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MATH 106 Finite Mathematics
Fall, 2012, 4.1
Page 1 of 10
MATH 106 FINAL EXAMINATION
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.
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. Tom purchases a car for $27,000, makes a down payment of 20%, and finances the rest with a
4-year car loan at an annual interest rate of 3.3% compounded monthly. What is the amount of
his monthly loan payment?
1. _______
A. $480.97
B. $509.40
C. $601.21
D. $636.75
2. Find the result of performing the row operation (5)R1 + R2 → R2 2. _______
�2 −13 9 �
1
−5
�
A. �10 −53 9 �
5
−5
� B. � 2 −113 9 �
1
−5
�
C. � 2 −113 4 �
1
0
� D. � 2 −117 44 �
1
−24
�
MATH 106 Finite Mathematics Fall, 2012, 4.1
Page 2 of 10
3. Find the values of x and y that maximize the objective function 3x + 5y for the feasible
region shown below. 3. _______
A. (x, y) = (0, 20)
B. (x, y) = (5, 15)
C. (x, y) = (8, 10)
D. (x, y) = (10, 0)
4. Adult American have normally distributed heights with a mean of 5.8 feet and a standard
deviation of 0.2 feet. What is the probability that a randomly chosen adult American male will
have a height between 5.6 feet and 6.0 feet? 4. ______
A. 0.9544
B. 0.7580
C. 0.6826
D. 0.5000
MATH 106 Finite Mathematics Fall, 2012, 4.1
Page 3 of 10
5. Determine which shaded region corresponds to the solution region of the system of linear
inequalities
x + 2y ≥ 4
4x + y ≥ 4
x ≥ 0
y ≥ 0
5. _______
GRAPH A.
GRAPH B.
GRAPH C.
GRAPH D.
MATH 106 Finite Mathematics Fall, 2012, 4.1
Page 4 of 10
For #6 and #7:
A merchant makes two raisin nut mixtures.
Each box of mixture A contains 10 ounces of peanuts and 3 ounces of raisins, and sells for $2.80.
Each box of mixture B contains 14 ounces of peanuts and 5 ounces of raisins, and sells for $4.00.
The company has available 5,200 ounces of peanuts and 1,800 ounces of raisins. The merchant
will try to sell the amount of each mixture that maximizes income.
Let x be the number of boxes of mixture A and let y be the number of boxes of mixture B.
6. Since the merchant has 1,800 ounces of raisins available, one inequality that must be satisfied
is: 6. _______
A. 2.8x + 4y ≤ 1,800
B. 3x + 5y ≤ 1,800
C. 5x + 3y ≥ 1,800
D. 10x + 3y ≤ 1,800
7. State the objective function. 7. _______
A. 5,200x + 1,800y
B. 10x + 14y
C. 10x + 3y
D. 2.8x + 4y
8. A jar contains 22 red jelly beans, 18 yellow jelly beans, and 14 orange jelly beans.
Suppose that each jelly bean has an equal chance of being picked from the jar.
If a jelly bean is selected at random from the jar, what is the probability that it is not red?
8. _______
A.
8
3
B.
27
11
C.
27
16
D.
8
5
MATH 106 Finite Mathematics Fall, 2012, 4.1
Page 5 of 10
9. When solving a system of linear equations with the unknowns x1 and x2
the following reduced augmented matrix was obtained. 9. _______
� 1 4 0 0 �
6
0
�
What can be concluded about the solution of the system?
A. The unique solution to the system is x1 = 4 and x2 = 6.
B. There are infinitely many solutions. The solution is x1 = − 4t + 6 and x2 = t, for any real
number t.
C. There are infinitely many solutions. The solution is x1 = 4t + 6 and x2 = t, for any real
number t.
D. There is no solution.
10. Which of the following is NOT true? 10. ______
A. If events E and F are independent events, then P(E ∩ F) = 0.
B. If an event cannot possibly occur, then the probability of the event is 0.
C. A probability must be less than or equal to 1.
D. If only two outcomes are possible for an experiment, then the sum of the probabilities of
the outcomes is equal to 1.
11. In a certain manufacturing process, the probability of a type I defect is 0.07, the probability
of a type II defect is 0.09, and the probability of having both types of defects is 0.04.
Find the probability that neither defect occurs. 11. ______
A. 0.96
B. 0.88
C. 0.84
D. 0.80
12. Which of the following statements is NOT true? 12. ______
A. The standard deviation is the square root of the variance.
B. The variance is a measure of the dispersion or spread of a distribution about its mean.
C. The variance can be a negative number.
D. If all of the data values in a data set are identical, then the standard deviation is 0.
MATH 106 Finite Mathematics Fall, 2012, 4.1
Page 6 of 10
SHORT ANSWER:
13. Let the universal set U = {1, 2, 3, 4, 5, 6}. Let A = {1, 3, 4} and B = {2, 3, 5}.
Determine the set A′ ∩ B . Answer: ______________
(Be sure to notice the complement symbol applied to A.)
14. Consider the following graph of a line.
(a) State the x-intercept. Answer: ______________
(b) State the y-intercept. Answer: ______________
(c) Determine the slope. Answer: ______________
(d) Find the slope-intercept form of the equation of the line. Answer: ____________________
(e) Write the equation of the line in the form Ax + By = C where A, B, and C are integers.
Answer: ____________________
MATH 106 Finite Mathematics Fall, 2012, 4.1
Page 7 of 10
15. A company compiled information about the gender and working status of its 420 employees,
as shown below.
Full-time Part-time Totals
Male 210 40 250
Female 90 80 170
Totals 300 120 420
(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)
Find the probability that a randomly selected employee is:
(a) a male employee or a full-time employee. Answer: ______________
(b) a male full-time employee. Answer: ______________
(c) male, given that the employee is full-time. Answer: ______________
SHORT ANSWER, with work required to be shown, as indicated.
16. For a six year period, Amanda deposited $700 each quarter into an account paying 5.6%
annual interest compounded quarterly. (Round your answers to the nearest cent.)
(a) How much money was in the account at the end of 6 years? Show work.
(b) How much interest was earned during the 6 year period? Show work.
Amanda then made no more deposits or withdrawals, and the money in the account continued to
earn 5.6% annual interest compounded quarterly, for 3 more years.
(c) How much money was in the account after the 3 year period? Show work.
(d) How much interest was earned during the 3 year period? Show work.
17. Twenty five athletes are competing in an Olympic event. The outcome of the event will be
the awarding of three medals, where one athlete wins the Gold Medal, one wins the Silver
Medal, and one wins the Bronze Medal. How many different outcomes are possible? Show
work.
MATH 106 Finite Mathematics Fall, 2012, 4.1
Page 8 of 10
18. A recreational club has 14 members. 4 of the members are men and 10 are women.
(a) In how many ways can the club choose 6 members to form a volleyball team? Show work.
(b) In how many ways can the club choose 6 members to form the volleyball team, if 3 team
members must be men and 3 team members must be women? Show work.
(c) If a 6-person volleyball team is selected at random from the 14 club members, what is the
probability the team consists of 3 men and 3 women? Show work.
19. In 2006, there were 750 students enrolled in an online training program, and in 2010, there
were 974 students enrolled in the program. Let y be enrollment in the year x, where x = 0
represents the year 2006.
(a) Which of the following linear equations could be used to predict the enrollment y in a given
year x, where x = 0 represents the year 2006? Explain/show work.
A. y = 750x + 56
B. y = 56x + 224
C. y = 224x + 750
D. y = 56x + 750
(b) Use the equation from part (a) to predict the enrollment for the year 2013. Show work.
(c) Fill in the blanks to interpret the slope of the equation: The rate of change of enrollment with
respect to time is ______________________ per ________________. (Include units of
measurement.)
20. Solve the system of equations using elimination by addition or by augmented matrix methods
(your choice). Show work.
3x + 4y = 2
x − 2y = 4
MATH 106 Finite Mathematics Fall, 2012, 4.1
Page 9 of 10
21. The feasible region shown below is bounded by lines 2x − y = 4, x + y = 3, and y = 0.
Find the coordinates of corner point A. Show work.
22. During the holidays, 42 people attended a holiday event. 26 of the attendees ate a piece of
cake. 14 of the attendees ate a piece of pie. 32 of the attendees ate a piece of cake or a piece of
pie (or both).
(a) How many of the attendees ate both a piece of cake and a piece of pie? Show work.
(b) Let C = {attendees eating a piece of cake} and P = {attendees eating a piece of pie}.
Determine the number of attendees belonging to each of the regions I, II, III, IV.
U
P C
II
IV
III I
MATH 106 Finite Mathematics Fall, 2012, 4.1
Page 10 of 10
23. Use the sample data 52, 22, 4, 22, 90, 48, 70.
(a) State the mode.
(b) Find the median. Show work/explanation.
(c) State the mean.
(d) The sample standard deviation is 30.1. What percentage of the data falls within one
standard deviation of the mean? Show work/explanation.
(d) _______
A. 71%
B. 68%
C. 57%
D. 50%
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 – 70 20 40 60
pi 0.20 0.25 0.45 0.10
25. The probability that an eligible voter voted in the November, 2012 presidential election was
0.58. Five eligible voters were randomly selected. Find the probability that exactly 3 of the 5
eligible voters voted in the election. Show work.
Math 106 Final Examination
Fall,
20
12
Math 106 Finite Mathematics Name______________________________
Final Examination: Fall, 2012 Instructor __________________________
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 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.
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.
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.
14.
(a)
(b)
(c)
(d)
(e)
15. (a)
(b)
(c)
SHORT ANSWER with Work Shown. Record your answers and work.
|
Problem Number |
Solution |
|
| 16 |
Answers: (a) Work for (a), (b), (c), and (d): |
|
|
17 |
Answer: Work: |
|
|
18 |
Answers: (a) (b) (c) Work for (a), (b), and (c): |
|
|
19 |
Answers: (a) (b) (c) Work for (a) and (b): |
|
| 20 |
Answer: Work: |
|
|
21 |
Answer: Work: |
|
|
22 |
Answers: (a) (b) Region I: Region II: Region III: Region IV: Work for (a): |
|
|
23 |
Answers: (a) (b) (c) (d) Work for (b) and (d): |
|
|
24 |
||
| 25 |
Answer: Work: |
Math
106 Final Examination Fall, 2012
Math 106 Finite Mathematics
Name______________________________
Final Examination: Fall, 2012 Instructor __________________________
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 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.
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.
Name _____________________ Date___________________
Math 106 Final Examination Fall, 2012
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.
14. (a)
(b)
(c)
(d)
(e)
15. (a)
(b)
(c)
Math 106 Final Examination Fall, 2012
SHORT ANSWER with Work Shown. Record your answers and work.
Problem
Number
Solution
16
Answers:
(a)
(b)
(c)
(d)
Work for (a), (b), (c), and (d):
17
Answer:
Work:
Math 106 Final Examination Fall, 2012
18
Answers:
(a)
(b)
(c)
Work for (a), (b), and (c):
19
Answers:
(a)
(b)
(c)
Work for (a) and (b):
Math 106 Final Examination Fall, 2012
20
Answer:
Work:
21
Answer:
Work:
Math 106 Final Examination Fall, 2012
22
Answers:
(a)
(b) Region I:
Region II:
Region III:
Region IV:
Work for (a):
23
Answers:
(a)
(b)
(c)
(d)
Work for (b) and (d):
Math 106 Final Examination Fall, 2012
24
Answer:
Work:
25
Answer:
Work:
