Quiz 4

MATH106 – 6380

Quiz 4

Directions:

• Read and sign the academic honesty certification statement below, then read the questions carefully and answer them to the best of your ability. You may write your answers on this sheet or on the sheet you do your work on, but PLEASE show your work. Answers shown without work will get no credit. Work shown with unclear derivations or key steps missing in the derivations of answers will not lead to full credit (even if the answer is correct). Follow directions as outlined in Quizzes folder under the “Assignments” link on our LEO classroom NavBar.

• The completed quiz that you submit/upload must be contained in one file (Word or .pdf format). Uploaded work in other formats or separated over more than one file will not be accepted.

• Test & work is due as specified in “Course Schedule”. I cannot accept any late submissions! This is open-book/notes: calculators, & graphing devices are authorized for use. Good luck!

Show your work!

• Evaluate manually and write/type it on the quiz document, or

• Provide scan/image of work done on calculator or other software, or

• Insert chart/graphic if using software that produces such objects.

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!

.

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:

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

1. 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)

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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