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Provide answer on a separate Word Doc., and please show your work for the non multiple choice questions.

There are 25 problems.

Problems #1–12 are Multiple Choice.

Problems #13–15 are Short Answer. (Work not required to be shown) Problems #16–25 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Which of the corner points for the system of linear inequalities graphed below maximizes the objective function P = 5x + 6y?

1. A. (0, 0) C. (1, 2)

B. (0, 3) D. (2, 0)

( P a g e 1 o f 9 )

2. Which of the following statements is NOT true:

2. A. A probability must be less than or equal to 1.

B. If an event cannot possibly occur, then the probability of the event is zero (0). C. If events G and H are independent events, then P (G ∩ H) = 0.

D. If only two outcomes are possible for an experiment, then the sum of the probabilities of

the outcomes = 1.

3. Find the equation of the line passing through (4, – 1) and (3, 1):

3. ____

A. 5x – 4y = 11 B. 3x + 4y = 8 C. 2x + 5y = 3 D. 2x + y = 7

4. The Johnson family buys a new house for $300,000, makes a down payment of 20%, and finances the rest with a 30-year fixed mortgage at an annual interest rate of 4.2% compounded monthly. What is the amount of the monthly loan payment to amortize the loan?

4. A. $1,173.64 C. $1,506.67

B. $1,467.05 D. $1,883.33

5. The mean time to get an oil change done at Leaky’s Garage is 58 minutes, with a standard deviation of 12 minutes. Assuming a normal distribution, what is the probability that a randomly chosen customer experiences an oil change done between 46 and 58 minutes?

A. 0.3413 C. 0.5000

B. 0.4772 D. 0.6826

6. In the dice game “Yahtzee”, five-of-a-kind gives the maximum score for a single turn. What

is the probability of getting 5 “3”s in a single roll of 5 six-sided dice?

6. _______

A. C.

B. D.

7. Which of the following statements is FALSE? 7.

A. If all of the data values in a data set are identical, then the standard deviation is 0. B. The median is one of the measures indicating approximate center of distribution. C. The standard deviation is the square of the variance.

D. The variance can never be a negative number.

8. – 9. Leaky’s Garage employs supervisors and technicians. According to the union contract, a supervisor does 2 brake jobs and 3 mufflers per day, whereas a technician does 6 brake jobs and

3 mufflers per day. The home office requires enough staff on hand for at least 24 brake jobs per day and at least 18 mufflers per day. A supervisor makes $90 per day and a technician makes

$100 per day. The home office is looking to minimize daily labor costs. Let x represent number of supervisors and y represent number of technicians.

8. Identify the daily production constraint for brakes:

A. C.

B. D.

9. State the objective function.

A. C.

B. D.

10. Identify the row operation that produces the resulting matrix: 10.

A. 2𝑅1 ↔ 𝑅2 C. 2𝑅2 + 𝑅1 →𝑅1

B. 2𝑅1 →𝑅1 D. 2𝑅1 + 𝑅2 →𝑅2

11. Determine which region defines the solution region of the following system of linear inequalities:

11.

III

A. Region I C. Region III B. Region II D. Region IV

12. A recent survey of Smallville residents revealed that 13,000 townspeople get their news from the local paper, 21,000 get it from the Internet, and 7,000 get their news information from both the local paper and the Internet. How many people get their news from either the local paper OR the Internet?

12.

A.	34,000	C.	20,000
B.	7,000	D.	27,000

SHORT ANSWER (work NOT required to be shown)

13. For the linear equation X + 2y = 6:

a. Determine the slope. ____________________________

b. Determine x – intercept if it exists:

c. Determine y – intercept if it exists:

d. Express equation in slope-intercept form:

14. Let A = {2, 4, 6, 8, 10, 12, 14, 16}, let B = {– 2, – 4, 6, – 10, 12, – 14}, and let U = A ∪ B.

List the elements of B’ :

List the elements of A ∩ B:

How many elements comprise U ?

