator: $40,560. 26. 40 ∙ $30 ∙ 50 = $60,000 per year. Calculator: $62,088 27. Estimate $600 month, 3 years and 10 months a year. You get about $18,000, but clearly more than that. Calculator: $21,780. Chapter 1, Section 2 31. About $60,000 per year, about 40 ∙ 50 = 2000 hours per year. That gives us about $30 per hour. Calculator: $29.57. 32. About $40,000 per year, about 40 ∙ 50 = 2000 hours per year. That gives us about $20 per hour. Calculator: 18.73 per hour. 33. If there about 400 days in a year and about 25 hours in a day, there are about 10,000 hours in a year. About 80 years would be about 800,000 hours. Calculator: 701,676 (not including leap years.) 34. Similarly, about half the years, about half the hours, about 400,000 hours. Calculator: 353,028. Chapter 1, Section 2 43. About half of approximately 200 million Americans. So, about 100,000,000. (100 million). 44. About ¼ of approximately 200 million Americans. So, about 50,000,000. (50 million). Chapter 1, Section 2 47. a) From 2002-2004, two years, TV went from $222 to $248 or up by $26. That averages to $13 a year. b) Assuming a steady rise, the cost in 2010, six years after 2004, would be about $248 + 6 ∙ $13 = $248 + $78 = about $316. 48. a) By similar reasoning, $172 - $135 = $37. About $18.50 a year. b) In 2010, $172 + 6 ∙ $18.50 = $172 + $111 = about $283. Chapter 1, Section 2 49. a) 1960. a bit above 4000 cigarettes, maybe 4100 to 4200. b) Looks like 1940 to 1950 was the greatest increase. c) Around 1930, consumption was around 1500 cigarettes. 50. a) Minimum is clearly in 1910. Seems to be around 100 cigarettes. b) Greatest drop-off from 1980 to 1990 c) Around 700 to 800 cigarettes in 1920. Chapter 1, Section 2 51. a) In 1998: about $13,800. In 2005, (7 years) about $20,000. $6,200/7 is about $900. b) C ≈ $14,000 + 900x, where x is years after 1998. c) C ≈ $14,000 + 900 ∙ 14 ≈ $26,600

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Thinking Mathematically, robert blitzer, Prentice Hall, Robert F. Blitzer, Pearson Education, College Algebra, Problem Solving, final exam, Buy It Now, 4th Edition

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posted: | 4/14/2011 |

language: | English |

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