1.1 Inductive and Deductive Reasoning 7 34. Triangles in a Triangle Four rows of a triangular figure are shown. a) If you added six additional rows to the bottom of this triangle, using the same pattern displayed, how many triangles would appear in the 10th row? 19 b) If the triangles in all 10 rows were added, how many triangles would appear in the entire figure? 100 35. Community College Tuition The following graph shows the annual tuition, to the nearest hundred dollars, at Clarence Community College for the years 2020–2024. a) Assuming this trend continues, use the graph to predict the annual tuition for the year 2025. $3700 b) Explain how you are using inductive reasoning to determine your answer. We are using specific cases to make a prediction. 36. Gym Membership Fees The following graph shows the annual membership fees for Crackle Fitness for the years 2020–2024. a) Assuming this trend continues, use the graph to predict the annual membership fee for the year 2025. $415 b) Explain how you are using inductive reasoning to determine your answer. We are using specific cases to make a prediction. $0 $50 $100 $150 $200 $250 $300 $350 $450 $400 2020 Annual Membership Fees Annual Membership Fees for Crackle Fitness 2021 2022 2023 2024 Year 30. Sum of the Digits a) Select a variety of one- and two-digit numbers between 1 and 99 and multiply each by 9. Record your results. Answers will vary. b) Determine the sum of the digits in each of your products in part (a). If the sum is not a one-digit number, determine the sum of the digits of the resulting sum again until you obtain a one-digit number. The sum is 9. c) Make a conjecture about the sum of the digits when a one- or two-digit number is multiplied by 9. The sum of the digits in the product when a one- or two-digit number is multiplied by 9 is 9. 31. A Square Pattern The ancient Greeks labeled certain numbers as square numbers. The numbers 1, 4, 9, 16, 25, and so on are square numbers. 1 4 9 16 25 a) Determine the next three square numbers. 36, 49, 64 b) Describe a procedure to determine the next five square numbers without drawing the figures. Square 6, 7, 8, 9 and 10 c) Is 72 a square number? Explain how you determined your answer. No, 72 is between 82 and 9 , 2 so it is not a square number. 32. A Triangular Pattern The ancient Greeks labeled certain numbers as triangular numbers. The numbers 1, 3, 6, 10, 15, 21, and so on are triangular numbers. 1 3 6 10 15 21 a) Can you determine the next two triangular numbers? 28, 36 b) Describe a procedure to determine the next five triangular numbers without drawing the figures. * c) Is 72 a triangular number? Explain how you determined your answer. No 33. Quilt Design The pattern shown is taken from a quilt design known as a triple Irish chain. Complete the color pattern by indicating the color assigned to each square. Blue: 1, 5, 7, 10, 12; Purple: 2, 4, 6, 9, 11; Yellow: 3, 8 1 8 9 10 11 4 5 6 2 3 7 12 *See Instructor Answer Appendix Annual Tuition at Clarence Community College $0 $500 $1000 $1500 $2000 $2500 $3000 $3500 $4000 2020 Annual Tuition 2021 2022 2023 2024 Year
RkJQdWJsaXNoZXIy NjM5ODQ=