36 CHAPTER 1 Critical Thinking Skills In Exercises 22 and 23, refer to the following graph, which illustrates the average daily high temperatures by month for the cities of Tampa and Chicago. 20 40 60 80 100 0 Month Degrees Fahrenheit Average Daily High Temperatures in Tampa and Chicago January February March April May June July August September October November December Tampa Chicago 10. Pick any number and multiply the number by 10. Add 5 to the product. Divide the sum by 5. Subtract 1 from the quotient. a) What is the relationship between the number you started with and the final number? The final number is twice the original number. b) Arbitrarily select some different numbers and repeat the process. Record the original number and the results. The final number is twice the original number. c) Make a conjecture about the original number and the final number. The final number is twice the original number. d) Prove, using deductive reasoning, the conjecture you made in part (c). n n n n n n n , 10 , 10 5, 10 5 5 2 1, 2 1 1 2 + + = + + − = 11. Pick any number between 1 and 20. Add 5 to the number. Multiply the sum by 6. Subtract 12 from the product. Divide the difference by 2. Divide the quotient by 3. Subtract the number you started with from the quotient. What is your answer? Try this process with a different number. Make a conjecture as to what your final answer will always be. This process will always result in an answer of 3. 12. Counterexample Determine a counterexample to the statement “The sum of two squares is an even number.” 1 2 5 2 2 + = 1.2 In Exercises 13–25, estimate the answer. Your answers may vary from those given in the back of the book, depending on how you round to arrive at the answer, but your answers should be something near the answers given. 13. × 205,123 4002 800,000,000 14. 215.9 128.752 3.6 861 792 + + + + 2000 15. 21% of 2095 400 16. Distance Estimate the distance from your wrist to your elbow and estimate the length of your foot. Which do you think is greater? With the help of a friend, measure both lengths to determine which is longer. Answers will vary. 17. Cost Estimate the cost of 48 decorative bricks if one brick costs $3.97. $200 18. Sales Tax Estimate the sales tax on a boat that costs $21,000 if the sales tax rate is 8%. $1600 19. Walking Speed Estimate your average walking speed in miles per hour if you walked 1.1 mi in 22 min. 3 mph 20. Groceries Estimate the total cost of six grocery items that cost $2.49, $0.79, $1.89, $0.10, $2.19, and $6.75. $14.00 21. A Walking Path The scale of the map is in. 0.1 mi. 1 4 = Estimate the distance of the walking path indicated in red. 2 mi HISTORIC PHILADELPHIA Independence Hall Liberty Bell U.S. Custom House Source: NOAA.gov 22. January Temperatures in Tampa and Chicago Estimate the difference in the average daily high temperatures for Tampa and Chicago in January. 40 F 23. July Temperatures in Tampa and Chicago Estimate the difference in the average daily high temperatures for Tampa and Chicago in July. 10 F 24. Estimating an Area If each square represents one square unit, estimate the size of the shaded area. 13 square units
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