G
Answers to Selected Exercises
Chapter 1 Logic
Section 1.1 Deductive vs. Inductive Reasoning
b. Valid
1. a. valid
Unemployed
master
x
photographers
Homeless
People
artists
x = Ansel Adams
b. Not Valid
x = Bill Gates
Artists
5. invalid
Master
Photographers
pesticides
x
things harmful
to environment
x = Ansel Adams
x = fertilizer
3. a. Not Valid
Unemployed
Homeless
People
7. valid
policemen
x
vegetarian
gunowners
x = Bill Gates
x = policeman
A-35
Truckee Meadows Community College Math Department
17. invalid
9. valid
police
officers
poets
x
x
loners
y
women
motorcycle
riders
taxi drivers
x = poet
x = policewoman
11. valid
y = motorcycle
officer
19. valid
Rectangles
Quiche
eaters
Squares
Real Men
Quadrilaterals
x = Quadrilateral
x = Clint Eastwood
13. valid
roads
x
things leading
to Rome
x = Route 66
15. invalid
dangerous
things
animals
x
Section 1.2 Symbolic Logic
x = tiger
A-36
APPENDIX
21. a. inductive
b. deductive
23. 23. Add 5 each time
25. 20. Add 2 to the first term to get the second term, add 4
to the second term to get the third term, add 6 to the third
term to get the fourth term, and so on.
27. 25. The first term is 12, the second term is 22, the third
term is 32, and so on.
29. 13. Each term is a prime number.
31. 5. Think of each number in the sequence as a time (5:00,
8:00, etc.). Add three hours each time.
33. f, s; first letter of the natural numbers
35. T, W. Each member of the sequence is the first letter of
the days of the week: Friday, Saturday, . . .
37. r. Each member of the sequence is the first letter of the
corresponding word.
39. f. Each member of the sequence is the first letter after the
first vowel in the corresponding word.
41. f. Look at the last letter in each word. Choose the next
letter in the alphabet for the sequence.
43. 13. Add 3 each time.
1. Think of the numbers as times and add 3 hours each
time.
47. x 3 12
G
1. (a) and (b) are statements
3. (a) and (d) are negations; (b) and (c) are negations
5. a. Her dress is red.
Answers to Selected Exercises Section 1.1–1.2
Truckee Meadows Community College Math Department
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
Section 1.3 Truth Tables
b. No computer is priced under $100. (All computers
are priced $100 or more.)
c. Some dogs are not four-legged animals.
d. Some sleeping bags are waterproof.
a. p ∧ q
b. p S q
c. ( p ∨ q)
d. p ∧ q
a. (p ∨ q) S r
b. q ∧ p ∧ r
c. r ∧ ( p ∨ q)
d. q S r
p: a shape is a square
q: a shape is a rectangle
pSq
p: a number is a whole number
q: a number is even
r: a number is odd
p S (q ∨ r)
p: a person is born in the U.S.
q: a person is an American citizen
pSq
p: a car is a muscle car from the 60’s
q: a car pollutes
pSq
p: I sleep soundly
q: I drink coffee
r: I eat chocolate
(q ∨ r) S (p)
p: your check is accepted
q: you have a driver’s license
r: you have a credit card
(q ∨ r) S (p)
p: You do drink.
q: You do drive.
r: You are fined.
s: You go to jail.
( p ∧ q) S (r ∨ s)
p: you get a refund
q: you get store credit
r: the product is defective
r S (p ∨ q)
a. I am an environmentalist and I recycle my aluminum
cans.
b. If I am an environmentalist, then I recycle my
aluminum cans.
c. If I do not recycle my aluminum cans, then I am not
an environmentalist.
d. I recycle my aluminum cans or I am not an
environmentalist.
a. If I recycle my aluminum cans or newspapers, then
I am an environmentalist.
b. If I am not an environmentalist, then I do not recycle
my aluminum cans or newspapers.
c. I recycle my aluminum cans and newspapers or I am
not an environmentalist.
d. If I recycle my newspapers and do not recycle
my aluminum cans, then I am not an
environmentalist.
APPENDIX
1.
p
q
q
p ∨ q
1.
T
T
F
T
2.
T
F
T
T
3.
F
T
F
F
4.
F
F
T
T
p
p
p ∨ p
1.
T
F
T
2.
F
T
T
3.
5.
p
q
q
p S q
1.
T
T
F
F
2.
T
F
T
T
3.
F
T
F
T
4.
F
F
T
T
7.
p
q
p
q
q S p
1.
T
T
F
F
T
2.
T
F
F
T
F
3.
F
T
T
F
T
4.
F
F
T
T
T
p
q
p
p∨q
( p ∨ q) S p
1.
T
T
F
T
F
2.
T
F
F
T
F
3.
F
T
T
T
T
4.
F
F
T
F
T
p
q
p∨q
p∧q
( p ∨ q) S ( p ∧ q)
1.
T
T
T
T
T
2.
T
F
T
F
F
3.
F
T
T
F
F
4.
F
F
F
F
T
9.
11.
G
Answers to Selected Exercises Section 1.2–1.3
Truckee Meadows Community College Math Department
A-37
13.
p
q
r
q∨r
(q ∨ r)
p ∧ (q ∨ r)
1.
T
T
T
T
F
F
2.
T
T
F
T
F
F
3.
T
F
T
T
F
F
4.
T
F
F
F
T
5.
F
T
T
T
6.
F
T
F
7.
F
F
8.
F
15.
21. p: It is raining.
q: The streets are wet.
pSq
p
q
pSq
1.
T
T
T
T
2.
T
F
F
F
F
3.
F
T
T
T
F
F
4.
F
F
T
T
T
F
F
F
F
F
T
F
p
q
r
1.
T
T
T
F
F
T
2.
T
T
F
F
F
T
p
q
p
p S q
3.
T
F
T
T
T
T
1.
T
T
F
T
4.
T
F
F
T
F
T
2.
T
F
F
T
5.
F
T
T
F
F
F
3.
F
T
T
T
6.
F
T
F
F
F
F
4.
F
F
T
F
7.
F
F
T
T
T
T
8.
F
F
F
T
F
F
17.
p
q q ∧ r p ∨ (q ∧ r)
q r r r ∨ p q ∧ p ( r ∨ p) S (q ∧ p)
23. p: It rains.
q: The water supply is rationed.
p S q
1.
