SOLUTIONS MANUAL FOR A SURVEY OF MATHEMATICS WITH APPLICATIONS NINTH EDITION BY TAMSEN HERRICK

SOLUTIONS MANUAL FOR A SURVEY OF MATHEMATICS WITH APPLICATIONS NINTH EDITION BY TAMSEN HERRICK CHAPTER ONE CRITICAL THINKING SKILLS Exercise Set 1.1 1. Counting 2. Divisible 3. Hypothesis 4. Counterexample 5. Inductive 6. Deductive 7. Deductive 8. Inductive 9. Inductive reasoning, because a general conclusion was made from observation of specific cases. 10. Inductive reasoning, because a general conclusion was made from observation of specific cases. 11. 5 5 25 × = 12. 12 14 168 × = 13. 1 5 1 4 10 4 6 10 6 4 5 4 1 1 ( ) ( ) ( )( ) =+ = + = + = + 14. 5 100,000 10 = 15. 16. 17. 18. 19. 10, 12, 14 (Add 2 to previous number.) 20. 19, 23, 27 (Add 4 to the previous number.) 21. 3, −3, 3 (Alternate 3 and −3.) 22. −3, −5, −7 (Subtract 2 from previous number.) 23. 111 , , (Increase the denominator value by 1.) 567 24. 2500, −12,500, 62,500 (Multiply previous number by –5.) 25. 36, 49, 64 (The numbers in the sequence are the squares of the counting numbers.) 26. 21, 28, 36 (15 6 21, 21 7 += + 28, 28 8 36) = += 1 Copyright © 2013 Pearson Education, Inc. 2 CHAPTER 1 Critical Thinking Skills 27. 34, 55, 89 (Each number in the sequence is the sum of the previous two numbers.) (Multiply previous number . , , 3 by .) 4 − − 29. There are three letters in the pattern. 39 3 117 × = , so the 117th entry is the second R in the pattern. Therefore, the 118th entry is Y. 30. a) Answers will vary. b) The sum of the digits is 9. c) When a one- or two-digit number is multiplied by 9, repeated summing of the digits in the product yields the number 9. 31. a) 36, 49, 64 b) Square the numbers 6, 7, 8, 9 and 10. c) 8 8 64 9 9 81 ×= ×= 72 is not a square number since it falls between the two square numbers 64 and 81. 32. a) 28 and 36 b) To find the 7th triangular number, add 7 to the 6th triangular number. To find the 8th triangular number, add 8 to the 7th triangular number. To find the 9th triangular number, add 9 to the 8th triangular number. To find the 10th triangular number, add 10 to the 9th triangular number. To find the 11th triangular number, add 11 to the 10th triangular number. c) 36 9 45; 45 10 55; 55 11 66; 66 12 78 += + = + = + = 72 is not a triangular number since it falls between the consecutive triangular numbers 66 and 78. 33. Blue: 1, 5, 7, 10, 12 Purple: 2, 4, 6, 9, 11 Yellow: 3, 8 34. a) 19 (Each new row has two additional triangles.) b) 1 3 5 7 9 100 +++++ + + + + = 35. a) ≈ $200,000 b) We are using observation of specific cases to make a prediction. 36. a) ≈ $3.7 trillion b) We are using observation of specific cases to make a prediction. 37. 38. 39. a) You should obtain the original number. b) You should obtain the original number. c) Conjecture: The result is always the original number. d) 4 12 4 12 , 4 , 4 12, 3, 3 3 4 44 n n nnn n n n + + = + = + +−= 40. a) You should obtain twice the original number. b) You should obtain twice the original number. c) Conjecture: The result is always twice the original number. d) 4 64 6 , 4 , 4 6, 2 3, 2 3 3 2 2 22 n n nnn n n n