Project #10919 - Finite Math

I have completed a few questions already, I have no idea if they are correct.  I need to pass this course for credit at work for CLE's. I need at least a 90% on this assignment.

 

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. Oscar purchases a car for $22,000, makes a down payment of 25%, and finances the rest with a 3-year car loan at an annual interest rate of 3.6% compounded monthly. What is the amount of his monthly loan payment?

A. $484.22 B. $507.83 C. $645.62 D. $677.11

2. Find the result of performing the row operation

(4)R1 + R2 R2

􏰀12􏰁3􏰂􏰃 7 0 7

2. _______

􏰀1 2􏰁3􏰂􏰃 3 −8 −5

A. 􏰀1 2􏰁3􏰂􏰃 7 −8 −5

C. 􏰀12􏰁3􏰂􏰃 4 8 12

B.

D. 􏰀12􏰁3􏰂􏰃 13 −30 −17

1. _______

Page 1 of 10

MATH 106 Finite Mathematics Summer, 2013, 3.2 3. Find the values of x and y that maximize the objective function 8x + 3y for the feasible

region

A. B. C. D.

4. The
and a standard deviation of 2 years. What is the probability that a randomly chosen dog of this species has a lifespan between 10 and 14 years?

shown below. 3. _______

(x, y) = (0, 20) (x, y) = (5, 15) (x, y) = (8, 10) (x, y) = (10, 0)

 

lifespans of dogs of a particular species are normally distributed, with a mean of 12 years 4. ______

  1. 0.5000

  2. 0.6826

  3. 0.7580

  4. 0.9544

Page 2 of 10

MATH 106 Finite Mathematics Summer, 2013, 3.2

5. Determine which shaded region corresponds to the solution region of the system of linear inequalities

x+3y 3 2x+y 4

x≥0 y≥0

5. _______

GRAPH A.

GRAPH B.

 
 

GRAPH C.

GRAPH D.

 
 

Page 3 of 10

MATH 106 Finite Mathematics Summer, 2013, 3.2

For #6 and #7:
A merchant makes two raisin nut mixtures.
Each box of mixture A contains 3 ounces of raisins and 15 ounces of peanuts, and sells for $5.10. Each box of mixture B contains 4 ounces of raisins and 8 ounces of peanuts, and sells for $3.60. The company has available 2,000 ounces of raisins and 6,200 ounces of peanuts. 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 2,000 ounces of raisins available, one inequality that must be satisfied

is:
A.

B. C. D.

6. _______

7x 2,000
5.1x + 3.6y
2,000 3x + 4y 2,000 3x+4y ≥2,000

7. State the objective function.

  1. 5.1x + 3.6y

  2. 3x + 4y

  3. 3x + 15y

  4. 23x + 7y

7. _______

8. A jar contains 16 red jelly beans, 20 yellow jelly beans, and 12 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 orange?

A. 1 B. 1 C. 2 D. 3 4334

8. _______

 
 
 
 

Page 4 of 10

MATH 106 Finite Mathematics

Summer, 2013, 3.2

9. When solving a system of linear equations with the unknowns x1 and x2 the following reduced augmented matrix was obtained.

􏰀1 6􏰁−9􏰂􏰃 001

9. _______

What can be concluded about the solution of the system?
A. There are infinitely many solutions. The solution is
x1 = 6t 9 and x2 = t, for any real

number t.
B. There are infinitely many solutions. The solution is x1 = 6t 9 and x2 = t, for any real

number t.
C. The unique solution to the system is x1 = 6 and x2 = −9.

D. There is no solution.

  1. Which of the following statements is NOT true? 10. ______

    A. The variance is a measure of the dispersion or spread of a distribution about its mean. B. The standard deviation is the square root of the variance.
    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.

  2. In a certain manufacturing process, the probability of a type I defect is 0.11, the probability

of a type II defect is 0.07, and the probability of having both types of defects is 0.05.

Find the probability that neither defect occurs.

A. 0.82 B. 0.77 C. 0.95 D. 0.87

12. Which of the following is NOT true?

A. If events E and F are independent events, then P(E F) = 0.

11. ______

12. ______

B. If only two outcomes are possible for an experiment, then the sum of the probabilities of the outcomes is equal to 1.

C. A probability must be less than or equal to 1.
D. If an event cannot possibly occur, then the probability of the event is 0.

Page 5 of 10

MATH 106 Finite Mathematics Summer, 2013, 3.2 SHORT ANSWER:

13. Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8}. Let A = {2, 4, 7, 8} and B = {1, 2, 3, 4}.

Determine the set A B'.
(Be sure to notice the complement symbol applied to B.)

14. Consider the following graph of a line.

Answer: ______________

 
 

(a) State the x-intercept. (b) State the y-intercept.

(c) Determine the slope.

Answer: ______________ Answer: ______________

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: ____________________

Page 6 of 10

MATH 106 Finite Mathematics Summer, 2013, 3.2

15. 400 employees at a particular company were asked their status (full-time or part-time) and their primary means of transportation to and from work. The following table was obtained.

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

 
 

Primary Transportation

 
 
 

Full-time

 
 
 
 
 

Part-time

 
 

Total

 
 
 

Car

 
 
 

188

 
 
 
 
 

60

 
 
 

248

 
 
 

Bus

 
 
 
 
 

32

 
 
 
 
 
 
 

44

 
 
 
 
 
 

76

 
 
 

Subway

 

30

 
 

27

 

57

 
 
 

On Foot

 
 
 
 
 

10

 
 
 
 
 
 
 

9

 
 
 
 
 
 

19

 
 
 

Total

 
 

260

 
 
 
 

140

 
 
 
 

400

 

(a) travels by subway and is full-time.
(b) travels by subway or is full-time.
(c) travels by subway, given that the employee is full-time.

Answer: ______________ Answer: ______________ Answer: ______________

 

SHORT ANSWER, with work required to be shown, as indicated.
16. For a six year period, Ted deposited $700 each quarter into an account paying 3.2% 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.
Ted then made no more deposits or withdrawals, and the money in the account continued to earn

3.2% annual interest compounded quarterly, for 5 more years.
(c) How much money was in the account after the 5 year period?
Show work.

(d) How much interest was earned during the 5 year period? Show work.

17. An artist has a portfolio of 16 paintings and plans to display three of the paintings in a row (left, middle, right) on the wall of an art gallery. How many different arrangements of the paintings are possible? Show work.

 
 

Page 7 of 10

MATH 106 Finite Mathematics Summer, 2013, 3.2

18. There is a collection of 13 prepared lunches. 8 of the lunches are sandwiches and 5 of the lunches are wraps.

(a) In how many ways can 6 of the 13 lunches be chosen for a group of co-workers? Show work. (b) In how many ways can the 6 lunches be chosen from the collection of 13 lunches, if 3 of the

lunches must be sandwiches and 3 of the lunches must be wraps? Show work.
(c) If the 6 lunches are selected at random from the collection of 13 lunches, what is the

probability that the lunches consist of 3 sandwiches and 3 wraps? Show work.

19. In the year 1980, the U.S. Consumer Price Index (CPI) was 82. In 2000, the CPI was 172. Let y be the U.S. Consumer Price Index in year x, where x = 0 represents the year 1980.

(a) Which of the following linear equations could be used to predict the U.S. Consumer Price Index y in a given year x, where x = 0 represents the year 1980? Explain/show work.

  1. y=4.5x+82

  2. y=90x+82

  3. y=4.5x−8828

  4. y = 90x 179,828

(b) Use the equation from part (a) to estimate the CPI in the year 2010. Show work. (c) Fill in the blank:

The average rate of change of the CPI with respect to time is _______ per year.

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

x + 2y = 1 5x−y =−17

 
 

Page 8 of 10

MATH 106 Finite Mathematics Summer, 2013, 3.2 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. A survey of 180 residents of Metropolis found the following:

62 went to the movies in the previous week. 50 attended a sports event in the previous week. 97 went to the movies or attended a sports event (or both) in the previous week.

(a) How many went to the movies and attended a sports event in the previous week? Show work.

(b) Let circle M = {survey respondents who went to the movies in the previous week} and circle S = {survey respondents who attended a sports event in the previous week}

Determine the number of survey respondents belonging to each of the regions I, II, III, IV.

 
 
 

U

 

MS

II

I

III

IV

 

Page 9 of 10

MATH 106 Finite Mathematics Summer, 2013, 3.2

23. Consider the sample data 50, 90, 50, 77, 45, 67, 55. (a) State the mode.

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

(c) State the mean.

(d) The sample standard deviation is 16.6. What percentage of the data fall within one standard deviation of the mean? Show work/explanation.

(d) _______

A. 57% B. 68% C. 71% D. 75%

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

 
 

– 60

 
 

10

 

25

 

30

 
 

pi

0.20

 

0.30

 

0.40

0.10

 
 

25. According to a recent report, 0.28 is the probability that an American adult male has high cholesterol requiring treatment. Seven American adult males are randomly selected. Find the probability that exactly 3 of the 7 American adult males have high cholesterol requiring treatment. Show work. 

 

Subject Mathematics
Due By (Pacific Time) 08/17/2013 12:00 am
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