T T T F
T
T
T
2.
T T F T
T
T
T
25. p: a shape is a square
q: a shape is a rectangle
pSq
3.
T F T F
T
F
F
p
q
pSq
4.
T F F T
T
F
F
T
T
T
5.
F T T F
F
F
T
T
F
F
6.
F T F T
T
F
F
F
T
T
7.
F F T F
F
F
T
F
F
T
8.
F F F T
T
F
F
19.
p
q
1.
T
T T
F
T
F
F
2.
T
T F
T
T
T
T
3.
T
F T
F
T
F
F
4.
T
F
F
T
T
F
F
5.
F
T T
F
T
F
F
6.
F
T F
T
F
T
T
7.
F
F T
F
T
F
F
8.
F
F
T
F
F
T
A-38
r r p ∨ r q ∧ r ( p ∨ r) S (q ∧ r)
F
APPENDIX
G
27. p: it is a square
q: it is a triangle
p S (q)
p
q
q
p S (q)
T
T
F
F
T
F
T
T
F
T
F
T
F
F
T
T
Answers to Selected Exercises Section 1.3
Truckee Meadows Community College Math Department
29. p: you have a drivers license
q: you have a credit card
r: your check is approved
( p ∨ q) S r
p
q
r
p∨q
( p ∨ q) S r
T
T
T
T
T
T
T
F
T
F
T
F
T
T
T
T
F
F
T
F
F
T
T
T
T
F
T
F
T
F
F
F
T
F
T
F
F
F
F
T
35. p: Proposition A passes.
q: Proposition B passes.
r: Jobs are lost.
s: New taxes are imposed.
(p ∧ q) S (r ∨ s)
31. p: Leaded gasoline is used.
q: The catalytic converter is damaged.
r: The air is polluted.
p S (q ∧ r)
p
q
r
q∧r
p S ( q ∧ r)
1.
T
T
T
T
T
2.
T
T
F
F
F
3.
T
F
T
F
F
4.
T
F
F
F
F
5.
F
T
T
T
T
6.
F
T
F
F
T
7.
F
F
T
F
T
8.
F
F
F
F
T
r
s q p ∧ q r ∨ s ( p ∧ q) S (r ∨ s)
p
q
1.
T
T T T
F
F
T
T
2.
T
T T F
F
F
T
T
3.
T
T F T
F
F
T
T
4.
T
T F F
F
F
F
T
5.
T
F T T
T
T
T
T
6.
T
F T F
T
T
T
T
7.
T
F F T
T
T
T
T
8.
T
F F F
T
T
F
F
9.
F
T T T
F
F
T
T
10.
F
T T F
F
F
T
T
11.
F
T F T
F
F
T
T
12.
F
T F F
F
F
F
T
13.
F
F T T
T
F
T
T
14.
F
F T F
T
F
T
T
15.
F
F F T
T
F
T
T
16.
F
F F F
T
F
F
T
p: Proposition A passes.
q: The legislature raises taxes.
r: The quality of education is lowered.
s: Unemployment rises.
37. equivalent
33. p: I have a college degree.
q: I have a job.
r: I own a house.
p ∧ (q ∨ r)
p
q
r
q∨r
(q ∨ r)
p ∧ (q ∨ r)
1.
T
T
T
T
F
F
2.
T
T
F
T
F
F
3.
T
F
T
T
F
F
4.
T
F
F
F
T
T
5.
F
T
T
T
F
F
6.
F
T
F
T
F
7.
F
F
T
T
8.
F
F
F
F
p
q
q
p ∨ q
qSp
1.
T
T
F
T
T
2.
T
F
T
T
T
3.
F
T
F
F
F
4.
F
F
T
T
T
39. equivalent
p
q
p
q
p ∨ q
p S q
1.
T
T
F
F
T
T
F
2.
T
F
F
T
T
T
F
F
3.
F
T
T
F
F
F
T
F
4.
F
F
T
T
T
T
APPENDIX
G
Answers to Selected Exercises Section 1.3
Truckee Meadows Community College Math Department
A-39
41. not equivalent
p
q
pSq qSp
1.
T
T
T
T
2.
T
F
F
T
3.
F
T
T
F
4.
F
F
T
T
p
q
p
q
1.
T
T
F
F
T
T
2.
T
F
F
T
F
F
3.
F
T
T
F
T
T
4.
F
F
T
T
T
T
43. equivalent
p S q q S p
45. not equivalent
p
q
p
q
p ∨ q
q ∧ p
1.
T
T
F
F
T
F
2.
T
F
F
T
T
F
3.
F
T
T
F
F
T
4.
F
F
T
T
T
F
49. I do not have a college degree or I am employed.
51. The television set is not broken and there is not a power
outage.
53. The building contains asbestos and the original
contractor is not responsible.
55. The lyrics are censored and the First Amendment has not
been violated.
Section 1.4 More on Conditionals
1. a. If she is a police officer, then she carries a gun.
b. If she carries a gun, then she is a police officer.
c. If she is not a police officer, then she does not carry
a gun.
d. If she does not carry a gun, then she is not a police
officer.
e. a and d; b and c
3. a. If I watch television, then I do not do my
homework.
b. If I do not do my homework, then I watch
television.
c. If I do not watch television, then I do my
homework.
d. If I do my homework, then I do not watch television.
e. a and d; b and c
A-40
APPENDIX
G
5. a. If you do not pass this mathematics course, then you
do not fulfill a graduation requirement.
b. If you fulfill a graduation requirement, then you pass
this mathematics course.
c. If you do not fulfill a graduation requirement, then
you do not pass this mathematics course.
7. a. If the electricity is turned on, then the television set
does work.
b. If the television set does not work, then the electricity
is turned off.
c. If the television set does work, then the electricity is
turned on.
9. a. If you eat meat, then you are not a vegetarian.
b. If you are a vegetarian, then you do not eat meat.
c. If you are not a vegetarian, then you do eat meat.
11. a. premise: I take public transportation.
conclusion: Public transportation is convenient.
b. If I take public transportation, then it is
convenient.
c. false statement when I take public transportation and
it is not convenient
13. a. premise: I buy foreign products.
conclusion: Domestic products are not available.
b. If I buy foreign products, then domestic products are
not available.
c. false statement when I buy foreign products and
domestic products are available
15. a. premise: You may become a United States senator.
conclusion: You are at least thirty years old and have
been a citizen for nine years.
b. If you become a United States senator, then you are
at least thirty years old and have been a citizen for
9 years.
c. false statement when you become a United States
senator and either you are not at least thirty years
old or have not been a citizen for nine years,
or both
17. If you obtain a refund, then you have a receipt,
and if you have a receipt, then you will obtain
a refund.
19. If ax2 bx c 0 has two distinct real solutions, then
b2 4ac 0 and if b2 4ac 0, then ax2 bx c 0
has two distinct real solutions.
21. If a polygon is a triangle, then the polygon has three sides,
and if a polygon has three sides, then the polygon is a
triangle.
23. equivalent
25. equivalent
27. equivalent
29. If I do not walk to work, then it is raining.
31. If it is not cold, then it is not snowing.
33. If you are a vegetarian, then you do not eat meat.
35. (i) and (iv); (ii) and (iii)
37. (i) and (iii); (ii) and (iv)
39. (i) and (iii); (ii) and (iv)
Answers to Selected Exercises Section 1.3–1.4
Truckee Meadows Community College Math Department
Section 1.5 Analyzing Arguments
19. Rewriting the argument:
If you are a poet, then you are a loner.
If you are a loner, then you are a taxi driver.
1. 1. p S q
2. p
If you are a poet, then you are a taxi driver.
p: you are a poet.
q: you are a loner.
r: you are a taxi driver.
pSq
qSr
q
3. 1. p S q
2. q
p
5. 1. p S q
2. p
7.
9.
11.
13.
15.
17.
pSr
{(p S q) ∧ (q S r)} S (p S r)
q
valid
valid
invalid; the argument is invalid when you do not exercise
regularly and you are healthy
invalid; the argument is invalid when the Democrats have
a majority and Smith is appointed and student loans are
funded
invalid; the argument is invalid when
(1) you do not argue with a police officer and you do get
a ticket and you do break the speed limit, or
(2) you do not argue with a police officer and you do not
get a ticket and you do break the speed limit
Rewriting the argument:
If it is a pesticide, then it is harmful to the environment.
If it is a fertilizer, then it is not a pesticide.
1
If it is a fertilizer, then it is not harmful to the environment.
p: it is a pesticide.
q: it is harmful to the environment.
r: it is a fertilizer.
pSq
r S p
2
3
qSr 1∧2 pSr
(1 ∧ 2) S 3
p
q
r
pSq
T
T
T
T
T
T
T
T
T
T
F
T
F
F
F
T
T
F
T
F
T
F
T
T
T
F
F
F
T
F
F
T
F
T
T
T
T
T
T
T
F
T
F
T
F
F
T
T
F
F
T
T
T
T
T
T
F
F
F
T
T
T
T
T
The argument is valid.
r S q
{(p S q)∧(r S p)} S (r S p)
1
2
3
p
q
r
p
q
pSq
r S p
1∧2
r S q
(1 ∧ 2) S 3
T
T
T
F
F
T
F
F
F
T
T
T
F
F
F
T
T
T
T
T
T
F
T
F
T
F
F
F
T
T
T
F
F
F
T
F
T
F
T
T
F
T
T
T
F
T
T
T
F
F
F
T
F
T
F
T
T
T
T
T
F
F
T
T
T
T
T
T
T
T
F
F
F
T
T
T
T
T
T
T
The argument is not valid if it is not a pesticide and if it
is harmful to the environment and it is a fertilizer.
APPENDIX
G
Answers to Selected Exercises Section 1.5
Truckee Meadows Community College Math Department
A-41
21. Rewriting the argument:
If you are a professor, then you are not a millionaire.
If you are a millionaire, then you are literate.
4. valid
If you are a professor, then you are literate.
p: you are a professor.
q: you are a millionaire.
r: you are literate.
p S q
qSr
truck
x
drivers
union members
pSr
{(p S q) ∧ (q S r)} S ( p S r)
1
2
x = Rocky
5. invalid
3
truck
drivers
p q r q p S q q S r 1 ∧ 2 p S r (1 ∧ 2) S 3
T T T
F
F
T
F
T
T
T T F
F
F
F
F
F
T
T F T
T
T
T
T
T
T
T F F
T
T
T
T
F
F
F T T
F
T
T
T
T
T
F T F
F
T
F
F
T
T
F F T
T
T
T
T
T
T
F F F
T
T
T
T
T
T
x
union members
x = Rocky
6. invalid
mechanics
x
engineers
23.
25.
27.
29.
31.
33.
35.
37.
The argument is not valid if you are a professor who is
not a millionaire and is illiterate.
valid
valid
invalid; the argument is invalid when
(1) you are in a hurry and you eat at Lulu’s Diner and
you do not eat good food, or
(2) you are not in a hurry and you eat at Lulu’s Diner and
you do not eat good food
valid
valid
valid
valid
valid
x = Casey Jones
7. valid
mechanics
engineers
x
x = Casey Jones
8. invalid
Chapter 1 Review
1. a. inductive b. deductive
2. g. The next letter in the sequence is the first consonant
after the first vowel in the word.
3. 9. Think of each number in the sequence as a time (1:00,
6:00, etc.). Add five hours to get the next number in the
sequence.
A-42
APPENDIX
G
dangerous
things
x
animals
x = gun
Answers to Selected Exercises Section 1.5–Chapter 1 Review
Truckee Meadows Community College Math Department
9. valid
19.
ele
ctr
contractors
car
pen
ici
an
s
p
p S q
1.
T
T
F
T
2.
T
F
F
T
3.
F
T
T
T
4.
F
F
T
F
p
q
q
p∧q
( p ∧ q) S q
1.
T
T
F
T
F
2.
T
F
T
F
T
3.
F
T
F
F
T
4.
F
F
T
F
T
p
q
r
p∨r
( p ∨ r)
q ∨ ( p ∨ r)
1.
T
T
T
T
F
T
2.
T
T
F
T
F
T
3.
T
F
T
T
F
F
4.
T
F
F
T
F
F
5.
F
T
T
T
F
T
6.
F
T
F
F
T
T
7.
F
F
T
T
F
F
8.
F
F
F
F
T
T
s
p
q
q
p ∨ q
1.
T
T
F
T
2.
T
F
T
T
3.
F
T
F
F
4.
F
F
T
T
18.
q
ter
10. (a) and (b) are statements
11. (a) and (d) are negations; (b) and (c) are negations.
12. a. His car is new.
b. No building is earthquakeproof.
c. Some children do not eat candy.
d. Sometimes I cry in a movie theater.
13. a. p ∧ q
b. q S p
c. p ∧ q d. ( p ∨ q)
14. a. q S p
b. r ∧ q ∧ p
c. r S p d. p ∧ (q ∨ r)
15. a. If it is expensive, then it is desirable.
b. It is undesirable if and only if it is not expensive.
c. It is not expensive or undesirable.
d. It is expensive and it is desirable, or it is not
expensive and it is undesirable.
16. a. If the movie is critically acclaimed or a box office hit,
then the movie is available on videotape.
b. If the movie is critically acclaimed and it is not
a box office hit, then the movie is not available
on videotape.
c. The movie is not critically acclaimed or a box office
hit and it is available on videotape.
d. If the movie is not available on videotape, then the
movie is not critically acclaimed and it is not a box
office hit.
17.
p
20.
21.
22.
p
q
r
p q ∨ r p S (q ∨ r)
1.
T T T
F
T
T
2.
T T F
F
T
T
3.
T F T
F
T
T
p
q
q
p ∧ q
4.
T F
F
F
F
T
1.
T
T
F
F
5.
F T T
T
T
T
2.
T
F
T
T
6.
F T F
T
T
T
3.
F
T
F
F
7.
F
F T
T
T
T
4.
F
F
T
F
8.
F
F
T
F
F
APPENDIX
G
F
Answers to Selected Exercises Chapter 1 Review
Truckee Meadows Community College Math Department
A-43
23.
p
q
r r
q ∧ p r ∨ p (q ∧ p) S (r ∨ p)
1.
T T T
F
T
T
T
2.
T T F
T
T
T
T
3.
T F T
F
F
T
T
4.
T F F
T
F
T
T
5.
F T T
F
F
F
T
6.
F T F
T
F
T
T
7.
F
F T
F
F
F
T
8.
F
F F
T
F
T
T
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
p q
r r p ∨ r q ∧ r ( p ∨ r) S (q ∧ r)
1. T T T
F
T
F
F
2. T T F
T
T
T
T
3. T F T
F
T
F
F
4. T F F
T
T
F
F
5. F T T
F
T
F
F
6. F T F
T
F
T
T
7. F F T
F
T
F
F
8. F F F
T
F
F
T
equivalent
not equivalent
not equivalent
equivalent
Jesse did not have a party or somebody came.
You pay the fine and you go to jail.
I am not the winner and you are not blind.
He is employed or he did apply for financial assistance.
His application is ignored and the selection procedure
has not been violated.
The jackpot is less than $1 million.
a. If you are an avid jogger, then you are healthy.
b. If you are healthy, then you are an avid jogger.
c. If you are not an avid jogger, then you are not healthy.
d. If you are not healthy, then you are not an avid jogger.
e. You are an avid jogger if and only if you are healthy.
a. If he is not elected, then the country is not in big trouble.
b. If the country is in big trouble, then he is elected.
c. If the country is not in big trouble, then he is not elected.
a. premise: The economy improves.
conclusion: Unemployment goes down.
b. If the economy improves, then unemployment goes
down.
a. premise: Unemployment goes down.
conclusion: The economy improves.
b. If unemployment goes down, then the economy
improves.
A-44
APPENDIX
G
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
If it is a computer, then it is repairable.
If it is a gemstone, then it is valuable.
not equivalent
equivalent
(i) and (iii); (ii) and (iv)
invalid
valid
invalid
valid
valid
invalid
invalid
invalid
p: a person is a professor
q: a person is educated
r: an animal is a monkey
pSq
r S q
p S r
{[p S q] ∧ [r S q]} S ( p S r)
The argument is valid.
53. p: a person is a professor
q: a person is educated
r: an animal is a monkey
pSq
r S p
r S q
{[p S q] ∧ [r S p]} S (r S q)
The argument is invalid.
54. p: vehicles stop
q: the traffic light is red
r: there is an accident
qSp
p S r
r
q
{(q S p) ∧ (p S r) ∧ r} S q
The argument is valid.
Chapter 2 Sets and Counting
Section 2.1
1. a. well-defined
b. not well-defined
c. well-defined
d. not well-defined
3. proper: , {Lennon}, {McCartney}
improper: {Lennon, McCartney}
5. proper: , {yes}, {no}, {undecided},
{yes, no}, {yes, undecided}, {no, undecided}
improper: {yes, no, undecided}
Answers to Selected Exercises Chapter 1 Review–Section 2.1
Truckee Meadows Community College Math Department
7. a. {4, 5}
b. {1, 2, 3, 4, 5, 6, 7, 8}
c. {0, 6, 7, 8, 9}
d. {0, 1, 2, 3, 9}
9. a. { }
b. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
c. {0, 2, 4, 6, 8}
d. {1, 3, 5, 7, 9}
11. {Friday}
13. {Monday, Tuesday, Wednesday, Thursday}
15. {Friday, Saturday, Sunday}
17.
25.
U
A
B
27. a. 21
U
U
A
A
B
21
B
63
16
50
b. 0
19.
U
U
B
84
A
A
B
37
29
29. a.
U
21.
U
A
62
A
M
29
94
B
315
b. 37.0%
31. a.
23.
U
U
child
394
A
career
135
78
B
143
b. 18.0%
APPENDIX
G
Answers to Selected Exercises
Truckee Meadows Community College Math Department
Section 2.1
A-45
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
65.
67.
69.
42
43
8
5
16
32
6
8
0
a. {1, 2, 3} A
b. {1, 2, 3, 4, 5, 6} B
c. E , F
d. E , F
a. , {a}; 2
b. , {a}, {b}, {a, b}; 4
c. , {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}; 8
d. , {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c},
{b, d}, {c, d}, {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d},
{a, b, c, d}; 16
e. yes; 2n(A)
f. 64
(d)
(c)
(e)
29.
U
A
B
C
35.
37.
39.
41.
(d)
(d)
(b)
(e)
Section 2.3 Introduction to Combinatorics
1. a. 8
b.
QH
DH
QT
NH
QH
DT
QT
Section 2.2 Applications of Venn Diagrams
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
a. 143
b.
a. 408
b.
a. 106
b.
a. x y z
b.
c. y z
d.
a. 43.8%
b.
a. 77%
b.
a. 0%
b.
a. 44.0%
b.
a. 20.0%
b.
16
{0, 4, 5}
{1, 2, 3, 6, 7, 8, 9}
16
c. 49
d. 57
1,343 c. 664 d. 149
448
c. 265 d. 159
xz
w (x y z)
10.8%
22%
54.1%
12.8%
58.8%
QH
DH
QT
NT
QH
DT
QT
3. a. 12
b.
BN
BW
NW
BN
M
WW
NW
U
BN
A
GW
B
NW
BN
C
BW
NW
BN
27.
BB
WW
U
NW
A
BN
B
GW
NW
C
A-46
APPENDIX
G
5. 24
7. 720
9. 2,646
Answers to Selected Exercises Section 2.1–2.3
Truckee Meadows Community College Math Department
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
51.
53.
216
1 billion
1010 or 10 billion
a. 128
b. 800
a. 1.17936 109
b. 6.76 1010
540,000
24
3,628,800
2.432902008 1018
17,280
a. 30
b. 360
56
70
3,321
1.046139494 1013
120
35
1
(b)
(d)
c. 4.2 1010
Section 2.5 Voting Systems
Section 2.4 Permutations and Combinations
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
a. 210
b. 35
a. 120
b. 1
a. 14
b. 14
a. 970,200
b. 161,700
a. x!
b. x
a. x2 x
b. x2 x
a. 6
2
b. {a, b}, {a, c}, {b, a}, {b, c}, {c, a}, {c, b}
a. 6
b. {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}
a. 479,001,600
b. 1
24
91
2,184
a. 420
b. 1,001
c. 406
2,598,960
a. 4,512
b. 58,656
123,552
22,957,480
376,992
5/36
The first five rows of triangle are:
1
1
1
1
1
a.
c.
e.
f.
g.
h.
1
2
3
4
1. a. 2,000
b. Cruz
c. Yes
3. a. 10,351
b. Edelstein
c. No
5. a. 30
b. Park
c. 47%
d. Beach
e. 53%
f. Beach
g. 63
h. Beach
i. 2
7. a. 65
b. Coastline
c. 48%
d. Coastline
e. 63%
f. Coastline
g. 150
h. Coastline
i. 2
9. a. 140
b. Shattuck
c. 40%
d. Nirglotis
e. 51%
f. Shattuck
g. 284
h. Nirglotis
i. 2
11. a. 1,342
b. Jones
c. 44%
d. Jones
e. 50.4%
f. Jones
g. 3,960
h. Jones
i. 3
13. a. 31,754
b. Darter
c. 52%
d. Darter (He has a majority, so no run off is needed.)
e. 52%
f. Darter
g. 138,797
h. Darter
i. 4
15. 6! 720
17. 6C2 15
19. a. 75
b. 25
21. a. 21
b. 0
Section 2.6
n(S ) 4, n(C ) 4; equivalent; state 4 capital city
n(R) 3, n(G ) 4, not equivalent
n(C ) 22, n(D) 22; equivalent; 3n 4 4n
n(G) 250, n(H) 251; not equivalent
n(A) 62, n(B) 62; equivalent, 2n 1 4 2n 123
a. n 4 2n 1 b. 918
c. x 2 1
d. 1,563
e. 2n 1
13. a. n 4 3n
b. 312
c. 3x
d. 2,808
e. 3n
15. a. 344
b. 248
c. 755
d. u 0
1.
3.
5.
7.
9.
11.
1
3
6
41. a. 4th row
b. nth row
c. no, the third
d. yes
e. nth row, (r 1)th number
45. (c)
47. (c)
49. (e)
1
4
Chapter 2 Review
1
1
b. 2
4
d. 8
Yes. The sum of each row is twice the previous sum.
We predict 2 · 8 16
The sum is 16. Our prediction was correct.
2n1
APPENDIX
G
1. a.
b.
c.
d.
2. a.
b.
Well defined.
Not well defined.
Not well defined.
Well defined.
{1, 3, 5, 7, 9}
{0, 2, 4, 6, 8}
Answers to Selected Exercises Section 2.3–Chapter 2 Review
Truckee Meadows Community College Math Department
A-47
c. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
d. 3. a. A B 5 {Maria, Nobuko, Leroy, Mickey, Kelly,
Rachel, Deanna}
b. A B 5 {Leroy, Mickey}
4. proper: , {Dallas}, {Chicago}, {Tampa}, {Dallas,
Chicago}, {Dallas, Tampa}, {Chicago, Tampa}
improper: {Dallas, Chicago, Tampa}
5. a. 18
b.
U
A
B
14
8
18
23. a. 3
b. 3
c. 1
d. 1
e. 8 f. 2n(S) 23 8
24. a. 74
b. Beethoven
c. 34%
d. Vivaldi
e. 59%
f. Beethoven
g. 197
h. Tie between Beethoven and Vivaldi
i. 2 points each
25. n(A) 5, n(B) 5; equivalent; Roman numeral 4
number word
26. n(C ) 450, n(D) 450; equivalent; 2n 1 4 2n
27. n(E) 1, n(F) 2; not equivalent
28. a. n 4 n2
b. 29
c. 1x
d. 20,736
29. a. 594
21
6. a. 1,670
7. 29%
8. a. {b, f}
9. 2a. 12
b. b.
b. 733
c. 346
e. n2
b. 264
c. 103
d. u 0
d. 330
Chapter 3 Probability
b. {a, c, d, e, g, h, i}
Le Club
Section 3.1
Stars
Lizards
Le Club
Johnny’s
Art
Lizards
Le Club
Chelsea
Lizards
Le Club
Stars
Lizards
Le Club
Johnny’s
Photo
5.
7.
9.
11.
13.
15.
17.
a. win $85
a. lose $20
a. lose $10
a. win $50
a. lose $50
a. lose $45
a. win $495
d. lose $15
19. $3
21. $500
23. a. 13
b.
b.
b.
b.
b.
b.
b.
win $85
win $160
win $50
lose $25
win $50
win $855
win $525
b.
25. a. 12
b.
27. a. 4
b.
c. lose $5
c. lose $20
c. win $675
c. lose $45
1
4
3
13
1
13
Lizards
Le Club
Section 3.2 Basic Terms of Probability
Lizards
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
Chelsea
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
22.
180
1,080,000
a. 3,628,800 b. 1
c. 531,360 d. 888,030
a. 165
b. 990
a. 32,760
b. 1,365 c. 54,486,432,000
a. 660
b. 1,540 c. 880
45
720
133,784,560
177,100,560
5,245,786
a. row 7, number 4 b. row 7, number 5
c. same
d. nth row, (r 1)th number
A-48
APPENDIX
G
selecting a jellybean
12
35
18
35
5
7
0
1223
1817
selecting a card
a. 12
a. 131
a. 521
a. 133
a. 10
13
a. 133
a. 381
Answers to Selected Exercises Chapter 2 Review–Section 3.2
Truckee Meadows Community College Math Department
b.
b.
b.
b.
b.
b.
b.
11
112
151
310
103
310
137
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
63.
a. 383
a. 385
a. 196
a. 199
14
b.
b.
b.
b.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
335
533
613
910
3
5
a: (b a)
a. 199
b. 910
a. {(b, b), (b, g), (g, b), (g, g)}
b. {(b, g), (g, b)}
c. {(b, g), (g, b), (g, g)}
d. {(g, g)}
e. 12
f. 43
g. 14
h. 11
i. 31
j. 13
a. {(b, b, b), (b, b, g), (b, g, b), (g, b, b), (b, g, g),
(g, b, g), (g, g, b), (g, g, g)}
b. {(b, g, g), (g, b, g), (g, g, b)}
c. {(b, g, g), (g, b, g), (g, g, b), (g, g, g)}
d. {(g, g, g)}
e. 83
f. 12
1
g. 8
h. 35
i. 11
j. 17
a. 41 b. 12
c. 41
d. equally likely
different
a. {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2),
(2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4),
(3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2),
(6, 3), (6, 4), (6, 5), (6, 6)}
b. {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}
c. {(6, 5), (5, 6)}
d. {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
e. 61 f. 181
g. 16 h. 15 i. 117 j. 15
a. 41
b. 14
c. 12
1
1
a. 4
b. 2
c. 41
1
a. 0
b. 2
c. 1
a. 21
b. 0
c. 12
not mutually exclusive
mutually exclusive
not mutually exclusive
mutually exclusive
mutually exclusive
a. 261
b. 137
1
a. 52
b. 134
2
a. 13
b. 135
9
a. 13
b. 138
b. 104
175
97
b. 140
17
b. 25
b. 16
25
b. 19
b. 187
b. 34
b. 12
b. 12
b. 21
b. 0.25
b. 0.95
c.
1
18
c.
c.
c.
c.
1
0
0.15
0.8
d. 0.6
Section 3.4 Combinatorics and Probability
1. 0.7063
1
1
3. a. 13,983,816
b. 22,957,480
1
c. 18,009,460
d. about 64% more likely
5. 0.00003
7. a. 0.000003080 b. 0.000462062
9. a. 0.000001737 b. 0.000295263
11. Easiest to win: 5/26, hardest to win: 6/53
13. a. 0.000004 b. 0.000160
c. 0.002367
d. 0.018303 e. 0.081504
f. 0.897662
15. a. 0.000495 b. 0.001981
c. 0.000015
d. 0.001966
17. 0.05
19. 0.48
21. 0.64
23. 0.36
25. a. 0.09
b. 0.42
c. 0.49
27. a. 0.0000000125
b. 0.0000000715
c. Winning the 6/49 is 5.7 times more likely.
Section 3.3
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
103
71
a. 175
151
a. 700
a. 258
a. 259
a. 61
a. 92
a. 61
a. 61
a. 43
a. 41
a. 0.35
a. 0.20
Section 3.5 Expected Value
c. 25
26
c. 51
52
c. 0
c. 134
1.
3.
5.
7.
9.
11.
13.
15.
19.
21.
23.
25.
27.
29.
31.
d. 137
d. 1
12
13
10
13
11
13
9
13
95
25; 52
ba
121
103
APPENDIX
G
a. $0.053
a. $0.053
a. $0.053
a. $0.053
a. $0.053
$549
1.75
$10.05
bank
0.59 or more
a. 0 b. 1/16 c. 3/8
$0.28
$0.55
more than $1,200/year
back yard
Answers to Selected Exercises Section 3.3–3.5
Truckee Meadows Community College Math Department
A-49
33. a. $12.32
b. $1.34
35. a. $.47
b. $2.74
c. $3.49
37. $7.8 million
39. a. 13,983,816
b. $13,983,816
41. 6 successive losses; win $1
c. $5.89
c. 97 days
Section 3.6 Conditional Probability
1. a. 0.23 b. 0.53 c. 0.14 d. 0.32
e. 0.08 f. 0.08
3. 0.20
5. 0.34
7. a. 14
b. 174
c. 171
13
1
13
9. a. 4
b. 51
c. 204
11. a. p(B A) b. p(A) c. p(C A)
13. a. 161
b. 31
c. 0
d. 1
5
15. a. 36
b. 185
c. 0
d. 1
17. a. 121
b. 103
c. 1
19. E2 is most likely; E3 is least likely
21. 0.46
23. 0.0005
25. 0.0020
27. 0.14
29. 0.20
31. 0.07
33. 0.00646
35. 0.01328
37. a. .2
b. .06
39. a. .105
b. .103
41. 92%
43. 39%
45. 0.05
47. a. 0.86
b. 0.34
c. 0.66
d. N W
49. A B
51. 0.14
Section 3.7 Independence; Trees in Genetics
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
a. dependent
a. dependent
a. independent
a. dependent
a. dependent
no
dependent
dependent
dependent
dependent
a. 0.000001
0.0101 ≈ 1%
a. 0.49
d. 0.000004
A-50
APPENDIX
b.
b.
b.
b.
b.
not mutually exclusive
mutually exclusive
not mutually exclusive
mutually exclusive
mutually exclusive
b. 4
b. 0.999996
e. a; c
G
c. 0.51
f. c; d
29.
31.
33.
35.
37.
39.
a. 961 ≈ 1%
0.7225, 0.2775
b.
1
144
≈ 0.7%
1
3
1
2
chestnut or shiny dark brown, each with p 21
light brown (81), reddish brown (41), dark red (81), medium
brown (81), chestnut (14), or auburn (18)
41. light brown (161 ), reddish brown (18 ), dark red (161 ),
medium brown (161 ), chestnut (18 ), auburn (161 ), dark
brown (161 ), shiny dark brown (18 ), glossy dark
brown (161 ), black (161 ), shiny black (81 ), glossy
black (161 )
625
43. a. 61
b. 56
c. 1,296
≈ 0.48
671
d. 1,296
≈ 0.52
e. $0.04
Chapter 3 Review
26
2. a. 52
12, 2626 11
4
b. 52 131 , 448 112
13
c. 52
14, 1339 13
1
d. 52, 151
16
e. 52
134 , 1636 49
48
f. 52 12
13 , 484 121
3. a. 383 ; 335 b. 196 ; 613 c. 199 ; 910
4. b. {(h, h, h), (h, h, t), (h, t, h), (t, h, h), (h, t, t), (t, h, t),
(t, t, h), (t, t, t)}
c. {(h, t, t), (t, h, t), (t, t, h)}
d. {(h, t, t), (t, h, t), (t, t, h), (t, t, t)}
e. 38; 35
f. 12; 11
5. a. 16
b. 181
c. 187
d. 16
e. 11
f. 187
18
6. a. 0.013 b. 0.138 c. 0.151 d. 0.000008
7. a. 0.005 b. 0.069 c. 0.074
8. a. 0.14
b. no
9. a. 12
b. 21
1
10. a. 2
b. 12
c. 41
1
1
11. a. 4
b. 2
c. 41
1
1
12. a. 2
b. 2
13. a. 0
b. 12
c. 12
1
14. 9
15. a. 0.56; 0.39
b. 0.40; 0.55 c. 0.67; 0.33
d. 0.50; 0.50
e. urban area; urban area
f. O’Neill; Bell g. no
h. O’Neill
16. a. dependent; not mutually exclusive
b. independent; not mutually exclusive
c. dependent; mutually exclusive
d. dependent; not mutually exclusive
e. independent; not mutually exclusive
17. a. 0.0000007 b. 0.00003
18. $0.053
19. $0.23
20. The low-number bet is the better bet.
24
21.
.0000092345
2,598,960
Answers to Selected Exercises Section 3.5–Chapter 3 Review
Truckee Meadows Community College Math Department
Chapter 4 Statistics
Section 4.1 Population, Sample and Data
1. a.
Number of visits to the Library
3. a.
Frequency
1
9
2
8
3
2
4
5
5
6
Number of
Children
Tally
Frequency
8
4
5
0
1
2
3
Total 30
0.2
Central
Angle
20%
72°
13
0.325 32.5%
117°
9
0.225 22.5%
81°
6
0.15 15%
54°
3
0.075 7.5%
27°
1
0.025 2.5%
9°
n 40
b.
Relative
Frequency
1.000 100% total 360°
b.
Number of Visits
1 child
32.5%
1–30%
2–26%
2 children
22.5%
0 children
20.0%
5–20%
3–7%
3 children
15.0%
4–17%
5 children
4 children
2.5%
7.5%
number of children per family
c.
c.
14
10
12
8
10
8
6
6
4
4
2
2
1
2
3
4
0
5
APPENDIX
G
1
2
3
4
Answers to Selected Exercises Section 4.1
Truckee Meadows Community College Math Department
5
A-51
5. a.
Speed
(in mph)
7.
Relative
Tally Frequency Frequency
51 x 56 f
2
0.05 5%
56 x 61 4
0.1 10%
250
61 x 66 66 x 71 71 x 76 76 x 81 7
0.175 17.5%
200
0.25 25%
150
10
300
9
0.225 22.5%
8
0.2 20%
n 40
rf
0.40
237
0.20
101
79
100
51
63
50
0.10
1.000 100%
10
0
b.
20
30
40
time in minutes
50
60
9.
f
rf
f
0.25
50
rf
10
10
9
8
7
6
0.20
40
0.15
30
0.10
20
4
4
0.05
2
18
9
4.00
5.50
10.00
13.00
8.50
11.50
wages in dollars
7.00
rf
f
1,200
0.30
1075
948
(thousands)
1,000
891
800
600
0.20
486
410
400
0.10
200
77
15
APPENDIX
G
20
0.20
27
10
56
61
66
71
76
81
speed of cars on Interstate 40 (in mph)
11.
35
21
2
51
0.30
42
8
A-52
0.30
169
25
30
35
40
ages of women giving birth
4
45
50
Answers to Selected Exercises Section 4.1
Truckee Meadows Community College Math Department
0.10
13.
b.
rfd
0.12
New AIDS cases - Female
0.1
0.08
White
18%
0.06
0.04
Native
American
0%
Black
65%
0.02
10
20 30 40 50 60
Age of male students
15. a. 28.5%
d. 97.5%
b. 32%
e. 50%
Asian
1%
Hispanic
16%
70
c. not possible
f. 52.5%
c.
New AIDS cases
17.
Reason for ER Visit
Chest Pain
25%
White
33%
1–30%
Stomach
Pain
29%
Black
49%
Cough
12%
5–20%
Hispanic
17%
Fever
21%4–17% Head
13%
21. a.
19. a.
Native
American
0%
Asian
1%
Specialties - Male
New AIDS cases - Male
Internal
36%
White
37%
Black
44%
Hispanic
18%
Family
19%
Native
American
0%
OB/GYN
10%
Asian
1%
General
13%
Ped
12%
APPENDIX
G
Answers to Selected Exercises
Truckee Meadows Community College Math Department
Psych
10%
Section 4.1
A-53
b.
Section 4.2 Measures of Central Tendency
Specialties - Female
Internal
32%
Family
17%
General 3%
OB/GYN
12%
Ped
26%
c.
