916 CHAPTER 13 Counting and Probability 31. Demographics The following data represent the marital status of men 15 years old and older in the U.S. in 2022. Source: United States Census Bureau. Number (in millions) Marital Status Married Widowed Divorced Separated Never married 63.8 3.7 11.0 2.0 48.8 (a) Determine the number of men 15 years old and older who are widowed or divorced. (b) Determine the number of men 15 years old and older who are married, divorced, or separated. 32. Demographics The following data represent the marital status of women 15 years old and older in the U.S. in 2022. Source: United States Census Bureau. Number (in millions) Marital Status Married Widowed Divorced Separated Never married 64.0 11.5 14.6 2.6 42.7 (a) Determine the number of women 15 years old and older who are divorced or separated. (b) Determine the number of women 15 years old and older who are married, widowed, or divorced. 33. Stock Portfolios As a financial planner, you are asked to select one stock each from the following groups: 8 Dow Jones stocks, 15 NASDAQ stocks, and 4 global stocks. How many different portfolios are possible? 34. Make up a problem different from any found in the text that requires the addition principle of counting to solve. Give it to a friend to solve and critique. 35. Investigate the notion of counting as it relates to infinite sets. Write an essay on your findings. Explaining Concepts Problems 36–45 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. Retain Your Knowledge 36. Graph ( ) ( ) − + + = x y 2 1 9. 2 2 37. If the sides of a triangle are = = a b 2, 2, and = c 3, find the measures of the three angles. Round to the nearest tenth. 38. Find all the real zeros of the function: ( ) ( ) ( ) = − − − f x x x x 2 3 10 2 39. Solve: + = − x log log 2 2 3 3 40. Solve: = x x 72 3 41. Solve the system: x y x y 5 1 2 − = − =− ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ 42. Multiply: ( ) ( ) − − + x x x 2 7 3 5 4 2 43. Determine whether the infinite series converges or diverges. If it converges, find the sum. + + + + 4 12 5 36 25 108 125 44. If ( ) ( ) ( ) ′′ = − + − − − f x x x 2 3 2 1 3 2 , 1/3 2/3 find where (a) ( ) ′′ = f x 0 (b) ( ) ′′ f x is undefined 45. Find the partial fraction decomposition: + + + + x x x x x 3 15 5 2 2 3 2 ‘Are You Prepared?’ Answers 1. union 2. intersection 3. True 4. True 13.2 Permutations and Combinations Now Work the ‘Are You Prepared?’ problems on page 923. • Factorial (Section 12.1, p. 858) • Binomial Coefficient (Section 12.6, pp. 899–902) PREPARING FOR THIS SECTION Before getting started, review the following: OBJECTIVES 1 Solve Counting Problems Using Permutations Involving n Distinct Objects (p. 917) 2 Solve Counting Problems Using Combinations (p. 919) 3 Solve Counting Problems Using Permutations Involving n Nondistinct Objects (p. 922)
RkJQdWJsaXNoZXIy NjM5ODQ=