Math 141 Final Review
1. A new car sells for $24,000. It depreciates linearly to a value of $16,500 in 3
years.
a) Find the value of the car, V(t), as a function of t=age in years of the car.
b) Find the value of the car when it is 5 years old.
2. A manufacturer has a monthly fixed cost of $800. Each unit he produces costs an
additional $5. The selling price per unit is p   . 02 x  15 for x=quantity
produced and sold.
a) Find the cost, revenue and profit functions, C(x), R(x) and P(x).
b) What is the maximum revenue?
c) What is the maximum profit?
d) Find the two quantities at which they break even.
3.a) Suppliers of a certain brand of refrigerator will supply none if the unit price is $500
or less. They will supply 300 when the unit price is $710.
a)Find the supply equation.
b) Demand for the refrigerator is 200 units when the price is $600 and demand decreases
by 50 units for each $25 increase in price. Find the demand equation.
c) Find the equilibrium quantity and price.
w
4. A   7
 3
2 

9

z 
2
B  
y
x
0
3

4
1
5. Find the product AB for A   3

 2
Compute 2 A  3 B T
a

0

1 
b
B  
2
1 

 1
6. A company produces 2 kinds of candy. Chocolate chunk uses 3 lb of butter, 1 lb of
chocolate and 2 lbs of sugar per batch. Fudge uses 2 lbs of butter, 2 lbs of chocolate, and
1.5 lbs of sugar per batch. Butter costs $3 per lb, chocolate costs $2.50 per lb and sugar
costs $1 per lb. They have an order for 5 batches of chocolate chunk and 6 batches of
fudge. What matrix product gives the total cost of the order?
7. Set up the inequalities and the objective function but do not solve.
A couple is investing up to $100,000 in a money market fund, gold and a stock fund. The
returns for the money market, gold and stocks are 5%, 6% and 10% respectively. They
have been advised that the sum of the amounts in gold and the money market should be
no more than 30% of the total. The amount in stocks should be at least three times the
amount in gold. How much should be invested in each to maximize return?
8.. Solve each system of equations or state there is no solution.
a) x+2y+3z=10, x – y - 2z=15, 5x - y=35
b) x+y+z=1, 2x – 3y+2z=0, 4x – y+4z=5
c)x+2y – z=3, 2x – 3y+z=5, x – 5y+2z=2
9. What row operations will perform the first pivot in the row reduction of
 3

2

  5
6
5
4
9

1 ? What is the result?

6 
10. Use the graphical method of corners to find the maximum and minimum of 4x+5y
subject to 3x+y<12, x+3y<12, x+y<5, 3x+2y>6, x>0, y>0.
11. A pet store is purchasing puppies and kittens. Each puppy requires 12 square feet of
living space and each kitten requires 8 square feet of living space. They have available
120 square feet for these animals. Each puppy costs them $12 and each kitten costs them
$10. They want to spend no more than $126 for animals.
Weekly care costs $3 for each animal. They want to spend no more than $36 per week.
Revenues are $80 per puppy and $70 per kitten. How many of each should they purchase
to maximize their revenue?
12. U is the universal set. A, B, and C are subsets of U. Describe with unions,
intersections and complements:
a) {x in U: x is in at least one of A, B, and C}
b) {x in U: x is in all of A, B, and C}
c) {x in U: x is in A and B but not C}
d) {x in U: x is in A or B but x is not in C}
e) {x in U: x is not in A or B but x is in C}
13. Seven movies are nominated for three different prizes. How many ways can the prizes
be awarded if:
a) no movie gets more than one prize?
b) any movie can get any number of prizes?
c) a single movie can get at most 2 prizes?
14.. How many distinguishable arrangements of 5 red, 4 blue and 3 yellow balls are
there?
Think of Mississippi.
15. How many ways can 1 1st prize, 5 2nd prizes, and 10 3rd prizes be awarded among 70
people if no-one gets more than one prize?
16. Twelve athletes are to line up for a photo. There are 5 football players, 3 swimmers
and 4 runners. How many ways can they line up if athletes of the same sport must be kept
together?
17. A box contains 50 apples. 17 are honeycrisp, 20 are gala, and 13 are cameo. 7 apples
are chosen at random. What is the probability of getting:
a) at least one honeycrisp?
b) at least 2 honeycrisp?
c) all of the same type?
d) exactly 2 honeycrisp or exactly 3 gala, still choosing 7 apples.?
18. A 5 sided die is tossed 15 times. The random variable X is the number of times the
die lands with either 1 or 2 on top probability that:
a) X is exactly 6?
b) X is at least 4 and at most 8.
19. A store survey asked 150 people to rate the sales service on a scale of 0=awful to
5=excellent. The results were
rating 5 4 3 2 1 0
# of respondents 55 40 25 15 5 10
If X is a randomly selected rating find:
a) P(X>3) b) E(X) c)  ( X ) d) median of X e) mode of X.
20. P(E)=.7 P(F)=.8 P( E C  F C )=.06 a) Find P( E  F ).
independent? Mutually exclusive?
b) Are E and F
21. Six people choose from 12 varieties of trees to plant. What is the probability :
a) at least 2 people will choose the same variety?
b) they will all choose the same variety?
c) exactly 3 people will choose the same variety and there are no other repeats?
22. A disease has a 15% rate of occurrence. A test for the disease is negative in 5% of
people who have the disease and positive in 7% of people who do not have the disease.
Let + be the event the test is positive and D the event the person has the disease. Find:
a) the test is positive b) the test is positive and the person has the disease c) a person
who has the disease gets a positive test. d) a person who gets a positive test actually has
the disease.
23. A fictitious study tested to see if caffeine could improve memory. 100 people drank
coffee and were asked to memorize a list. 100 people consumed no caffeine and
memorized the same list. 110 people remembered at least 90% of the list. 75 of the
people who drank coffee remembered at least 90% of the list. Let C represent those who
drank coffee and M those who remembered at least 90% of the list.
a) Are C and M independent? Why or why not?
b) Does the study show coffee helps memory? Why or why not?
c) What is the probability someone who did not drink coffee remembered at least
90% of the list?
24. a) The odds in favor of a certain team winning a game are 3:4. What is the probability
this team will win?
b) The chance of rain is 40%. What are the odds in favor of rain?
25. Three security checkpoints 1, 2, and 3 have independent probabilities of letting an
intruder pass through of .05, .06, and .04 respectively. What is the probability an intruder
a) will be detected by at least one checkpoint?
b) will be detected by checkpoints 1 or 2?
26. A city has 3 hospitals A, B, and C. 40% of new babies in the year were born at
hospital A and had an average weight of 7.2 lbs. 35% were born at hospital B and had an
average weight of 6.9 lbs. 25% were born at hospital C and had an average weight of 6.5
lbs. What is the average weight of babies born in the city hospitals that year?
27. A stock is watched for 14 days with the following results:
price/share $45 $47 $49 $50 $52 $53
# days
1
3
2
2
2
4
a) What is the expected price per share?
b) What is the standard deviation of the price per share?
28. A student takes 14 credits and receives the following grades.
Grade
A
B
C
D
F
# credits
3
4
4
3
0
a) Find the students gpa for the 14 credits.
b) If he previously had a gpa of 3.0 for 70 credits, find the new gpa.
29. A set of exam grades is normally distributed with a mean of 75 and a standard
deviation of 12.
a) Find the probability that a randomly selected score is better than 80. Round to 2
decimal places. Use 10^9 for the right endpoint.
b) What is the probability a score is between 70 and 80 rounded to four decimal places?
c) Find a so the probability a randomly selected score is less than a is 0 .7.
d) Find b so the probability that a randomly selected score is greater than b is 0 .7.
30. The lengths of babies born at a certain hospital are normally distributed with a mean
of 20 inches and a standard deviation of .75 inches. Twenty babies are selected at random
and X is the number who are between 19 and 21 inches long.
a) What is the expected value of X?
b) What is the probability that X is at least 14?
c) Find P(15<X<18).
d) Find a length L so that 75% of babies are longer than L.
31. A person will buy a $250,000 home paying 20% down and financing the rest at the
annual interest rate of 7% compounded monthly. He will make monthly payments for 30
years to pay off the loan.
a) Find the monthly payment.
b) How much of the first payment is interest?
c) How much is still owed after 10 years? There are 2 ways to do this in the tvmsolver.
d) How much of the 121st payment is interest?
e) If he refinances after 10 years at annual interest rate 6% compounded monthly,
what is his new payment, assuming the loan is paid off in the remaining 20 years.
32. a) How much should you deposit in the bank at annual interest rate 4%
compounded monthly to be able to withdraw $750 per month for 10 years?
b) If no withdrawals will be made until 20 years from now, how much would you
need to deposit today?
.