1. A politician received 12,457 votes in his first election, and 15,322 in his second election. 9,345 voted for him in both the first and second elections. How many people voted for this politician in the first OR second election? 2. Write the resulting set using the listing method: a. {5, 7, 8, 13} { - 7, - 5, 8, - 13} b. { x|x 5 =32} _____________________________ _____________________________ c. {3, 21, 6, 12} { - 3, - 21, - 6, - 12} _____________________________ 3. Maximize P=x+ 3 y subject to: (use following grid if desired) 2xy4 x +2 y 4 y6 x , y 0 1 y x . 4. A city council voted to conduct a study on inner-city community problems using sociologists and research assistants from UMUC. Allocation of time and costs per week are given in the following table: Fieldwork Research center Costs per week a. Labor hours Sociologist 10 30 $500 Labor hours - research assistant 30 10 $300 MINIMUM labor hours needed per week 180 140 How many sociologists and how many research assistants should be hired to MINIMIZE the cost and meet the weekly labor-hour requirement? b. What is the MINIMUM weekly cost? 2 5. A college offers 3 introductory courses in history, 4 in science, 3 in philosophy, 4 in mathematics, and 2 in English. If a freshman takes one course in each area during her first semester, how any course selections are possible? 6. If n ( A ' )=35, n ( B' )=75, n ( A ' B ' )=95, n ( U )=120 , complete the following table: A A' Totals B B' Totals 7. A couple is planning to have 4 children. They could be all girls, all boys, or a combination. How many combinations are possible? Solve using the multiplication principle of counting. 8. Evaluate the expression: 3 a. 8! ( 86 ) ! __________________________________ b. ( n+ 2 ) ! (n aninteger , n 1) 4 ! ( n1 ) ! __________________________________ 9. Winning the Armageddon Lottery's \"Match 6 Lotto\" jackpot requires ticket buyers to pick 6 different numbers from 1 to 49, and the same 6 numbers must be drawn in the lottery. The winning numbers can be drawn in any order, so order does not make a difference. What number of different possible 6-number combinations exist? 10. The Apocalyptic Fitness Equipment Corporation must appoint a president, chief executive officer (CEO), and chief operating officer (COO). There are 11 qualified candidates. How many different ways can the officers be appointed? 4