MATH106 6380

Quiz 4

1. An orchestra has 44 members. 12 play the saxophone, 15 play the clarinet, and 7 play both saxophone and clarinet. How many orchestra members play neither the saxophone nor the clarinet?

Answer: ___________________________

2. List the elements of the sets defined by the following:

a. {3, 21, 6, 12} { 3, 21, 6, 12} _____________________________

b. _____________________________

c. {4, 6, 8, 11} { 4, 6, 8, 11} _____________________________

3. Maximize objective profit function

subject to:

Attach image from graphing calculator or use grid below if desired must show feasible region and identify critical (corner) points to receive full credit!

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Maximum profit occurs at x = _________ , y = ____________

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:

	Labor hours - Sociologist	Labor hours research assistant	MINIMUM labor hours needed per week
Fieldwork	10	30	180
Research center	20	10	160
Costs per week	$500	$300

How many sociologists and how many research assistants should be hired to MINIMIZE the cost and meet the weekly labor-hour requirement? What is the MINIMUM weekly cost?

Answers: a. _____ sociologists, _____ research assistants

b. ____________________________________________

5. A college offers 2 introductory courses in history, 3 in science, 2 in philosophy, 4 in mathematics, and 3 in English. If a freshman takes one course in each area during her first semester, how many course selections are possible?

Answer: _____________________________________

6. If , complete the following table (see Content > Course Content > Week 4 Activities in our LEO classroom and select Contingency Table Construction and Use if you need help completing this table)

	A	A	Totals
B
B
Totals

7. A couple is planning to have 4 children. They could be all girls, all boys, or some of each. How many groupings are possible? Solve using the multiplication principle of counting.

Answer: ________________________________

8. Evaluate the expression:

__________________________________

__________________________________

9. Because of declining profits, corporate headquarters at Belchfire Motor Industries has decided to keep only 4 of its 7 existing auto assembly plants open after summer 2016. How many groupings of the four plants to remain open are possible? (Hint: Does order matter?)

Answer: _______________________________

10. Apocalyptic Biomedical Company must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief marketing officer. There are 11 qualified candidates. How many different ways can the 4 officers be appointed? (Hint: Does order matter?)

Answer: _______________________________

Do the following problems using the expected value concepts learned in this section

11. In a town, 40% of the men and 30% of the women are overweight. If the town has 46% men and 54% women, what percent of the people are overweight?

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