Finite Mathematics

Record your answers and work on the separate answer sheet provided. PLEASE SEE BOTH ATTACHED FILES

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

• – 2. Lakisha is a financial planner. One of her clients has $24,000 to invest in AAA and B bonds. The AAA bonds yield an average of 6%, and the B bonds yield 10%. Her client requires that at least three times as much money should be invested in AAA bonds as in B bonds. If (“x”) represents the amount of money invested in AAA bonds, and (“y”) represents the amount of money invested in B bonds, how should Lakisha invest her client’s money in to maximize the investment income I earned?
  • Identify the constraint on amount invested in B bonds:
  • State the objective function.
  • Which of the following statements is true:
    • If events E and F are independent events, then ( ∩ ) = ∅.
    • If an event cannot possibly occur, then the probability of the event is negative.
    • If events E and F are mutually exclusive events, then ( ∩ ) = ∅.
    • Conditional probability is defined as
  • Which histogram below accurately reflects 30 survey responses presented in the following frequency table?
  • Find the equation of the line passing through (8, 3) and (−6, −5): 5.
  • The shaded “feasible region” graphed below satisfies which system of linear inequalities?
  • The Johnson family buys a new home for $298,000. They make a down payment of 20% and finance the rest with a 30-year fixed mortgage at an annual interest rate of 4.35% compounded monthly. What is the amount of their monthly mortgage payment to amortize the loan?
  • The slope m of a line perpendicular to graph of equation 5x – 3y = 17 equals:
    • – 5
  • Given that ≥ 0 , ≥ 0, 3 + ≤ 9, and + 2 ≤ 8, which of the corner points for the system of linear inequalities graphed below maximizes the objective function P = 3x + 4y ?
  • The mean lifetime for a Zap™ car battery is 180 weeks, with a standard deviation of 15 weeks. Assuming a normal distribution, what is the probability that the measured lifetime of a randomly chosen Zap™ car battery is less than 150 weeks?
  • Two balls are drawn in succession, without replacement, out of a box containing 5 red and 3 white balls. What is the probability that the first ball drawn is white and the second ball drawn is white?
    • 37 56
    • 5 15
    • 3 32
    • 3 28
  • A local bakery is contracted to bake pies for local grocery stores to sell. The bakery’s daily production costs are $2.00 per pie baked plus a fixed cost of $576. The pies are sold by the grocery stores for $6.50 each. How many total pies must be sold daily for the local bakery to break even? Round answer to the nearest whole pie.
  • Consider the following graph of a line.

A. + ≥ 24000 C. 3 + ≥ 24000

B. ≥ 3 D. ≤ 3

A. = 0.06 + 0.10 C. = 1.10 + 1.06

B. = 0.10 + 0.06 D. = 1.06 + 1.10

1.

2.

3.

( | ) = ( ∩ )

( )

4.

Value	Frequency
0	XX
1	XXXXXXXXX
2	XXXXXX
3	XXXXX
4	XXX
5	XXX
6	XX

A. x – y = 5 B. 4x – 3y = 21 C. x – y = – 1 D. 4x – 7y = 11

6.

	A. 3 + 2 ≤ 18	+ 2 ≥ 10	≥ 0	≥ 0
	B. 3 + 2 ≥ 18	+ 2 ≤ 10	≥ 0	≥ 0
	C. 3 + 2 ≤ 18	+ 2 ≤ 10	≥ 0	≥ 0
	D. 3 + 2 ≥ 18	+ 2 ≥ 10	≥ 0	≥ 0

7. A. $1186.78 B. $1182.57 C. $1187.63 D. $1483.48

B. – (5/3)

C. + (5/3)

8.

D. Cannot determine without knowing at least one ordered pair on perpendicular line

9.

A. (0, 9) C. (3, 0)

B. (2, 3) D. (0, 4)

10.

A. 0.0228 C. 0.1587

B. 0.3413 D. 0.6826

11.

12.

A. 70 C. 832

B. 68 D. 128

SHORT ANSWER (work NOT required to be shown)

• State the y-intercept.
• Determine the slope.
• Find the slope-intercept form of the equation of the line.
  • Use the following table showing political party affiliation of each of 66 US Senate members in Jan 2017, and when they are up for re-election:

(Source: www.senate.gov)

Up for Re-election	Democrat	Republican	Other	Total
Nov 2018	23	8	2	33
Nov 2020	11	22	0	33
Total	34	30	2	66

(Report your answers as fractions or as decimal values rounded to the nearest hundredth.) Find the probability that a single randomly selected senator is:

• Republican or is up for re-election in November 2020: Answer:
• Democrat and is up for re-election in November 2018: Answer:
  • Seventeen people are summoned to jury duty. 10 are women and 7 are men.

