Name:    MAT 120 Fall 2011 Semester Exam Review Questions

True/False
Indicate whether the statement is true or false.

1.

If the addition or subtraction of two linear equations results in the equation 0 = 5, then the graphs of those equations are parallel.

2.

The number of ordered lists of 7 different items, chosen 3 at a time is 210.

Multiple Choice
Identify the choice that best completes the statement or answers the question.

3.

Given , determine .
 A B C D E

4.

Function is .

Calculate .
 A B C D E

5.

Calculate the slope of the straight line that contains the points (4, 3) and (9, 13).
 A B C D E

6.

A piano maker has a daily fixed cost of \$1,600 and a marginal cost of \$2,100 per piano. On a given day, what is the cost of making 5 pianos?
 A B C D E

7.

You can sell 65 pet chias per week if they are marked as \$2 each,but only 40 per week if they are marked \$3 per chia. Your chia supplier is prepared to sell you 10 chias per week if they are marked \$2 per chia, and 35 per week if they are marked \$3 per chia. At what price should the chias be marked so that there is neither surplus nor a shortage of chias?
 A B C D E

8.

Following are forecasts of worldwide annual cell phone handset sales.

 Year x 3 5 7 Sales y (Millions) 500 600 800

(x = 3 represents 2003)

Use your calculator to determine the associated regression line. (Round coefficients to 2 decimal places if necessary.) Use your regression equation to project the 2015 sales.
 A 1393.33 B 1383.33 C 1363.33 D 1394.33 E 1365.33

9.

If the addition or subtraction of two linear equations results in the equation 9 = 9, then the graphs of those equations are _______.
 A not parallel B perpendicular C parallel D equal E none of these

10.

Find the solution to the system of equations.

 A B C D E

11.

Use Gauss-Jordan row reduction to solve the system.

 A B C D E inconsistent

12.

Use Gauss-Jordan row reduction to solve the given system of equations.

 A B C D E

13.

You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 16 bread rolls, 23 defrosted beef patties, and 18 opened cheese slices. Rather than throw them out, you decide to use them to make burgers that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bread roll, double cheeseburgers each require 2 beef patties, 1 bread roll, and 2 slices of cheese, and regular cheeseburgers each require 1 beef patty, 1 bread roll, and 1 slice of cheese. How many of each should you make?
 A Plain burgers:                   5Double cheeseburgers:     7Regular cheeseburgers:     4 D Plain burgers:                   8Double cheeseburgers:     5Regular cheeseburgers:     4 B Plain burgers:                   4Double cheeseburgers:     8Regular cheeseburgers:     5 E Plain burgers:                    7Double cheeseburgers:     5Regular cheeseburgers:     5 C Plain burgers:                   7Double cheeseburgers:     4Regular cheeseburgers:     5

14.

You invested a total of \$6,100 in three funds at the beginning of 2003, including an equal amount in PNF and CMBFX. You earned a total of \$367 in interest for the year. How much did you invest in each of the three funds? Use the data given in the figure below.

 2003 Yield PNF (Pimco N. Y.) 6% CMBFX (Columbia Ore) 5% SFCOX 7%

 A PNF (Pimco N. Y.): \$2,200CMBFX (Columbia Ore): \$2,200SFCOX      : \$2,100 D PNF (Pimco N. Y.): \$2,000CMBFX (Columbia Ore): \$2,000SFCOX      : \$1,700 B PNF (Pimco N. Y.): \$2,200CMBFX (Columbia Ore): \$2,200SFCOX      : \$1,700 E PNF (Pimco N. Y.): \$2,000CMBFX (Columbia Ore): \$2,000SFCOX      : \$2,100 C PNF (Pimco N. Y.): \$1,900CMBFX (Columbia Ore): \$1,900SFCOX      : \$2,300

15.

Determine the dimension of the matrix.

 A B C D E

16.

If and then calculate .
 A D B E C

17.

Calculate the matrix product, if possible.

 A D B E Undefined C

18.

Calculate the matrix product, if possible.

 A D B E Undefined C

19.

The following matrix equation is equivalent to which system of linear equations?

 A B C D E

20.

Compute the product of the two matrices (if possible).

 A B C D E Not possible

21.

Determine which pair of matrices is an inverse pair.
 A D B E None of these C

22.

Determine the inverse of the given matrix, if it exists.

 A D B E The inverse matrix does not exist. C

23.

Use matrix inversion to solve the given system of linear equations.

 A B C D E The system is inconsistent.

24.

Determine whether or not the pair of matrices is an inverse pair.

 A inverse B not inverse

25.

Production of 1 unit of cologne requires 0.7 units of perfume and 0.4 units of cologne. Into 1 unit of perfume goes 0.1 unit of perfume and 0.6 units of cologne. With sector 1 as cologne and sector 2 as perfume, set up the technology matrix A.
 A D B E C

26.

Given the technology matrix , and an external demand vector , calculate the production vector .

,
 A D B E C

27.

Obtain the technology matrix from the input-output table.

 to A B C from   A 0 200 300 B 300 500 300 C 0 0 600 Total Output 1,000 2,000 3,000

 A D B E C

28.

A \$7,000 loan, taken now, with a simple interest rate of 8% per year, will require a total payment of \$11,480. When will the loan mature?
 A 8 years B 20 years C 6 months D 18 years E 6 years

29.

Find the simple interest on a \$3,000 investment made for 5 years at an interest rate of 3% per year. What is the future value?
 A The simple interest is \$450, the future value is \$3,450. B The simple interest is \$470, the future value is \$3,430. C The simple interest is \$435, the future value is \$3,435. D The simple interest is \$470, the future value is \$3,435. E The simple interest is \$475, the future value is \$3,425.

30.

Calculate the future value of an investment of \$3,000, after one year, if it is deposited in a savings account that is compounded quarterly at an annual rate of 12%.
 A \$3,376.53 B \$3,960.00 C \$3,576.95 D \$3,380.00 E None of these

31.

How much would you have to invest when you are 22 years old at 7% compounded monthly to end up with a million dollars by age 52? Round your answer to the nearest thousand.
 A \$213,000 B \$123,000 C \$215,000 D \$131,000 E None of these

32.

Calculate, to the nearest cent, the future value of an investment of \$11,000 at 4.5% per year, compounded quarterly ( 4 times / year ), after 10 years.
 A B C D E

33.

Calculate the amount accumulated in the increasing annuity of \$200 deposited monthly for 10 years at 7%/year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round to the nearest cent.
 A \$68,902.68 B \$3,461.70 C \$34,616.96 D \$8,038.65 E \$25,680.00

34.

Determine the monthly payment necessary to accumulate \$30,000 in a fund paying 5% per year, compounded monthly, for 5 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
 A \$478.62 per month B \$483.62 per month C \$498.49 per month D \$441.14 per month E \$417.61 per month

35.

Find the present value of the decreasing annuity necessary to fund a withdrawal of \$100/month for 20 years, if the annuity earns 3%/year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
 A \$18,261.48 B \$18,147.60 C \$18,003.50 D \$18,916.64 E \$18,031.09

36.

List the elements of all outcomes of rolling two indistinguishable dice such that the numbers add up to 7.
 A {(1, 6),(2, 5),(3, 4),(4, 3),(2, 5),(1, 6)} B {(1, 6),(2, 5),(3, 4)} C {(1, 6),(2, 5),(3, 4),(4, 3),(5, 2),(6, 1)} D {(6, 1),(5, 2),(4, 3),(3, 4),(5, 2),(6, 1)} E

37.

Let

{Jello, Jeffrey, Solly, Lucy}
{Jeffrey, Lucy, Jelly}
{Joan, Jeffrey, Lucy}

Find the set .
 A {Jeffrey, Lucy} B {Jello, Jeffrey, Solly, Lucy, Joan} C {Jello, Jeffrey, Lucy, Joan} D {Jello, Jeffrey, Solly, Joan, Jelly} E

38.

Let

{Jello, Jill, Solly, Lucy}
{Jill, Lucy, Jennifer}
{Joan, Jill, Lucy}

Find the set .
 A {Jill, Lucy} B {Joan, Jennifer} C {Jill, Lucy, Joan, Jennifer} D {Jello, Jill, Lucy} E

39.

In December 2001 a search using the Web search engine GoogleTM for "Costenoble" yielded 10,000 Web sites containing that word. A search for "Waner" yielded 66,000 sites. A search for sites containing both words yielded 4,056 sites. How many Web sites contained either "Costenoble" or "Waner" or both?
 A 71,944 B 76,000 C 70,056 D 14,056 E 80,056

40.

Use the given information to complete the solution to the partially solved Venn diagram.

, , , , and

 A D B E C

41.

If , , and , determine .
 A 140 B 155 C 45 D 75 E 105

42.

The following table shows the results of a survey of authors by a fictitious publishing company.

 New Authors Established Authors Total Successful 2 24 26 Unsuccessful 12 60 72 Total 14 84 98

Consider the following subsets of the set S of all authors represented in the table: C, the set of successful authors; U, the set of unsuccessful authors; N, the set of new authors; and E, the set of established authors. Determine the number of elements that set contains.

Use the table to compute .
 A 24 B 12 C 40 D 38 E 42

43.

Professor Tough's final examination has 13 true/false questions followed by 7 multiple choice questions. In each of the multiple choice questions you must select the correct answer from a list of 6. How many answer sheets are possible?
 A 963,780,608 B 1,092 C 344,064 D 288,128 E 2,293,235,712

44.

A Social Security number is a sequence of nine digits. How many Social Security numbers are possible that have the same first 4 digits?
 A 10,000 numbers B 50 numbers C 40 numbers D 9,765,625 numbers E 100,000 numbers

45.

How many six-letter sequences are possible that contain only the letters R and D, with D occurring only once?
 A 6 sequences B 720 sequences C 7 sequences D 216 sequences E 36 sequences

46.

Evaluate .
 A 120 B 6,720 C 40,320 D 336 E 56

47.

Evaluate .
 A 6 B 120 C 6,720 D 336 E 56

48.

How many six-letter sequences are possible that use the letters g, o, b, l, i, n once each?
 A 216 B 720 C 120 D 36 E 6

49.

A bag contains 3 red marbles, 5 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many sets of 4 marbles include at most one of the yellow marbles?
 A 660 B 330 C 450 D 420 E 210

50.

The following table shows the results of a survey of authors by a (fictitious) publishing company:

 New Authors Established Authors Total Successful 5 25 30 Unsuccessful 15 55 70 Total 20 80 100

Consider the following events:

S: An author is successful; U: An author is unsuccessful; N: An author is new; and E: An author is established.

Which of the following pairs of events are mutually exclusive?
 A N and S B both S and E, and N and S C N and E D both S and E, and N and E E S and E

51.

The following table shows the results of a survey of 360 authors by a (fictitious) publishing company:

 New Authors Established Authors Total Successful 60 20 80 Unsuccessful 120 160 280 Total 180 180 360

An author is chosen at random.

Compute the estimated probability of the event that the author is established and successful.
 A B C D E

52.

A pair of dice is cast, and the number that appears uppermost on each die is observed.

Calculate the probability of the event that the sum of the numbers is 5.
 A B C D E

53.

Three coins are tossed. What is the probability that there will be at most one tail?
 A B C D E

54.

Determine if .
 A B C D E

55.

If , , and , calculate .
 A 0.09 B 0.21 C 0.57 D 0.33 E 0.24

56.

and . Calculate .
 A B C D E

57.

Complete the probability distribution table and then calculate .

 Outcome Probability ?
 A B C D E

58.

Lance the Wizard has been informed that tomorrow there will be a 50% chance of encountering the evil Myrmidons and a 20% chance of meeting up with the dreadful Balrog. Moreover, Hugo the Elf has predicted that there is a 15% chance of encountering both tomorrow. What is the probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog?
 A 0.4 B 0.45 C 0.44 D 0.34 E 0.47

59.

The Sorry State Lottery requires you to select 4 different numbers drawn at random from a set numbered 1 to 41. (Order is not important.) You are a Big Winner if the 4 numbers you select agree with those in the drawing.

What is the probability of being a Big Winner?
 A B C D E

60.

Suzy grabs four marbles from a bag containing four white marbles and five blue marbles. Compute the probability that exactly three of the marbles are blue.
 A B C D E

61.

A bag contains 4 red marbles, 3 green ones, 3 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Determine the probability that she has 2 red ones and 1 of each of the other colors.
 A B C D E

62.

Determine whether the given events A and B are independent, mutually exclusive, or neither.

A: Your new skateboard design is a success.
B: Your new skateboard design is popular with the teen set.
 A independent B neither C mutually exclusive

63.

, . Calculate .
 A B C D E

64.

Compute the following quantities.

, , , and

 A and B and C and D and E and

65.

Determine the conditional probability of the event "The red one is 3, given that the sum is 6" when two fair dice (one red and one green) are rolled.
 A B C D E

66.

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence.

A: The red die is 2, 4, or 5; B: The green die is even.
 A A and B are dependent B A and B are independent

67.

The table shows the results of a survey of 100 authors by a publishing company. Compute the conditional probability: An unsuccessful author is established.

 New Authors Established Authors Total Successful 5 25 30 Unsuccessful 15 55 70 Total 20 80 100
 A B C D E

68.

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round the answer to four decimal places.

. Find
 A B C D E

69.

It rains in Spain an average of once in 10 days, and when it does, hurricanes have a 4% chance of happening in Hartford. When it does not rain in Spain, hurricanes have a 1% chance of happening in Hartford. What is the probability that it rains in Spain when hurricanes happen in Hartford? Round your answer to four decimal places.
 A 0.15 B 0.0342 C 0.3478 D 0.3077 E 0.05

70.

According to a study in The New England Journal of Medicine, 85 of a sample of 5,990 middle-aged men had developed heart disease. It also found that men who were very active (burning about 3,500 calories daily) were half as likely to develop heart disease compared with men who were sedentary. Assume that one-fourth of all middle-aged men are very active, and the rest are classified as sedentary. What is the probability that a middle-aged man with heart disease is very active? Round your answer to two decimal places.
 A 0.11 B 0.14 C 0.86 D 0.57 E 0.25

71.

A random variable has the probability distribution table as shown. Calculate .

 x 1 3 5 7 9 P ( X = x ) 0.2 0.2 0.1 0.1
 A 0.6 B 0.7 C 0.5 D 0.1 E 0.2

72.

State the probability distribution for the indicated random variable.

A black and white die are rolled, and consider the following random variable.

 A B C D E

73.

Your class is given a physics exam worth 50 points; X is the average score, rounded to the nearest whole number.

Classify the random variable X as finite, discrete infinite, or continuous.
 A finite B continuous C discrete infinite

74.

Consider a Bernoulli experiment with and . What is ?
 A 0.000796262 B 0.05184 C 0.2592 D 0.0768 E 0.01536

75.

You are performing 4 independent Bernoulli trials with and . Calculate the probability of no failures.
 A 0.0019 B 0.1944 C 0.0078 D 0.2401 E 0.0081

76.

Your manufacturing plant produces air bags, and it is known that 3% of them are defective. Ten air bags are tested. Determine the probability that at least two of them are defective.
 A B C D E

77.

Assume that on a standardized test of 100 questions, a person has a probability of 86% of answering any particular question correctly. Calculate the probability of answering between 75 and 85 questions, inclusive, correctly. (Assume independence, and round your answer to four decimal places.)
 A 0.5717 B 0.892 C 0.6797 D 0.3203 E 0.4283

78.

Determine the median of 8, 4, 6, 7, 13, 8, 21, and 3.
 A 10 B 8.9 C 8 D 7.5 E 13

79.

Calculate the expected value of the following probability distribution.

 x 1 7 13 19 P ( X = x ) 0.1 0.5 0.1 0.3
 A 10.5 B 2.5 C 10.6 D 10 E 4

80.

A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on two numbers pays 17 to 1 (that is, if one of the two numbers you bet comes up, you get back your \$1 plus another \$17). How much do you expect to win with a \$6 bet on two numbers? Round your answer to the nearest thousandth of a dollar.
 A You expect to lose \$0.318 on each spin of the wheel. B You expect to win \$6 on each spin of the wheel. C You expect to lose \$6 on each spin of the wheel. D You expect to win \$0.636 on each spin of the wheel. E You expect to win \$0.318 on each spin of the wheel.

81.

Compute the standard deviation of the data sample.

 A B C D E

82.

Calculate the standard deviation of X for the probability distribution.

 3 1 4 2 0.5 0.2 0.1 0.2
 A 2.5 B 5 C 1.25 D 0.85 E 0.92

83.

Calculate the standard deviation of the given random variable . Please round your answer to two decimal places.

Fifty-five darts are thrown at a dartboard. The probability of hitting a bull's-eye is . Let be the number of bull's-eyes hit.
 A B C D E

84.

Which is greater: the sample standard deviation or the population standard deviation?
 A the sample standard deviation B the population standard deviation

85.

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Determine the probability that a randomly chosen test taker will score between 300 and 600. Round your answer to four decimal places.
 A 0.8185 B 0.4093 C 0.5907 D 0.8175 E 0.1815

86.

Determine the probability for the standard normal variable Z corresponding to the shaded area under the standard normal curve.

 A B C D E

87.

Suppose is a normal random variable with and . Calculate . Round the answer to four decimal places.
 A B C D E

88.

The probability of a plane crashing on a single trip in 1989 was 0.00000165. Determine the approximate probability that in 100,000,000 flights, there will be fewer than 150 crashes.