15. 1000 students at a particular college were asked their status (full-time or part-time) and their chosen undergraduate degree field of study. The following table was obtained.

Undergraduate Major	Full-time	Part-time	Total
Business	183	23	206
Cybersecurity	52	84	136
Health Sciences	215	111	326
Social Sciences	170	162	332
Total	620	380	1000

(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)

Find the probability that a randomly selected student:

(a) majors in cybersecurity and is part-time. Answer:

(b) majors in cybersecurity or is part-time. Answer:

SHORT ANSWER, with work required to be shown, as indicated.

16. Eleven people work in an office. 7 are women and 4 are men. The flu virus is coming. (a) In how many ways can the flu virus randomly select 6 workers out of the 11 to get sick?

Show work.

(b) In how many ways can the flu choose 6 workers, if 4 must be women and 2 must be men?

Show work.

(c) If the flu virus randomly selects 6 workers from the 11 in the office, what is the probability that 2 are men and 4 are women? Answer in fraction form, or as decimal to nearest ten- thousandth (4 places after decimal). Show work.

17. Solve the system of equations using substitution, elimination by addition, or augmented matrix methods (your choice). Show work.

3x + 2y = 4

4x + 3y = 7

18. Cara needs $9,000 in 11 years. What amount can she deposit at the end of each quarter at

8% annual interest compounded quarterly so she will have her $9,000? Show work.

A. $540.69 C. $129.49

B. $134.01 D. $12519

19. According to the US Department of Justice’s Bureau of Justice Statistics, 2.4% of US firearms purchase/transfer applications submitted in 1999 were rejected due to background check information. In 2009, the rejection rate of applications submitted due to background check information was 1.4%.

(a) Which of the following linear equations could be used to predict application rejection rate y in a given year x, where x = 0 represents the year 1999? Explain/show work.

y = – 0.1x + 2.4

y = – 10x + 2.4

y = – 0.1x + 1999

y = – 10 x + 1999

(b) Use the equation from part (a) to predict the firearms application rejection rate (%) in the year 2022. Round answer to nearest hundredth of a percent. Show work.

(c) Fill in the blanks to interpret the slope of the equation: The rate of change of application rejection rate with respect to time is

per . (Include units of measurement.)

20. LaToya’s savings account has a current balance of $9200.00. Exactly 20 years from now, how much interest will she have earned at 5% compounded annually? Show work

21. According to a recent Pew Research Center report, 0.8 is the probability that a randomly selected American adult knows what Twitter™ is. Eight American adults are randomly selected. Find the probability that exactly 7 of the 8 American adults randomly selected knows what Twitter™ is. Round answer to nearest ten-thousandth (4 places after decimal). Show work

22. The feasible region shown below is bounded by lines x + y = 3, 4x – y = 6, and y = 0. Find the coordinates of corner point A. Show work.

23. A developmental psychologist studies the number of words that eight children have learned at a particular age. The numbers are 11, 20, 7, 4, 5, 12, 9, and 20.

(a) State the mode (if one exists).

(b) Find the median. Show work/explanation.

(d) Using the sample mean found in part (c), and given that the sample standard deviation of the data set above is 6.2, what percentage of the data set falls within one standard deviation of the mean? Show work/explanation.

A. 87.5% C. 68.3% B. 75.0% D. 62.5%

(d)

24. A local car rental agency charted daily demand as shown in the following table:

Number of customers	6	8	10	12	14
Probability	0.15	0.20	0.25	0.30	0.10

Find the expected number of customers. Show work.

25. An instructor surveyed her class of 45 students and found that most of them watched TV and/or got on the Internet last night. 10 students said they watched TV but did not get on the Internet. 16 students said they got on the Web but did not watch TV last night. 41 of the students watched TV or got on the Internet (or both) last night.

(a) How many of the students watched TV and got on the Internet last night? Show work.

(b) Let T = {students who watched TV} and W = {students who got on the Internet}. Determine the number of attendees belonging to each of the regions I, II, III, IV.

T W

I III

Region I:

Region II:

Region III:

Region IV: