Find the slope of the line. 9)Regrind, Inc. regrinds used ... tests/1324... · in dollars to...

Find the slope of the line.

1) 5x - 2y = 3

2) y = 1

8x

Solve the problem.

3) Suppose the function y = 3.4t - 2.8 determines

the actual time that has elapsed, in minutes, for

t minutes of a person's estimate of the elapsed

time. Find the actual time that has elapsed for

an estimate of t = 60 minutes.

4) The information in the chart below gives the

salary of a person for the stated years. Model

the data with a linear function using the points

(1, 24,500) and (3, 26,100). Then use this

function to predict the salary for the year 2003.

Year, x Salary, y

1990, 0 $23,500

1991, 1 $24,500

1992, 2 $25,200

1993, 3 $26,100

1994, 4 $27,200

5) A car rental company charges $35 per day to

rent a particular type of car and $0.12 per mile.

Juan is charged $49.64 for a one-day rental.

How many miles did he drive?

6) In a lab experiment 17 grams of acid were

produced in 13 minutes and 20 grams in 26

minutes. Let y be the grams produced in x

minutes. Write a linear equation for grams

produced.

7) Suppose that the population of a certain town,

in thousands, was 105 in 1990 and 141 in

2002. Assume that the population growth can

be approximated by a straight line. Find the

equation of a line which will estimate the

population of the town, in thousands, in any

given year since 1990.

8) Assume that the sales of a certain appliance

dealer can be approximated by a straight line.

Suppose that sales were $10,000 in 1982 and $

85,000 in 1987. Let x = 0 represent 1982. Find

the equation giving yearly sales S.

9) Regrind, Inc. regrinds used typewriter platens.

The cost per platen is $2.50. The fixed cost to

run the grinding machine is $300 per day. If

the company sells the reground platens for $

5.50, how many must be reground daily to

break even?

10) Midtown Delivery Service delivers packages

which cost $1.70 per package to deliver. The

fixed cost to run the delivery truck is $44 per

day. If the company charges $5.70 per package,

how many packages must be delivered daily to

break even?

11) In deciding whether or not to set up a new

manufacturing plant, analysts for a popcorn

company have decided that a linear function is

a reasonable estimation for the total cost C(x)

in dollars to produce x bags of microwave

popcorn. They estimate the cost to produce

10,000 bags as $5250 and the cost to produce

15,000 bags as $7770. Find the marginal cost of

the bags of microwave popcorn to be produced

in this plant.

12) Midtown Delivery Service delivers packages

which cost $1.70 per package to deliver. The

fixed cost to run the delivery truck is $84 per

day. If the company charges $3.70 per package,

how many packages must be delivered daily to

make a profit of $22?

13) The temperature of water in a certain lake on a

day in October can be determined by using the

model y = 15.2 - 0.537x where x is the number

of feet down from the surface of the lake and y

is the Celsius temperature of the water at that

depth. Based on this model, how deep in the

lake is the water 11 degrees? (Round to the

nearest foot.)

14) Find the temperature at which the Celsius and

Fahrenheit scales coincide.

15) Given the supply and demand functions

below, find the demand when p = $12.

S(p) = 5p

D(p) = 120 - 4p

1

16) Let the demand and supply functions be

represented by D(p) and S(p), where p is the

price in dollars. Find the equilibrium price and

equilibrium quantity for the given functions.

D(p) = 3840 - 50p

S(p) = 250p - 960

17) Alan invests a total of $16,000 in three different

ways. He invests one part in a mutual fund

which in the first year has a return of 11%. He

invests the second part in a government bond

at 7% per year. The third part he puts in the

bank at 5% per year. He invests twice as much

in the mutual fund as in the bank. The first

year Alan's investments bring a total return of

$1300. How much did he invest in each way?

18) A shopkeeper orders a total of 24 pounds of

cashews and peanuts. If the amount of

cashews he orders is 20 pounds less than the

amount of peanuts, then how many pounds of

peanuts does he order?

19) There were 470 people at a play. The

admission price was $2 for adults and $1 for

children. The admission receipts were $640.

How many adults and how many children

attended?

20) Best Rentals charges a daily fee plus a mileage

fee for renting its cars. Barney was charged $

114 for 3 days and 300 miles, while Mary was

charged $212 for 5 days and 600 miles. What

does Best Rental charge per day and per mile?

21) A politician is planning to spend a total of 20

hours on a campaign swing through the

southern states of Arkansas, Louisiana,

Mississippi, Alabama, and Georgia. Assume

that he spends the same amount of time in

Mississippi as in Alabama; half the amount of

time in Georgia as in Arkansas; and the same

amount of time in Mississippi, Alabama, and

Georgia (combined) as in Arkansas and

Louisiana (combined). How can he distribute

his time among the five states? (Let a be the

hours spent in Arkansas, b the hours spent in

Louisiana, c the hours spent in Mississippi, d

the hours spent in Alabama, and e the hours

spent in Georgia. Let e be the parameter.)

22) A recording company is to release 210 new

CDs in the categories of rock, country, jazz,

and classical. If twice the number of rock CDs

is to equal three times the number of country

CDs and if the number of jazz CDs is to equal

the number of classical CDs, how can the CDs

be distributed among the four types? (Let x be

the number of rock CDs, y the number of

country CDs, z the number of jazz CDs, and w

the number of classical CDs. Let w be the

parameter.)

23) Janet is planning to visit Arizona, New Mexico,

and California on a 10-day vacation. If she

plans to spend as much time in New Mexico as

she does in the other two states combined, how

can she allot her time in the three states? (Let x

denote the number of days in Arizona, y the

number of days in New Mexico, and z the

number of days in California. Let z be the

parameter.)

24) A company is introducing a new soft drink

and is planning to have 48 advertisements

distributed among TV ads, radio ads, and

newspaper ads. If the cost of TV ads is $500

each, the cost of radio ads is $200 each, and the

cost of newspaper ads is $200 each, how can

the ads be distributed among the three types if

the company has $12,000 to spend for

advertising? (Let x denote the number of TV

ads, y the number of radio ads, and z the

number of newspaper ads. Let z be the

parameter.)

Use the Gauss-Jordan method to solve the system of

equations.

25) x + 3y + 2z = 11

4y + 9z = -12

x + 7y + 11z = - 1

26) x + y - 2z = 8

3x + z = - 6

2x - y + 3z = -14

27) 2x - 5y + z = 11

3x + y - 6z = 1

5x - 4y - 5z = 12

2

28) x + y + z = 9

2x - 3y + 4z = 7

x - 4y + 3z = -2

Solve the problem.

29) Barnes and Able sell life, health, and auto

insurance. Their sales, in dollars, for May and

June are given in the following matrices.

Life Health Auto

May:20,000 15,000 8000

30,000 0 17,000

Able

Barnes

June:70,000 0 30,000

20,000 25,000 32,000

Able

Barnes

Find a matrix that gives total sales, in dollars,

of each type of insurance by each salesman for

the two-month period.

30) An appliance dealer has three stores in the

town of Washingwell.

During a given week, they have a beginning

inventory of

Washing Dish

Machines Washers

B = 18 11

40 31

25 29

Store 1

Store 2

Store 3

a sales matrix of

Washing Dish

Machines Washers

S = 4 1

9 8

2 2

Store 1

Store 2

Store 3

and an ending inventory of

Washing Dish

Machines Washers

E = 21 13

46 35

33 35

Store 1

Store 2

Store 3

Find the purchase matrix.

Write a matrix to display the information.

31) A bakery sells three types of cakes. Cake I

requires 2 cups of flour, 2 cups of sugar, and 2

eggs. Cake II requires 4 cups of flour, 1 cup of

sugar, and 1 egg. Cake III requires 2 cups of

flour, 2 cups of sugar, and 3 eggs. Make a 3 × 3

matrix showing the required ingredients for

each cake. Assign the cakes to the rows and the

ingredients to the columns.

32) In the first heat of the 100-yd dash, Russell's

time was 15.5 sec, Sergy's time was 15.8 sec,

and Omar's time was 16.2 sec. In the second

heat, Russell's time was 15.3 sec, Sergy's time

was 15.4 sec, and Omar's time was 15.7 sec.

Write a 3 × 1 matrix that gives the change in

each of their times from the first heat to the

second.

33) Barges from ports X and Y went to cities A and

B. Shipping costs $220 from X to A, $300 from

X to B, $400 from Y to A, and $180 from Y to B.

Make a 2 × 2 matrix showing the shipping

costs. Assign the ports to the rows and the

cities to the columns.

Find the values of the variables in the equation.

34) 4 2

-2 -9 = x y

-2 z

35) -6 8 x

6 y -5 = m 8 1

n -7 p

36) t + 7 5 4

7 -7 2 = -3 5 4

7 x - 8 2

Find the value.

37) Let A = 3 3

2 6 and B = 0 4

-1 6; 2A + B

38) Let A = -3 2 and B = 1 0 ; 3A + 4B

Find the matrix product, if possible.

39) 3 -1

6 0

0 -1

3 6

40) -1 3

4 2

-2 0

-1 1

3

41) 1 3 -2

3 0 5

3 0

-2 1

0 5

42) -1 3

5 6

0 -2 7

1 -3 2

Solve the problem.

43) A company makes three chocolate candies:

cherry, almond, and raisin. Matrix A gives the

amount of ingredients in one batch. Matrix B

gives the costs of ingredients from suppliers X

and Y. Multiply the matrices.

A =

sugar

4

5

3

choc

6

3

3

milk

1

1

1

cherry

almond

raisin

B =

X

3

3

2

Y

2

4

2

sugar

choc

milk




gives the costs of ingredients from suppliers X

and Y. What is the cost of 100 batches of each

candy using ingredients from supplier X?

A =

sugar

4

5

3

choc

6

3

3

milk

1

1

1

cherry

almond

raisin

B =

X

3

3

2

Y

2

4

2

sugar

choc

milk




gives the costs of ingredients from suppliers J

and K. What is the cost of 100 batches of each

candy using ingredients from supplier J?

A =

sugar

6

6

5

choc

8

4

7

milk

1

1

1

cherry

almond

raisin

B =

J

4

4

2

K

3

5

2

sugar

choc

milk




gives the costs of ingredients from suppliers J

and K. What is the cost of 100 batches of each

candy using ingredients from supplier K?

A =

sugar

6

6

5

choc

8

4

7

milk

1

1

1

cherry

almond

raisin

B =

J

4

4

2

K

3

5

2

sugar

choc

milk

Graph the linear inequality.

47) x - y > -2

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

4

48) x ≥ 1

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

Graph the feasible region for the system of inequalities.

49) 2x + y ≤ -3

x - y ≥ 3

x + 2y < -12

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

50) 2x + 3y ≤ 6

x - y ≤ 3

x ≥ 1

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

Graph the feasible region of the system.

51) A summer camp wants to hire counselors and

aides to fill its staffing needs at minimum cost.

The camp can accommodate up to 45 staff

members and needs at least 30 to run

properly. They must have at least 10 aides, and

may have up to 3 aides for every 2 counselors.

Let x represent the number of counselors and y

the number of aides.

x

y

x

y

Write the system of inequalities that describes the

possible solutions to the problem.

52) A certain area of forest is populated by two

species of animals, which scientists refer to as

A and B for simplicity. The forest supplies two

kinds of food, referred to as F1 and F2. For one

year, an animal of species A requires 1.35 units

of F1 and 1.25 units of F2. For one year an

animal of species B requires 2.1 units of F1 and

1.7 units of F2. The forest can normally supply

at most 938 units of F1 and 469 units of F2 per

year. Let a represent the number of animals of

species A and b represent the number of

animals of species B.

5

53) The Pen-Ink Company manufactures two

ballpoint pens: silver and gold. The silver

requires 9 minutes in a grinder and 7 minutes

in a bonder. The gold requires 13 minutes in a

grinder and 14 minutes in a bonder. The

grinder can be run no more than 460 minutes

per day and the bonder no more than 290

minutes per day. Let x represent the number of

silver pens, and let y represent the number of

gold pens. Find the system of inequalities that

represents this company's daily production of

silver and gold pens.

54) A manufacturer of wooden chairs and tables

must decide in advance how many of each

item will be made in a given week. Use the

table to find the system of inequalities that

describes the manufacturer's weekly

production.

Use x for the number of chairs and y for the

number of tables made per week. The number

of work-hours available for construction and

finishing is fixed.

Hours

per

chair

Hours

per

table

Total

hours

available

Construction 2 4 48

Finishing 2 3 42

Use the indicated region of feasible solutions to find the

maximum and minimum values of the given objective

function.

55) z = 7x + 9y.

x

y

(0, 5) (2.5, 5)

(0, 4)

(6, 0) (10, 0) x

y

(0, 5) (2.5, 5)

(0, 4)

(6, 0) (10, 0)

56) z = 6x + 5y + 24

x

y

(0, 1)

(1, 0) x

y

(0, 1)

(1, 0)

Use graphical methods to solve the linear programming

problem.

57) Minimize z = 4x + 5y

subject to: 2x - 4y ≤ 10

2x + y ≥ 15

x ≥ 0

y ≥ 0

x-10 10

y

10

-10

x-10 10

y

10

-10

6

58) Maximize z = 6x + 7y

subject to: 2x + 3y ≤ 12

2x + y ≤ 8

x ≥ 0

y ≥ 0

x-10 10

y

10

-10

x-10 10

y

10

-10

59) Minimize z = 0.18x + 0.12y

subject to: 2x + 6y ≥ 30

4x + 2y ≥ 20

x ≥ 0

y ≥ 0

x-10 10

y

10

-10

x-10 10

y

10

-10

60) Maximize z = 8x + 12y

subject to: 40x + 80y ≤ 560

6x + 8y ≤ 72

x ≥ 0

y ≥ 0

x-10 10

y

10

-10

x-10 10

y

10

-10

Solve the problem.

61) The Acme Class Ring Company designs and

sells two types of rings: the VIP and the SST.

They can produce up to 24 rings each day

using up to 60 total man-hours of labor. It

takes 3 man-hours to make one VIP ring and 2

man-hours to make one SST ring. How many

of each type of ring should be made daily to

maximize the company's profit, if the profit on

a VIP ring is $40 and on an SST ring is $30?

62) Zach is planning to invest up to $45,000 in

corporate and municipal bonds. The least he

will invest in corporate bonds is $8000 and he

does not want to invest more than $28,000 in

corporate bonds. He also does not want to

invest more than $28,311 in municipal bonds.

The interest is 8.2% on corporate bonds and

5.9% on municipal bonds. This is simple

interest for one year. What is the maximum

value of his investment after one year?

63) Wally's Warehouse sells trash compactors and

microwaves. Wally has space for no more than

90 trash compactors and microwaves together.

Trash compactors weigh 26 pounds and

microwaves weigh 55 pounds. Wally is limited

to a total of 8100 pounds for these items. The

profit on a microwave is $43 and on a

compactor $27. How many of each should

Wally stock to maximize profit potential?

7

64) Suppose an animal feed to be mixed from

soybean meal and oats must contain at least

100 lb of protein, 20 lb of fat, and 12 lb of

mineral ash. Each 100-lb sack of soybean meal

costs $20 and contains 50 lb of protein, 10 lb of

fat, and 8 lb of mineral ash. Each 100-lb sack of

alfalfa costs $11 and contains 30 lb of protein, 8

lb of fat, and 3 lb of mineral ash. How many

sacks of each should be used to satisfy the

minimum requirements at minimum cost?

65) An airline with two types of airplanes, P1 and

P2, has contracted with a tour group to

provide transportation for a minimum of 400

first class, 900 tourist class, and 1500 economy

class passengers. For a certain trip, airplane P1

costs $10,000 to operate and can accommodate

20 first class, 50 tourist class, and 110 economy

class passengers. Airplane P2 costs $8500 to

operate and can accommodate 18 first class,

30 tourist class, and 44 economy class

passengers. How many of each type of

airplane should be used in order to minimize

the operating cost?

66) A breed of cattle needs at least 10 protein and 8

fat units per day. Feed type I provides 6

protein and 2 fat units at $4 per bag. Feed type

II provides 2 protein and 3 fat units at $3 per

bag. What mixture of Feed type I and Feed

type II will fill the dietary needs at minimum

cost?

67) Suppose that Janine desires 46 grams of

protein and 38 grams of dietary fiber daily.

One serving of kidney beans has 8 grams of

protein and 6 grams of dietary fiber. One

serving of refried pinto beans has 6 grams of

protein and 6 grams of dietary fiber. If a

serving of kidney beans costs $0.45 and a

serving of refried pinto beans costs $0.35, then

how many servings of each should Janine eat

to minimize cost and still meet her

requirements?

68) June made an initial deposit of $5100 in an

account for her son. Assuming an interest rate

of 4% compounded quarterly, how much will

the account be worth in 10 years?

69) Under certain conditions, Swiss banks pay

negative interest: they charge you. Suppose a

bank "pays" -2.5% interest compounded

annually. Find the compound amount for a

deposit of $160,000 after 2 years.

70) If inflation is 3% a year compounded annually,

what will it cost in 12 years to buy a house

currently valued at $56,000?

71) Barry Newman's savings account has a balance

of $67. After 12 years, what will the amount of

interest be at 6% compounded annually?

Find the future value of the annuity due. Assume that

interest is compounded annually, unless otherwise

indicated.

72) R = 3300; i = 0.06; n = 15

73) $200 deposited at the beginning of each

quarter for 10 years at 4.7% compounded

quarterly

74) $1500 deposited at the beginning of each year

for 18 years at 4% compounded annually

75) R = 800; i = 0.06; n = 14

Find the future value of the ordinary annuity. Interest is

compounded annually, unless otherwise indicated.

76) R = $7,500, i = 6.4% interest compounded

semiannually for 4 years

77) R = $900, i = 10% interest compounded


78) R = $2,500, i = 9% interest compounded

quarterly for 16 years

Find the amount of each payment to be made into a

sinking fund so that enough will be present to accumulate

the following amount. Payments are made at the end of

each period. The interest rate given is per period.

79) $63,000; money earns 5% compounded


80) $8900; money earns 7% compounded annually;

15 annual payments

8

Solve the problem. Round to the nearest cent.

81) Lou has an account with $10,000 which pays

6% interest compounded annually. If to that

account, Lou deposits $5000 at the end of each

year for 5 years, find out the amount in the

account after the last deposit.

82) $765.13 is deposited at the end of each month

for 2 years in an account paying 2% interest

compounded monthly. Find the final amount

of the account.

83) How much should be deposited semiannually

into a sinking fund over 5 years to accumulate

$218,000 if the money earns 5% compounded

semiannually?

84) If $100,000 is to be saved over 14 years, how

much should be deposited monthly if the

investment earns 8.25% interest compounded

monthly?

85) Find the amount of each payment into a

sinking fund if $10,000 must be accumulated.

Payments are made at the end of each quarter

for 3 years, with interest of 8% compounded

quarterly.

86) Mark wants to start an IRA that will have

$250,000 in it when he retires in 29 years. How

much should he invest quarterly in his IRA to

do this if the interest is 8% compounded

quarterly?

Suppose that in the loan described, the borrower paid off

the loan after the time indicated. Calculate the amount

needed to pay off the loan.

87) $6700; 6% compounded monthly; 24 monthly

payments; paid off after 10 months.

88) $70,000; 6% compounded annually; 12 annual

payments; paid off after 3 years

Suppose that in the loan described, the borrower made a

larger payment, as indicated. Calculate (a) the time needed

to pay off the loan, (b) the total amount of the payments,

and (c) the amount of interest saved, compared with the

original loan and payments.

89) $7400; 6.2% compounded semiannually; 18

semiannual payments; with larger payment of

$910.


payments; with larger payment of $14,000.

Find the lump sum deposited today that will yield the

same total amount as this yearly payment made at the end

of each year for 20 years at the given interest rate,

compounded annually.

91) $11,100 at 4%

92) $55,000 at 5%

Find the monthly house payment necessary to amortize

the following loan.

93) $60,000 at 6.69% for 15 years

94) $90,000 at 6.3% for 30 years

Find the payment necessary to amortize the loan.

95) $14,400; 8.25% compounded monthly; 48

monthly payments

96) $10,000; 7% compounded semiannually; 10

semiannual payments


payments

Find the present value of the ordinary annuity.

98) Payments of $2200 made annually for 25 years

at 6% compounded annually

99) Payments of $50,000 made semiannually for 12

years at 5% compounded semiannually

100) Payments of $11,000 made annually for 10

years at 6% compounded annually

9

Solve the problem.

101) Cara has a loan from her credit union at a rate

of 9.5% for which her payments are $185 per

month. The interest is computed on a daily

basis on the unpaid balance of the loan. If the

loan balance after her last payment was $2356

and Cara makes her next payment 34 days

later, how much of the payment is paid toward

interest?

102) You want to take out a loan to buy a new car

for which you need to finance $26,118. Your

bank will give you a loan at 4% compounded

monthly. You look at your budget and decide

that you can afford a payment of $295 a

month. How many years, to the nearest tenth

of a year, must the loan be taken out to meet

these conditions?

103) In order to purchase a home, a family borrows

$80,000 at an annual interest rate of 5.66%, to

be paid back over a 25 year period in equal

monthly payments. What is their monthly

payment?

104) Tasha borrowed $11,000 to purchase a new car

at an annual interest rate of 6.7%. She is to pay

it back in equal monthly payments over a 4

year period. How much total interest will be

paid over the period of the loan? Round to the

nearest dollar.

Let U = {all soda pops}; A = {all diet soda pops};

B = {all cola soda pops}; C = {all soda pops in cans}; and

D = {all caffeine-free soda pops}. Describe the given set in

words.

105) A ∪ D

106) (A ∩ B) ∩ C'

107) A' ∩ C

108) (A ∪ B) ∪ D

Find the number of subsets of the set.

109) {mom, dad, son, daughter}

110) {x | x is an even number between 19 and 39}

Tell whether the statement is true or false.

111) {6, 17, 27, 11, 33} = {33, 17, 11, 72, 6}

112) {4, 7, 12} = {0, 4, 7, 12}

113) 8 ∉ {16, 24, 32, 40, 48}

114) 0 ∉ ∅

Let A = { 6, 4, 1, {3, 0, 8}, {9} }. Determine whether the

statement is true or false.

115) 4 ∈ A

116) {{9}} ⊂ A

117) {9} ⊂ A

118) {6, 4, {9}} ⊆ A

Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and

U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given

statement is true or false.

119) B ⊆ B

120) U ⊆ A

121) B ⊄ D

122) A ⊄ {7, 5, 3, 1}

Decide whether the statement is true or false.

123) {7, 9, 11} ∪ {8, 10, 11} = {7, 9, 11, 8, 10}

124) {7, 14, 21, 28} ∩ {7, 21} = {7, 14, 21, 28}

125) {3, 5, 7} ∩ {4, 6, 7} = {7}

126) {15, 9, 11} ∪ {11, 15, 9} = {15, 11}

Insert "⊆" or "⊈" in the blank to make the statement true.

127) {16, 28, 33} {4, 28, 33, 43}

128) {e, d, j, h} {e, d, j, h, m}

129) {5, 7, 9} {x | x is an odd counting number}

10

130) {0, 10} { 8, 10}

The lists below show five agricultural crops in Alabama,

Arkansas, and Louisiana.

Alabama Arkansas Louisiana

soybeans (s) soybeans (s) soybeans (s)

peanuts (p) rice (r) sugarcane (n)

corn (c) cotton (t) rice (r)

hay (h) hay (h) corn (c)

wheat (w) wheat (w) cotton (t)

Let U be the smallest possible set that includes all of the

crops listed; and let A, K, and L be the sets of five crops in

Alabama, Arkansas, and Louisiana, respectively. Find the

indicated set.

131) L' ∩ (A ∪ K)

132) A ∩ K ∩ L

133) L' ∪ K'

134) A' ∩ K'

135) A ∪ L

136) A' ∪ L

Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y};

B = {q, s, y, z}; and C = {v, w, x, y, z}. List the members of

the indicated set, using set braces.

137) B'

138) C' ∩ A'

139) (A ∩ B)'

140) B ∪ C

141) A ∩ B'

142) A ∪ (B ∩ C)

Find the number of elements in the indicated set by

referring to the given table.

143) V ∩ W,

given the following table:

U.S. Production (in Thousands of Tons) of Certain Nuts

Year Pecans (P) Almonds (A) Walnuts (W)

1993 (T) 184 584 232

1994 (F) 99 587 232

1995 (V) 134 304 232

1996 (S) 111 412 205

144) The table below shows the results of a poll

taken in a U.S. city in which people are asked

which candidate they intend to vote for in an

upcoming presidential election.

NonHispanic

White

(A)

Hispanic

(B)

African

American

(C)

Democrat (D) 237 112 86

Republican (R) 241 64 32

Other (O) 25 23 12

Totals 503 199 130

Find the number of people in the set D ∪ (B ∩

O)





NonHispanic

White

(A)

Hispanic

(B)

African

American

(C)

Democrat (D) 237 112 86


Other (O) 25 23 12

Totals 503 199 130

Find the number of people in the set O ∩ (C' ∪

E')

11





NonHispanic

White

(A)

Hispanic

(B)

African

American

(C)

Democrat (D) 237 112 86


Other (O) 25 23 12

Totals 503 199 130

Find the number of people in the set O ∩ A'





NonHispanic

White

(A)

Hispanic

(B)

African

American

(C)

Democrat (D) 237 112 86


Other (O) 25 23 12

Totals 503 199 130

Find the number of people in the set R ∪ F





NonHispanic

White

(A)

Hispanic

(B)

African

American

(C)

Democrat (D) 237 112 86


Other (O) 25 23 12

Totals 503 199 130

Find the number of people in the set R' ∪ (A ∪

F)

Shade the Venn diagram to represent the set.

149) A ∪ (B ∩ C')

150) B ∪ (A ∩ C')

151) (A ∩ B ∩ C')'

152) A' ∪ B'

12

153) A' ∪ (A ∩ B)

154) (A ∪ B) ∩ (A ∩ B)'

Use a Venn diagram to answer the question.

155) A survey of a group of 113 tourists was taken

in St. Louis. The survey showed the following:

63 of the tourists plan to visit Gateway Arch;

47 plan to visit the zoo;

9 plan to visit the Art Museum and the zoo,

but not the Gateway Arch;

13 plan to visit the Art Museum and the

Gateway Arch, but not the zoo;

18 plan to visit the Gateway Arch and the zoo,

but not the Art Museum;

7 plan to visit the Art Museum, the zoo, and

the Gateway Arch;

16 plan to visit none of the three places.

How many plan to visit the Art Museum only?

156) At East Zone University (EZU) there are 627

students taking College Algebra or Calculus.

417 are taking College Algebra, 261 are taking

Calculus, and 51 are taking both College

Algebra and Calculus. How many are taking

Algebra but not Calculus?

157) A local television station sends out

questionnaires to determine if viewers would

rather see a documentary, an interview show,

or reruns of a game show. There were 200

responses with the following results:

60 were interested in an interview show and a

documentary, but not reruns;

8 were interested in an interview show and

reruns, but not a documentary;

28 were interested in reruns but not an

interview show;

48 were interested in an interview show but

not a documentary;

20 were interested in a documentary and

reruns;

12 were interested in an interview show and

reruns;

16 were interested in none of the three.

How many are interested in exactly one kind

of show?

Use the union rule to answer the question.

158) If n(A) = 10, n(A ∪ B) = 28, and n(A ∩ B) = 6;

what is n(B)?

159) If n(B) = 24, n(A ∩ B) = 5, and n(A ∪ B) = 42;

what is n(A)?

Use a Venn diagram to decide if the statement is true or

false.

160) A ∪ (B ∩ C)' = (A ∪ B') ∩ (A ∪ C')

13

161) (A ∪ B) ∪ (A ∪ C) = A ∪ (B ∪ C)

162) (A' ∪ B)' = A' ∩ B

Use a Venn Diagram and the given information to

determine the number of elements in the indicated region.

163) n(U) = 83, n(A) = 41, n(B) = 34, n(C) = 23, n(A ∩

B) = 9, n(A ∩ C) = 6, n(B ∩ C) = 6, and

n(A ∩ (B ∩ C)) = 5. Find n(((A ∪ B) ∪ C)').

164) n(A) = 35, n(B) = 16, n(A ∩ B) = 5, n(A' ∩ B') =

14. Find n(U)

165) n(U) = 91, n(A) = 45, n(B) = 26, n(C) = 35, n(A ∩

B) = 5, n(A ∩ C) = 9, n(B ∩ C) = 5, and

n(A ∩ (B ∩ C)) = 4. Find n(A ∩ (B ∪ C)').

166) n(A) = 33, n(B) = 15, n(A ∪ B) = 42, n(B') = 40.

Find n(A ∩ B)'.

Identify the probability statement as empirical or not.

167) The probability of a forest fire in Yellowstone

National Park this year is 0.30.

168) The probability of rolling an even number on a

fair die is 0.50.

169) The probability of curing a certain type of

cancer if detected early is 0.70.

170) The probability that a brand-name computer

hard drive will crash during its first year of use

is 0.10.

Find the probability.

171) When a single card is drawn from a

well-shuffled 52-card deck, find the

probability of getting a black 9 or a red 2.



probability of getting a red card.



probability of getting a club.

174) A card is drawn from a well-shuffled deck of

52 cards. What is the probability of drawing a

face card or a 3?

Find the probability of the given event.

175) A single fair die is rolled. The number on the

die is less than 6.

176) Two fair dice are rolled. The sum of the

numbers on the dice is greater than 10.

177) A single fair die is rolled. The number on the

die is a multiple of 3.

178) Two fair dice are rolled. The sum of the

numbers on the dice is 1 or 5.


179) A bag contains 6 red marbles, 9 blue marbles,

and 4 green marbles. What is the probability

that a randomly selected marble is blue?

180) A spinner has equal regions numbered 1

through 15. What is the probability that the

spinner will stop on an even number or a

multiple of 3?

181) A bag contains 17 balls numbered 1 through

17. What is the probability that a randomly

selected ball has an even number?

182) Each of ten tickets is marked with a different

number from 1 to 10 and put in a box. If you

draw a ticket at random from the box, what is

the probability that you will draw 4, 9, or 2?

14

Find the indicated probability.

183) The table below shows the soft drink

preferences of people in three age groups.

cola root beer lemon-

under 21 years of age 40 25

between 21 and 40 35 20

over 40 years of age 20 30

If one of the 255 subjects is randomly selected,

find the probability that the person is over 40

years of age.

184) The following contingency table shows the

popular votes cast in the 1984 presidential

election by region and political party. Round

your answer to three decimal places.

Political Party

Region Democratic Republican Other

Northeast 9046 11,336 101

Midwest 10,511 14,761 169

South 10,998 17,699 136

West 7022 10,659 214

Totals 37,577 54,455 620

A person who voted Democratic in the 1984

presidential election is selected at random.

Find the probability that the person was from

the West.

185) The following table shows the grades of

college students in an advanced mathematics

course, broken down by year. Use the table

below to find the probability that a randomly

selected sophomore gets a B.

A B C D E

Totals

(%)

Freshmen 1 5 6 4 1 17

Sophomores 6 2 8 2 3 21

Juniors 5 7 14 6 2 34

Seniors 5 4 1 5 5 20

Grad Students 4 2 2 0 0 8

Totals (%) 21 20 31 17 11 100

186) The distribution of B.A. degrees conferred by a

local college is listed below, by major.

Major Frequency

English 2073

Mathematics 2164

Chemistry 318

Physics 856

Liberal Arts 1358

Business 1676

Engineering 868

9313

What is the probability that a randomly

selected degree is in Chemistry or Physics?



Major Frequency

English 2073

Mathematics 2164

Chemistry 318

Physics 856

Liberal Arts 1358

Business 1676

Engineering 868

9313


selected degree is not in Business and is not in

Engineering?



Major Frequency

English 2073

Mathematics 2164

Chemistry 318

Physics 856

Liberal Arts 1358

Business 1676

Engineering 868

9313


selected degree is not in English?

15

A die is rolled twice. Write the indicated event in set

notation.

189) The sum of the rolls is 5.

190) The first roll is a 5 and so is the second.

191) The sum of the rolls is 13.

Write the indicated event in set notation.

192) The event that Charlie is selected as a board

member when three board members are

selected at random from the following group:

Allison, Betty, Charlie, Dave, and Emily.

[The possible outcomes can be represented as

follows.

ABC ABD ABE ACD ACE

ADE BCD BCE BDE CDE]

193) The event that both prize winners are women

in a competition in which two people are

selected from four finalists to receive the first

and second prizes. The prize winners will be

selected by drawing names from a hat. The

names of the four finalists are Jim, George,

Helen, and Maggie.

[The possible outcomes can be represented as

follows.

JG JH JM GJ GH GM

HJ HG HM MJ MG MH

Here, for example, JG represents the outcome

that Jim receives the first prize and George

receives the second prize.]

194) When four coins are tossed, the first three

tosses come up the same.

[Hint: when four coins are tossed, the

following 16 outcomes are possible:

HHHH HHHT HHTH HHTT

HTHH HTHT HTTH HTTT

THHH THHT THTH THTT

TTHH TTHT TTTH TTTT ]


195) A spinner has regions numbered 1 through 15.

What is the probability that the spinner will

stop on an even number or a multiple of 3?

196) Of the 69 people who answered "yes" to a

question, 12 were male. Of the 62 people who

answered "no" to the question, 9 were male. If

one person is selected at random from the

group, what is the probability that the person

answered "yes" or was male?


52 cards. What is the probability of obtaining a

diamond or a card smaller than 5? [Assume

that ace is low]

198) Each digit from the number 5,929,889 is

written on a different card. If one of these cards

is selected at random, what is the probability

of drawing a card that shows 5 or 8?

199) Find the probability that the sum is either 10 or

at most 6 when two fair dice are rolled.


52 cards. What is the probability of drawing a

face card or a 5?

Solve the problem.

201) A survey revealed that 38% of people are

entertained by reading books, 27% are

entertained by watching TV, and 35% are

entertained by both books and TV. What is the

probability that a person will be entertained by

either books or TV? Express the answer as a

percentage.

16

202) 100 employees of a company are asked how

they get to work and whether they work full

time or part time. The figure below shows the

results. If one of the 100 employees is

randomly selected, find the probability of

getting someone who carpools or someone

who works full time.

1. Public transportation: 8 full time, 9 part time

2. Bicycle: 5 full time, 5 part time

3. Drive alone: 34 full time, 26 part time

4. Carpool: 7 full time, 6 part time

203) Of the coffee makers sold in an appliance store,

6.0% have either a faulty switch or a defective

cord, 2.7% have a faulty switch, and 0.2% have

both defects. What is the probability that a

coffee maker will have a defective cord?

Express the answer as a percentage.

204) Below is a table of data from a survey given to

1600 teenagers asking them to estimate what

percentage of their classmates are using drugs.

If a girl is selected at random, find the

probability that her estimate of the percentage

using drugs is 50% or higher. Round to the

nearest hundredth.

None 1% - 24% 25% - 49% 50% - 74%

Boys 26 182 450 114

Girls 46 232 350 164

205) The table below shows the probabilities of a

person accumulating specific amounts of credit

card charges over a 12-month period. Find the

probability that a person's total charges during

the period are $500 or more.

Charges Probability

Under $100 0.49

$100-$499 0.35

$500-$999 0.11

$1000 or more 0.05

206) The age distribution of students at a

community college is given below.

Age (years) Number of students (f)

Under 21 410

21-25 408

26-30 215

31-35 54

Over 35 20

1107

A student from the community college is

selected at random. Find the probability that

the student is between 26 and 35 inclusive.

Round to the nearest thousandth.

Provide an appropriate response.

207) In a local election, 51.1% of those aged under

40 and 44.6% of those aged over 40 vote in

favor of a certain ballot measure. Are age and

"voting in favor" independent? How can you

tell?

208) When a balanced die is rolled twice, 36 equally

likely outcomes are possible. Let

A = event the sum of the two rolls is 8

B = event the first roll comes up 3.

Find P(A) and P(A|B).

Are A and B independent events? How can

you tell?

17

209) When a coin is tossed three times, eight equally

likely outcomes are possible.

HHH HHT HTH HTT

THH THT TTH TTT

Let

A = event the first two tosses are the same

B = event the last two tosses are the same.

Find P(A), P(B), and P(A ∩ B).

Are A and B independent events? How can

you tell?

210) Is P(A∣B) always less than or equal to P(A)?

211) If P(A ∩ B) = 0.2, P(A) = 0.8, P(B) = 0.7, can A

and B be independent events? How can you

tell?

212) Can P(A∣B) = P(B∣A) if A and B are different?

Solve the problem.

213) If three cards are drawn without replacement

from an ordinary deck, find the probability

that the third card is a heart, given that the first

two cards were hearts.

214) If two cards are drawn without replacement


that the second card is a spade, given that the

first card was a spade.

215) If two cards are drawn without replacement


that the second card is a face card, given that

the first card was a queen.

216) If three cards are drawn without replacement


that the third card is a face card, given that the

first card was a queen and the second card was

a 5.

Use the given table to find the indicated probability.

217) The following table contains data from a study

of two airlines which fly to Smalltown, USA.

Number of flights

arrived on time

Number of flights

arrived late

Podunk Airlines 33 6

Upstate Airlines 43 5

If a flight is selected at random, what is the

probability that it was on Upstate Airlines and

that it arrived on time?

218) The following table contains data from a study

of two airlines which fly to Smalltown, USA.

Number of flights

arrived on time

Number of flights

arrived late

Podunk Airlines 33 6

Upstate Airlines 43 5

If a flight is selected at random, what is the

probability that it was on Upstate Airlines

given that it arrived late?

219) College students were given three choices of

pizza toppings and asked to choose one

favorite. The following table shows the results.

Toppings Freshman Sophomore Junior Senior

Cheese 13 14 19 22

Meat 28 22 14 13

Veggie 14 13 28 22

A student is selected at random. Find the

probability that the student's favorite topping

is meat given that the student is a junior.

18

220) College students were given three choices of

pizza toppings and asked to choose one

favorite. The following table shows the results.

Toppings Freshman Sophomore Junior Senior

Cheese 11 14 29 28

Meat 24 28 14 11

Veggie 14 11 24 28

A student is selected at random. Find the

probability that the student's favorite topping

is veggie given that the student is a junior or

senior.


221) The following contingency table provides a

joint frequency distribution for the popular

votes cast in the 1984 presidential election by

region and political party. Data are in

thousands, rounded to the nearest thousand.

Political Party

Region Democratic Republican Other Totals

Northeast 9046 11,336 101 20,483

Midwest 10,511 14,761 169 25,441

South 10,998 17,699 136 28,833

West 7022 10,659 214 17,895

Totals 37,577 54,455 620 92,652

A person who voted in the 1984 presidential

election is selected at random. Compute the

probability that the person selected voted

Democrat.

222) The table below describes the smoking habits

of a group of asthma sufferers.

Nonsmoker Light

smoker

Heavy

smoker Total

Men 326 71 78

Women 368 78 60

Total 694 149 138

If one of the 981 subjects is randomly selected,

find the probability that the person chosen is a

nonsmoker given that it is a woman. Round to

the nearest thousandth.

223) The following contingency table provides a

joint frequency distribution for the popular

votes cast in the 1984 presidential election by

region and political party. Data are in

thousands, rounded to the nearest thousand.

Political Party

Region Democratic Republican Other Totals

Northeast 9046 11,336 101 20,483

Midwest 10,511 14,761 169 25,441

South 10,998 17,699 136 28,833

West 7022 10,659 214 17,895

Totals 37,577 54,455 620 92,652

A person who voted in the 1984 presidential

election is selected at random. Compute the

probability that the person selected was in the

West and voted Republican.

Solve the problem.

224) Two stores sell a certain product. Store A has

32% of the sales, 3% of which are of defective

items, and store B has 68% of the sales, 4% of

which are of defective items. The difference in

defective rates is due to different levels of

pre-sale checking of the product. A person

receives one of this product as a gift. What is

the probability it is defective?

225) In a certain U.S. city, 51.4% of adults are

women. In that city, 13.4% of women and

10.7% of men suffer from depression. If an

adult is selected at random from the city, find

the probability that the person is a man who

does not suffer from depression.

226) 38% of a store's computers come from factory

A and the remainder come from factory B. 1%

of computers from factory A are defective

while 4% of computers from factory B are

defective. If one of the store's computers is

selected at random, what is the probability that

it is defective and from factory B?


227) If two cards are drawn with replacement from

an ordinary deck, find the probability the first

card is a heart and the second is a diamond.

19

228) A family has five children. The probability of

having a girl is 1/2. What is the probability of

having 2 girls followed by 3 boys? Round your

answer to four decimal places.

229) A basketball player hits her shot 45% of the

time. If she takes four shots during a game,

what is the probability that she misses the first

shot and hits the last three? Express the answer

as a percentage, and round to the nearest tenth

(if necessary). Assume independence of shots.


230) You are dealt two cards successively (without

replacement) from a shuffled deck of 52

playing cards. Find the probability that both

cards are black.

231) Assume that two marbles are drawn without

replacement from a box with 1 blue, 3 white, 2

green, and 2 red marbles. Find the probability

that the first marble is white and the second

marble is blue.

232) Assume that two marbles are drawn without

replacement from a box with 1 blue, 3 white, 2

green, and 2 red marbles. Find the probability

that both marbles are white.

Use Bayes' rule to find the indicated probability.

233) Two stores sell a certain product. Store A has

44% of the sales, 5% of which are of defective

items, and store B has 56% of the sales, 3% of

which are of defective items. The difference in

defective rates is due to different levels of

pre-sale checking of the product. A person

receives a defective item of this product as a

gift. What is the probability it came from store

B?

234) A company is conducting a sweepstakes, and

ships two boxes of game pieces to a particular

store. Box A has 5% of its contents being

winners, while 3% of the contents of box B are

winners. Box A contains 36% of the total

tickets. The contents of both boxes are mixed in

a drawer and a ticket is chosen at random.

What is the probability it came from box A if it

is a winner?

235) Two shipments of components were received

by a factory and stored in two separate bins.

Shipment I has 2% of its contents defective,

while shipment II has 5% of its contents

defective. If it is equally likely an employee

will go to either bin and select a component

randomly, what is the probability that a

defective component came from shipment II?

The table shows, for some particular year, a listing of

several income levels and, for each level, the proportion of

the population in the level and the probability that a

person in that level bought a new car during the year.

Given that one of the people who bought a new car during

that year is randomly selected, find the probability that

that person was in the indicated income category. Round

your answer to the nearest hundredth.

Income level

Proportion

of population

Probability that

bought a new car

$0 - 4,999 5.2% 0.02

$5,000 - 9,999 6.4% 0.03

$10,000 - 14,999 5.4% 0.06

$15,000 - 19,999 8.7% 0.07

$20,000 - 24,999 9.4% 0.09

$25,000 - 29,999 10.2% 0.10

$30,000 - 34,999 13.8% 0.11

$35,000 - 39,999 10.7% 0.13

$40,000 - 49,999 15.5% 0.15

$50,000 and over 14.7% 0.19

236) $20,000 - $24,999

237) $15,000 - $19,999

238) $25,000 - $29,999

239) $0 - $4,999

How many distinguishable permutations of letters are

possible in the word?

240) MISSISSIPPI

241) LOOK

242) GIGGLE

20

An order of award presentations has been devised for

seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and

Paul.

243) In how many ways can the people be

presented?

244) In how many ways can the awards be

presented so that Maria and Olivia will be next

to each other?

Four accounting majors, two economics majors, and three

marketing majors have interviewed for five different

positions with a large company. Find the number of

different ways that five of these could be hired.

245) There is no restriction on the college majors

hired for the five positions.

246) Two accounting majors must be hired first,

then one economics major, then two marketing

majors.

247) Instead of five positions, the company has

decided that only three positions, with no

restriction on the college majors, must be filled.

Given a group of students:

G = {Allen, Brenda, Chad, Dorothy, Eric} or

G = {A, B, C, D, E}, count the different ways of choosing

the following officers or representatives for student

congress. Assume that no one can hold more than one

office.

248) A male president and three representatives

249) Three representatives, if two must be male and

one must be female

250) A treasurer and a secretary if the two must not

be the same sex

Solve the problem.

251) How many 6-digit numbers can be formed

using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if

repetitions of digits are allowed?

252) At a lumber company that sold shelves, a

customer could choose from 5 types of wood, 4

different widths and 3 different lengths. How

many different types of shelves could be

ordered?

253) License plates are made using 3 letters

followed by 2 digits. How many plates can be

made if repetition of letters and digits is

allowed?

Suppose a traveler wanted to visit a museum, an art

gallery, and the state capitol building. 45-minute tours are

offered at each attraction hourly from 10 a.m. through 3

p.m. (6 different hours). Solve the problem, disregarding

travel time.

254) In how many ways could the traveler schedule

two of the three tours in one day?


all three tours in one day, with the museum

tour being after noon?


all three tours in one day, with the art gallery

being the last tour of the day?

To win the World Series, a baseball team must win 4

games out of a maximum of 7 games. To solve the

problem, list the possible arrangements of losses and

wins.

257) How many ways are there of winning the

World Series in exactly 6 games if the winning

team wins the first two games?



team wins the last two games?



team wins the first game?

Of the 2,598,960 different five-card hands possible from a

deck of 52 playing cards, how many would contain the

following cards?

260) Two black cards and three red cards

261) All diamonds

Decide whether the situation involves permutations or

combinations.

262) An arrangement of 9 people for a picture.

21

263) A blend of 2 spices taken from 8 spices on a

spice rack.

264) A selection of a chairman and a secretary from

a committee of 17 people.

Solve the problem.

265) If you toss four fair coins, in how many ways

can you obtain at least one head?

266) A bag contains 5 apples and 3 oranges. If you

select 4 pieces of fruit without looking, how

many ways can you get exactly 3 apples?

267) How many 5-card poker hands consisting of 3

aces and 2 kings are possible with an ordinary

52-card deck?

268) If the police have 7 suspects, how many

different ways can they select 5 for a lineup?

269) In how many ways can a student select 8 out of

10 questions to work on an exam?

270) Three noncollinear points determine a triangle.

How many triangles can be formed with 8

points, no three of which are collinear?

271) How many different three-number

"combinations" are possible on a combination

lock having 25 numbers on its dial? Assume

that no numbers repeat. (Combination locks

are really permutation locks.)

272) If a license plate consists of four digits, how

many different licenses could be created

having at least one digit repeated.

273) How many two-digit counting numbers do

not contain any of the digits 1, 3, or 9?

Find the probability of the following card hands from a

52-card deck. In poker, aces are either high or low. A

bridge hand is made up of 13 cards.

274) In bridge, all cards in one suit

275) In bridge, exactly 3 kings and exactly 3 queens

276) In bridge, 6 of one suit, 4 of another, and 3 of

another

A bag contains 6 cherry, 3 orange, and 2 lemon candies.

You reach in and take 3 pieces of candy at random. Find

the probability.

277) 2 orange, 1 lemon

278) 1 cherry, 2 lemon

279) All cherry

Solve the problem.

280) A roulette wheel contains 32 slots numbered 1

through 32. The odd number slots are colored

purple and even number slots are colored blue.

When the wheel is spun, a ball rolls around the

rim and falls into a slot. What is the probability

that the ball falls into an even number slot?

281) At the first tri-city meeting, there were 8

people from town A, 7 people from town B,

and 5 people from town C. If the council

consists of 5 people, find the probability of 2

from town A, 2 from town B, and 1 from town

C.

282) A ring contains 8 keys: 1 red, 1 blue, and 6

gold. If the keys are arranged at random on the

ring, find the probability that the red is next to

the blue.

283) What is the probability that at least 2 students

in a class of 36 have the same birthday?

284) A roulette wheel contains 84 slots numbered 1

through 84. The slots 1,4,7,... are red, the slots

2,5,8,... are green, and the slots 3, 6, 9,.... are

brown. When the wheel is spun, a ball rolls

around the rim and falls into a slot. What is the

probability that the ball falls into a green slot?

285) What is the probability that at least 2 of the 435

members of the House of Representatives have

the same birthday?

22

Solve.

286) In a state lotto you have to pick 4 numbers

from 1 to 42. If your numbers match those that

the state draws, you win. If you buy 3 tickets,

what is your probability of winning?

287) Two 6-sided dice are rolled. What is the

probability that the sum of the two numbers on

the dice will be greater than 10?

288) Two 6-sided dice are rolled. What is the

probability the sum of the two numbers on the

die will be 5?

Prepare a probability distribution for the experiment. Let

x represent the random variable, and let P represent the

probability.

289) Three coins are tossed, and the number of tails

is noted.

290) A ball player batting .300 comes to bat 3 times

in a game. The number of hits is counted.

291) Four coins are tossed and the number of heads

is counted.

Give the probability distribution and sketch the

histogram.

292) The telephone company kept track of the calls

for the correct time during a 24-hour period

for two weeks. The results are shown in the

table.

Number

of Calls Frequency

59 1

60 2

61 3

62 4

63 2

64

65

5

1

Total: 14

293) A class of 44 students took a 10-point quiz.

The frequency of scores is given in the table.

Number of

Points Frequency

5 2

6 5

7 10

8 15

9 9

10 3

Total: 44

Find the expected value of the random variable in the

experiment.

294) Three coins are tossed, and the number of tails

is noted.

295) Five rats are inoculated against a disease. The

number contracting the disease is noted and

the experiment is repeated 20 times. Find the

probability distribution and the expected

number of rats contracting the disease.

Number with Disease Frequency

0 2

1 4

2 7

3 3

4 1

5 3

Total: 20

Solve the problem.

296) Suppose you pay $1.00 to roll a fair die with

the understanding that you will get back $3.00

for rolling 4 or 5. What is your expected

payback?

297) Numbers is a game where you bet $1.00 on any

three-digit number from 000 to 999. If your

number comes up, you get $600.00. Find the

expected payback.

23

298) An insurance company says that at age 50 one

must choose to take $10,000 at age 60, $30,000

at 70, or $50,000 at 80 ($0 death benefit). The

probability of living from 50 to 60 is 0.88, from

50 to 70, 0.65, and from 50 to 80, 0.4. Find the

expected value at each age.

299) A contractor is considering a sale that promises

a profit of $32,000 with a probability of 0.7 or a

loss (due to bad weather, strikes, and such) of $

15,000 with a probability of 0.3. What is the

expected profit?

300) Find the expected number of girls in a family

of 7 children.

301) If 2 cards are drawn from a deck of 52 cards,

what is the expected number of spades?

Find the mean. Round to the nearest tenth.

302) Value Frequency

13 1

18 4

24 4

31 6

34 3

303) Value Frequency

154 2

178 2

260 7

294 4

365 3

384 3

Find the mean for the list of numbers.

304) 73, 50, 73, 97, 50 (Round to the nearest tenth, if

necessary.)

305) 72, 150, 272, 161 (Round to the nearest tenth.)

Find the median for the list of numbers.

306) 5, 6, 13, 25, 32, 37, 47

307) 2, 9, 21, 26, 36, 50

Find the mode or modes.

308) 20, 27, 46, 27, 49, 27, 49

309) 87, 72, 32, 72, 29, 87

Prepare a frequency distribution with a column for

intervals and frequencies.

310) Use five intervals, starting with 0 - 4.

3 7 10 15 22 20 17 13 9 3 6 14 17

21 15 12 5 9 14 20

311) Use six intervals, starting with 0 - 49.

25 76 113 185 235 211 197 147 95 24 97 264

85 129 181 245 167 112 49 99 149 199 155

267

Solve the problem.

312) The following data gives the number of

applicants that applied for a job at a given

company each month of 1999: 62, 70, 68, 76, 84,

77, 79, 86, 81, 68, 65, 62. What is the median of

the data?

313) The following data gives the number of

applicants that applied for a job at a given

company each month of 1999: 65, 68, 93, 77, 79,

85, 86, 88, 91, 93, 75, 65. What is the mode of the

data?

Find the range for the set of numbers.

314) 25, 38, 11, 46, 56

315) 115, 560, 165, 668, 362, 234

Solve the problem.

316) The manager of an electrical supply store

measured the diameters of the rolls of wire in

the inventory. The diameters of the rolls (in m)

are listed below. Find the standard deviation.

Round your result to four decimal places.

0.209 0.252 0.525 0.459 0.648 0.151 0.199

317) The table gives the number of new homes

constructed in a certain town in recent years.

Find the standard deviation for the data.

Round to the nearest tenth.

Year Number of Homes Year Number of Homes

1997 49 2002 33

1998 50 2003 30

1999 52 2004 39

2000 63 2005 46

2001 61 2006 51

24

Find the percent of the total area under the standard

normal curve between the given z-scores.

318) z = -0.55 and z = 0.55

319) z = -1.93 and z = -0.46

320) z = -2.41 and z = 0.0

Find the percent of the area under a normal curve between

the mean and the given number of standard deviations

from the mean.

321) 0.83

322) -2.91

323) 1.64

Find a z-score satisfying the given condition.

324) 30.2% of the total area is to the right of z.

325) 4% of the total area is to the right of z.

326) 30.2% of the total area is to the left of z.

A company installs 5000 light bulbs, each with an average

life of 500 hours, standard deviation of 100 hours, and

distribution approximated by a normal curve. Find the

approximate number of bulbs that can be expected to last

the specified period of time.

327) Less than 500 hours

328) Between 290 hours and 540 hours

329) More than 740 hours

330) Between 500 hours and 675 hours

Assume the distribution is normal. Use the area of the

normal curve to answer the question. Round to the nearest

whole percent.

331) A certain grade of egg must weigh at least 2.5

oz. If the average weight of an egg is 1.5 oz,

with a standard deviation of 0.4 oz, how many

eggs in a sample of 9 dozen would you expect

to weigh more than 2.5 oz?

332) The average middle-distance runner at a local

high school runs the mile in 4.5 minutes, with a

standard deviation of 0.3 minute. What is the

probability that a runner will run the mile in

less than 4 minutes?

333) A machine fills quart soda bottles with an

average of 32.3 oz per bottle, with a standard

deviation of 1.2 oz. What is the probability that

a filled bottle will contain less than 32.0 oz?

334) At a local market, the average weekly grocery

bill is $57.85 with a standard deviation of

$14.25. What is the lowest amount spent by the

upper 25% of market customers?

At one high school, girls can run the 100-yard dash in an

average of 15.2 seconds with a standard deviation of 0.9

second. The times are very closely approximated by a

normal curve. Find the percent of times that are:

335) Less than 15.2 seconds

336) Greater than 16.1 seconds

337) Between 14.3 and 16.1 seconds

338) Less than 17 seconds

Solve the problem.

339) The life span of a certain type of car timing

belt, calculated in miles, is normally

distributed, with a mean of 80,000 miles and a

standard deviation of 6500 miles. If the maker

of the timing belt wants less than 4% of the

belts to fail while under warranty, for how

many miles should the timing belts be

guaranteed?

340) If the life, in years, of a washing machine is

normally distributed with a mean of 16 years

and a standard deviation of 3 years, what

should be the guarantee period if the company

wants less than 1% of the machines to fail

while under warranty?

25

Answer KeyTestname: 1324-PT-FINAL1

1)5

2

2)1

8

3) 201.2 min

4) $33,900

5) 122 mi

6) y = 3

13x + 14

7) y = 3x + 105

where x is the

number of

years since

1990

8) S = 15,000x

+ 10,000

9) 100 platens

10) 11 packages

11) $0.50

12) 53 packages

13) 8 feet

14) -40°

15) 72

16) $16; 3040

17) $6000 in

mutual fund, $

7000 in bond,

and $3000 in

bank

18) 22 pounds

19) 170 adults, 300

children

20) $16 per day,

22¢ per mile

21) a = 2e, b = 10 -

2e, c = 5 - e/2,

d = 5 - e/2, 0 ≤

e ≤ 5

22) x = 126 - 6w/5,

y = 84 - 4w/5,

z = w, 0 ≤ w ≤

105

23) x = 5 - z, y = 5,

0 ≤ z ≤ 5

24) x = 8, y = 40 -

z, 0 ≤ z ≤ 40

25)19z + 80

4, -9z -

4

26)-z - 6

3,

7z + 30

3

27)29z + 16

17,

15z -

17

28)-7z + 34

5,

2z + 11

5

29) 90,000 15,000

50,000 25,000

30) Washing

Dish

Machines

Washers

P =

7 3

15 12

10 8

Store 1

Store 2

Store 3

31)2 2 2

4 1 1

2 2 3

32)-0.2

-0.4

-0.5

33) 220 300

400 180

34) x = 4, y = 2, z =

-9

35) m = -6, x = 1,

n = 6, y = -7, p

= -5

36) t = -10, x = 1

37) 6 10

3 18

38) -5 6

39) -3 -9

0 -6

40) -1 3

-10 2

41) -3 -7

9 25

42) 3 -7 -1

6 -28 47

43)

X

32

26

20

Y

34

24

20

cherry

almond

raisin

44) $7800

45) $15,000

46) $15,200

47)

-10 -5

10

-10

-10 -5

10

-10

48)

-10 -5

10

-10

-10 -5

10

-10

49)

-10 -5

10

-10

-10 -5

10

-10

50)

-6 -4 -2-6 -4 -2

51) 30 ≤ x + y ≤ 45,

y ≥ 10, y ≤ 3

2x,

x ≥ 0

5 10 15

y45

40

35

30

25

20

15

10

5

5 10 15

y45

40

35

30

25

20

15

10

5

52) 1.35a + 2.1 b ≤

938

1.25 a + 1.7b ≤

469

a ≥ 0, b ≥ 0

53) 9x + 13y ≤ 460

7x + 14y ≤ 290

x ≥ 0, y ≥ 0

54) 2x + 4y ≤ 48

2x + 3y ≤ 42

x ≥ 0

y ≥ 0

55) Maximum of

70; minimum

of 36

56) No maximum;

minimum of

29

57) Minimum of

33 when x = 7

and y = 1

58) Maximum of

32 when x = 3

and y = 2

59) Minimum of

1.02 when x =

3 and y = 4

60) Maximum of

100 when x = 8

and y = 3

61) 12 VIP and 12

SST

62) $48,299

63) 0 trash

compactors, 90

microwaves

64)2

3 sacks of

soybeans and

20

9 sacks of

alfalfa

65) 14 P1 planes

and 7 P2

planes

66)5

3 bags of Feed

type I, 0 bags

of Feed type II

67)7

3 servings of

refried pinto

beans and 4

servings of

kidney beans

68) $7593.21

69) $152,100.00

70) $79,842.61

71) $67.82

72) $81,419.34

73) $10,257.28

74) $40,006.84

75) $17,820.78

76) $67,167.73

77) $34,654.69

78) $350,429.33

26


79) $1197.43

80) $354.17

81) $41,567.72

82) $18,719.42

83) $19,458.68

84) $318.07

85) $745.60

86) $558.95

87) $4005.47

88) $56,789.98

89) (a) 10

semiannual

periods

(b) $8661.65

(c) $1105.15

90) (a) 9 years

(b) $117,174.69

(c) $11,644.47

91) $150,852.62

92) $685,421.57

93) $528.95

94) $557.08

95) $353.24

96) $1202.41

97) $14,902.91

98) $28,123.38

99) $894,249.29

100) $80,960.96

101) $20.85

102) 8.8 years

103) $498.94

104) $1570

105) All soda pops

that are diet or

caffeine-free

soda pops

106) All diet-cola

soda pops not

in cans

107) All non-diet

soda pops in

cans

108) All soda pops

that are diet,

cola, or

caffeine-free

109) 16

110) 1024

111) False

112) False

113) True

114) True

115) True

116) True

117) False

118) True

119) True

120) False

121) True

122) False

123) True

124) False

125) True

126) False

127) ⊈

128) ⊆

129) ⊆

130) ⊈

131) {h, p, w}

132) {s}

133) {c, h, n, p, w}

134) {n}

135) {c, h, n, p, r, s,

t, w}

136) {c, n, r, s, t}

137) {r, t, u, v, w, x}

138) {r, t}

139) {r, t, u, v, w, x,

z}

140) {q, s, v, w, x, y,

z}

141) {u, w}

142) {q, s, u, w, y, z}

143) 232

144) 614

145) 92

146) 67

147) 550

148) 929

149)

150)

151)

152)

153)

154)

155) 12

156) 366

157) 96

158) 24

159) 23

160) False

161) True

162) False

163) 1

164) 60

165) 35

166) 49

167) Empirical

168) Not empirical

169) Empirical

170) Empirical

171)1

13

172)1

2

173)1

4

174)4

13

175)5

6

176)1

12

177)1

3

178)1

9

179)9

19

180)2

3

181)8

17

182)3

10

183)1

3

184) 0.187

185)2

21

186) 0.126

187) 0.727

188) 0.777

189) {(1, 4), (2, 3),

(3, 2), (4, 1)}

190) {(5, 5)}

191) ∅

192) ABC, ACD, ACE, BCD, BCE, CDE

193) HM, MH

194)

HHHH, HHHT, TTTH, TTTT

195)2

3

196) 0.595

197)25

52

198)3

7

199)1

2

200)4

13

201) 30%

202) 0.6

203) 3.5%

204) 0.22

205) 0.16

206) 0.243

207) No; P(vote in

favor|under

40) ≠ P(vote in

favor|over 40)

208) P(A) = 5

36 ;

P(A|B) = 1

6

No; P(A) ≠

P(A|B).

209) P(A) = 1

2, P(B)

= 1

2, and P(A ∩

B) = 1

4

Yes; P(A) ·

P(B) = P(A ∩

B).

210) No

211) No, because

P(A ∩ B) ≠

P(A) · P(B)

212) Yes

213)11

50

214)4

17

27


215)11

51

216)11

50

217)43

87

218)5

11

219) 0.230

220) 0.388

221) 0.406

222) 0.727

223) 0.115

224) 0.037

225) 0.434

226) 0.025

227)1

16

228) 0.0313

229) 5%

230)25

102

231)3

56

232)3

28

233) 0.4308

234) 0.486

235) 0.714

236) 0.08

237) 0.05

238) 0.09

239) 0.01

240) 34,650

241) 12

242) 120

243) 5040

244) 1440

245) 15,120 ways

246) 144 ways

247) 504 ways

248) 72

249) 12

250) 12

251) 1,000,000

six-digit

numbers

252) 60 types

253) 1,757,600

plates

254) 30

255) 60

256) 40

257) 3 ways

258) 10 ways

259) 6 ways

260) 845,000 hands

261) 1287 hands

262) Permutation

263) Combination

264) Permutation

265) 15 ways

266) 30 ways

267) 24 five-card

hands

268) 21 ways

269) 45 ways

270) 56 triangles

271) 13,800

three-number

"combinations"

272) 4960 licenses

273) 42 numbers

274) 6.30 × 10-12

275) 0.00097

276) 0.0133

277) 0.0364

278) 0.0364

279) 0.1212

280) 0.5

281) 0.189

282) 0.286

283) 0.832

284)1

3

285) 1

286)1

37310

287)1

12

288)1

9

289)

x P(x)

0 1/8

1 3/8

2 3/8

3 1/8

290)

x P(x)

0 0.343

1 0.441

2 0.189

3 0.027

291)

x P(x)

0 1/16

1 1/4

2 3/8

3 1/4

4 1/16

292) x 59 60

P(x) 0.07 0.14 0.21

293) x 5 6

P(x) 0.05 0.11

294) 1.5

295) 2.3

296) $0

297) -$0.40

298) 60 - $8800

70 - $19,500

80 - $20,000

299) $17,900

300) 3.5

301) 0.50

302) 26.1

303) 281.3

304) 68.6

305) 163.8

306) 25

307) 23.5

308) 27

309) 87, 72

310)

Interval Frequency

0 - 4

5 - 9

10 - 14

15 - 19

20 - 24

311)

Interval Frequency

0 - 49

50 - 99

100 - 149

150 - 199

200 - 249

250 - 299

312) 73

313) 93 and 65

314) 45

315) 553

316) 0.1929

317) 10.8

318) 0.4176

319) 0.2960

320) 0.4920

321) 29.67%

322) 49.82%

323) 44.95%

324) 0.52

325) 1.75

326) -0.52

327) 2500

328) 3188

329) 41

330) 2300

331) 1 egg

332) 5%

333) 40%

334) $67.40

335) 50%

336) 16%

337) 68%

338) 97.7%

339) Less than

68,625 miles

340) Less than 9.01

years

28

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