(c)up for re-election in November 2018 given that

the selected Senator is Republican: Answer:

Use the following information to answer parts a-c.

a. List elements of ∩ ′ : b. List elements of ( ∪ ) − ( ∩ ) :

c. List elements of ′ ∩ ′ :

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

• In how many ways can 12 jurists be randomly selected out of the 17 people? Show work.
• In how many ways can 12 jurists be chosen, if 7 must be women and 5 must be men? Show work.
• If 12 jurists are randomly selected from the 17 people, what is the probability that 5 are men and 7 are women? Round answer to nearest ten-thousandth (4 places after decimal). Show work.
  • Solve the system of equations using substitution, elimination by addition, or augmented matrix methods (your choice). Show work.
  • A freight-hauling firm estimates that it will need a new forklift in six years. The estimated cost of the vehicle is $50,000. The company sets up a sinking fund that pays 8% compounded semiannually, into which it will make semiannual payments to achieve the goal. Calculate the size of the payments. Show work.
  • According to Symantec Corporation, “2016 Internet Security Threat Report” (https://www.symantec.com/security-center/threat-report), “spear-phishing” cyberattacks against American small businesses are steadily increasing. 18% of all “spear-phishing” cyberattacks against American businesses in 2011 targeted “small” businesses (those with less than 250 employees). In 2015, 43% of all “spear-phishing” cyberattacks against American businesses targeted “small” businesses.

5 − 2 = 7

4 − 3 = 0

A. $2662.09 C. $3327.61

B. $4262.09 D. $5327.61

• Which of the following linear equations could be used to predict annual percentage of all “spear-phishing” cyberattacks against US businesses that target “small” businesses (“y”) in a given year “x” since 2011, where x = 0 represents the year 2011? Explain/show work.
• Use the equation from part (a) to predict the percentage of all “spear-phishing” cyberattacks against US businesses that will target “small” businesses in the year 2022. Round answer to nearest tenth of a percent. Show work.
• Fill in the blanks to interpret the slope of the equation: The rate of change of percent of all “spear-phishing” cyberattacks against US businesses that target “small” businesses with respect to time is per . (Include units of measurement.)
  • Bank A pays 5.0% interest compounded quarterly, while Bank B pays 4.98% compounded monthly. Which bank pays more interest? Explain. Show work
  • A recent poll of Smallville voters showed that 50% of them support the mayor. What is the probability that in a random sample of 14 Smallville voters, exactly 7 of them support the mayor? Round answer to the nearest thousandth (three places after decimal). Show work.
  • The feasible region in the graph below is bounded by lines x = 0, y = 0, and the lines shown. Find the coordinates of corner point A. Show work.
  • A UMUC criminal justice grad works in the Smith County public defenders’ office tracking weekly caseload to identify trends. Numbers for 6 recent weeks are 68, 66, 66, 43, 71, and 70.

A. = 6.25 + 18 C. = 0.16 + 2011

B. = 0.16 + 18 D. = 6.25 + 2011

• State the mode (if one exists).
• Find the median. Show work/explanation.
• Determine the sample mean. Show work
• Using the sample mean found in part (c), and given that the sample standard deviation of the data set above is 10.49, what percentage of the data set falls within one standard deviation of the mean? Show work/explanation.
  • If the probability distribution for the random variable X is given in the table, what is the expected value of X? Show work.
  • A marketing survey of 2000 randomly-selected convenience store customers found that 1415 of them bought a glazed donut yesterday. 1605 said they bought a frosted crème-filled donut yesterday. 180 customers said they bought neither yesterday.

(d)

A. 68.3% C. 66.7%

B. 83.3% D. 50.0%

xi	– 30	15	30	100
pi	0.45	0.25	0.20	0.10

• What is the probability that a single randomly-selected customer bought only a frosted crème-filled donut yesterday? Round answer to nearest hundredth. Show work.
• Let G = {customers who bought a glazed donut yesterday} and C = {customers who bought a frosted crème-filled donut yesterday}. Determine the number of attendees belonging to each of the regions I, II, III, IV.

Region I: Region II: Region III: Region IV: