Expert answer:Finite Mathematics
Expert answer: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 asWhich 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:– 5Given 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?37 565 153 323 28A 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 workA 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 workUsing 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:
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Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator.
Record your answers and work in this document.
There are 25 problems.
Problems #1-12 are multiple choice. Record your choice for each problem.
Problems #13-15 are short answer. Record your answer for each problem.
Problems #16-25 are short answer with work required when directed. When requested, show all
work and write all answers in the spaces allotted on the following pages. You may type your
work using plain-text formatting or an equation editor, or you may hand-write your work and
scan it. In either case, show work neatly and correctly, following standard mathematical
conventions. Each step should follow clearly and completely from the previous step. If
necessary, you may attach extra pages.
Upload this answer sheet (with your extra work, if needed) to the MATH 106 Final Exam
folder under the “Assignments” link in LEO classroom. DO NOT SUBMIT THE EXAM
ITSELF (it will not be accepted under any circumstance).
You must complete the exam individually. Neither collaboration nor consultation with
others is allowed. Your exam will receive a zero grade unless you complete the following
honor statement.
Please sign (or type) your name below the following honor statement:
I have completed this final examination myself, working independently and not consulting
anyone except the instructor. I have neither given nor received help on this final examination.
I have not used any instructors’ solutions manual or any online problem solving service.
Name _____________________
Date___________________
MULTIPLE CHOICE. Record your answer choices.
1.
7.
2.
8.
3.
9.
4.
10.
5.
11.
6.
12.
SHORT ANSWER. Record your answers below.
13.
(a)
(b)
(c)
14.
(a)
(b)
(c)
15.
(a)
(b)
(c)
SHORT ANSWER with Work Shown. Record your answers and work.
Problem
Number
Solution
Answers:
(a)
(b)
(c)
Work for (a), (b), and (c):
16
Answer:
Work:
17
Answer:
Work:
18
Answers:
(a)
(b)
(c)
Work for (a) and (b):
19
Answer:
Work:
20
Answer:
Work:
21
Answer:
Work:
22
Answers:
(a)
(b)
(c)
(d)
23
Work for (b), (c), and (d):
Answer:
Work:
24
Answers:
(a)
(b) Region I:
Region II:
Region III:
Region IV:
25
Work:
2178-OL4-7980-V1
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed. Use of instructors’ solutions
manuals or online problem solving services in NOT allowed.
Record your answers and work on the separate answer sheet provided.
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. – 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?
1. Identify the constraint on amount invested in B bonds:
1.
A. + ≥ 24000
C. 3 + ≥ 24000
B. ≥ 3
D. ≤ 3
2. State the objective function.
2.
A. = 0.06 + 0.10
C. = 1.10 + 1.06
B. = 0.10 + 0.06
D.
= 1.06 + 1.10
3. Which of the following statements is true:
3.
A.
B.
C.
D.
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
( ∩ )
( | ) =
( )
Page 1 of 10
2178-OL4-7980-V1
4. Which histogram below accurately reflects 30 survey responses presented in the following
frequency table?
4.
Value
Frequency
0
XX
1
XXXXXXXXX
2
XXXXXX
3
XXXXX
4
XXX
5
XXX
6
XX
HISTOGRAM B
HISTOGRAM A
8
7
6
5
4
3
2
1
0
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
0
HISTOGRAM C
1
2
3
4
5
6
5
6
HISTOGRAM D
10
9
8
7
6
5
4
3
2
1
0
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
0
1
2
5. Find the equation of the line passing through (8, 3) and (−6, −5):
A. x – y = 5
B. 4x – 3y = 21
C. x – y = – 1
3
4
5.
D. 4x – 7y = 11
Page 2 of 10
2178-OL4-7980-V1
6. The shaded “feasible region” graphed below satisfies which system of linear inequalities?
6.
12
10
(0,9)
8
6
(0,5)
4
(4,3)
2
0
-1
0
1
2
3
4
5
6
7
8
9
10
11
≥0
≥0
≥0
≥0
-2
-4
-6
-8
-10
A.
B.
C.
D.
3 + 2
3 + 2
3 + 2
3 + 2
≤ 18
≥ 18
≤ 18
≥ 18
+ 2 ≥ 10
+ 2 ≤ 10
+ 2 ≤ 10
+ 2 ≥ 10
≥0
≥0
≥0
≥0
7. 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?
7.
A. $1186.78
B. $1182.57
C. $1187.63
D. $1483.48
8. The slope m of a line perpendicular to graph of equation 5x – 3y = 17 equals:
8.
–5
A.
B. – (5/3)
C. + (5/3)
D. Cannot determine without knowing at least one ordered pair on perpendicular line
Page 3 of 10
2178-OL4-7980-V1
9. 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 ?
9.
A. (0, 9)
C. (3, 0)
B. (2, 3)
D. (0, 4)
10. 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?
10.
A. 0.0228
C. 0.1587
B. 0.3413
D. 0.6826
11. 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?
11.
37
5
3
3
A. 56
B. 15
C. 32
D. 28
12. 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.
12.
A. 70
C. 832
B. 68
D.
128
Page 4 of 10
2178-OL4-7980-V1
SHORT ANSWER (work NOT required to be shown)
13. Consider the following graph of a line.
(a) State the y-intercept.
(b) Determine the slope.
(c) Find the slope-intercept form of the
equation of the line.
14. 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
Nov 2018
Nov 2020
Total
Democrat
23
11
34
Republican
8
22
30
Other
2
0
2
Total
33
33
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:
(a) Republican or is up for re-election in November 2020:
Answer:
(b) Democrat and is up for re-election in November 2018:
Answer:
(c) up for re-election in November 2018 given that
the selected Senator is Republican:
Answer:
Page 5 of 10
2178-OL4-7980-V1
15. 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.
16. Seventeen people are summoned to jury duty. 10 are women and 7 are men.
(a) In how many ways can 12 jurists be randomly selected out of the 17 people? Show work.
(b) In how many ways can 12 jurists be chosen, if 7 must be women and 5 must be men? Show
work.
(c) 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.
Page 6 of 10
MATH 106 Finite Mathematics
2178-OL4-7980-V1
17. Solve the system of equations using substitution, elimination by addition, or augmented
matrix methods (your choice). Show work.
5 − 2 = 7
4 − 3 = 0
18. 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.
A. $2662.09
C. $3327.61
B. $4262.09
D. $5327.61
19. 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.
(a) 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.
A. = 6.25 + 18
C. = 0.16 + 2011
B. = 0.16 + 18
D. = 6.25 + 2011
(b) 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.
(c) 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.)
Page 7 of 10
MATH 106 Finite Mathematics
2178-OL4-7980-V1
20. Bank A pays 5.0% interest compounded quarterly, while Bank B pays 4.98% compounded
monthly. Which bank pays more interest? Explain. Show work
21. 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.
22. 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.
14
12
10
8
6
4
2
0
-2
0
1
2
3
4
5
6
7
8
9
10
11
-4
Page 8 of 10
MATH 106 Finite Mathematics
2178-OL4-7980-V1
23. 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) State the mode (if one exists).
(b) Find the median. Show work/explanation.
(c) Determine the sample mean. Show work
(d) 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.
(d)
A. 68.3%
C. 66.7%
B. 83.3%
D. 50.0%
24. If the probability distribution for the random variable X is given in the table, what is the
expected value of X? Show work.
xi
pi
– 30
0.45
15
0.25
30
0.20
100
0.10
Page 9 of 10
MATH 106 Finite Mathematics
2178-OL4-7980-V1
25. 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.
(a) 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.
(b) 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.
II
III
IV
Region I:
Region II:
Region III:
Region IV:
Page 10 of 10
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