Psych
10%
Specialties
1. mean 12.5; median 11.5; mode 9
3. mean 1.45; median 1.5; mode 1.7
5. a. mean 11; median 10.5; mode 9
b. mean 25.5; median 10.5; mode 9
7. a. mean 7; median 7; mode none
b. mean 107; median 107; mode none
9. mean 10.88, median 10, mode 9 and 15
11. mean 36.1, median 34, mode none
(many numbers have frequency 2)
13. mean 7.6; median 8; mode 6 and 9
15. 16.028 oz
17. a. 42
b. 92
c. impossible (it would require a score of 142)
19. $51,600
21. 51.4 mph
23. 39 years old
25. a. $40,750
b. $42,000 (it does not change)
27. a. $3,583.09
b. $4,274.41
29. 36.5 years old
31. a. 23 years old
b. 28.5 years old
Section 4.3 Measures of Dispersion
1.
3.
5.
7.
Internal
35%
Family
18%
OB/GYN
11%
General
10%
Psych
10%
Ped
16%
9.
11.
13.
15.
17.
19.
25.
a.
a.
a.
a.
b.
c.
16.4; 4.0
b. 16.4; 4.0
0
b. 0
22; 7.5
b. 1100; 374.2
Joey, 168; Dee Dee, 167; Joey has the higher mean.
Joey, 30.9; Dee Dee, 18.2
Dee Dee is more consistent because his standard
deviation is lower.
13.4
a. 67.5; 7.1
b. 80% c. 90%
a. 3.175; 1.807 b. 58% c. 100%
a. 8; 1.4
b. 71% c. 94%
d. 100%
0.285
6.30
13.5; 11.3
Section 4.4 The Normal Distribution
29.
1. a. 34.13% b. 34.13% c. 68.26%
3. a. 49.87% b. 49.87% c. 99.74%
5. a. one [22.4, 27.0]; two [20.1, 29.3]; three [17.8, 31.6]
b. 68.26%; 95.44%; 99.74%
c.
f
25
20
20
16
15
10
7
4
5
3
9
18
27
36
45
0
percent of legislators with links to insurers
who sit on committees focusing on insurance issues
A-54
APPENDIX
G
X
17.8 20.1 22.4
7. a.
d.
9. a.
d.
0.4474
0.0281
0.34
0.27
b.
e.
b.
e.
24.7 27.0 29.3
0.0639
0.0960
2.08
1.64
Answers to Selected Exercises Section 4.1–4.4
Truckee Meadows Community College Math Department
c.
f.
c.
f.
0.5884
0.8944
0.62
1.28
31.6
b. 0.42
e. 2.96
b. 0.6272
e. 0
b. 49.72%
b. 0.7745
b. 79.67%
b. 62
11. a. 0.42
d. 1.46
13. a. 0.3413
d. 0.9282
15. a. 4.75%
17. a. 0.1894
19. a. 95.25%
21. a. 87
23. 9.1 min
c.
f.
c.
f.
b. ŷ 1.4x 0.3
d.
2.08
2.21
0.8997
0.3300
y
18
16
*
*
14
12
*
8
1. a. 0.68 b. 0.31
c. 1.39 d. 2.65
3. a. 1.44 b. 1.28
c. 1.15 d. 2.575
5. 1.75
7. 1.15
9. a. 2.6%
b. 3.7%
11. a. 75.0% 3.4%
b. 75.0% 4.0%
13. a. 79.0%
b. 21.0%
c. 1.6%
15. a. 86.0%
b. 70.0%
c. 2.8% for the men; 2.5% for the women
17. a. 57.0%
b. 43.0%
c. 2.2%
19. a. 36.0%
b. 1.6% c. 2.3%
21. a. 4.7% b. 3.5% c. 2.8%
23. 96.4%
25. 95.3%
6
*
4
2
2
4
6
8
e. 0.9479459
7. a. no
y
10
12
14
16
18 x
14
16
18 x
f. yes
18
16
*
14
*
*
12
10
8
Section 4.6 Linear Regression
ŷ 1.0x 3.4
15.6
0.9529485
ŷ 20.1x 8.2
12
no
yes
*
10
Section 4.5 Polls and Margin of Error
1. a.
c.
d.
3. a.
c.
e.
5. a.
c. 12.3
6
b. 14.4
4
e. yes
b. 7.7
d. 20.0951819
2
*
*
*
2
4
6
10
8
b. ŷ 0.0x 9.1
d.
y
12
c. 9.1
y
18
18
16
*
16
*
14
*
14
12
12
*
10
*
*
10
*
8
8
6
6
*
4
*
*
4
2
*
2
2
4
6
8
10
12
14
16
18 x
APPENDIX
2
G
4
6
8
10
12
14
16
Answers to Selected Exercises Section 4.4–4.6
Truckee Meadows Community College Math Department
18 x
A-55
e. 0.0062782255
f. no
9. a. yes
$4000
b. 1.8
f.
d. 2
0
1
e. 1.3
f
12
*
*
3000
tuition
c. 2
*
*
*
10
*
8
*
2000
6
4
1000
2
$10.00
13.00
12.00
11.00
hourly wage
3. a.
d.
4. a.
b.
c.
b. ŷ 21779.2 398.0x
c. $3,195.80
d. $12.01
e. 0.9878803778
f. yes; r is close to 1
11. a. yes
divorces
(in millions)
1.2
1.0
0.8
0.6
0.4
0.2
40% b. 28%
14% e. 50%
10.17
3.21
5
c. 86%
f. cannot determine
f 70
64
60
***
*
50
42
*
40
*
35
30
18
20
1.8
2.0
2.2
2.4
12
2.6
marriages (in millions)
b. ŷ 1.1130x 1.5239
c. 1.5369 million
d. 2.7169 million
e. 0.9338946
f. yes
10
0
3
6
Chapter 4 Review
1. a. 7.1 b. 7.5
2. a.
Number of
Children
c. 8
Relative
Frequency
8
0.2 20%
10
0.25 25%
11
0.275 27.5%
7
0.175 17.5%
4
3
0.075 7.5%
5
1
0.025 2.5%
n 40
1.000 100%
2
3
APPENDIX
G
12
15
18
d. 2.1
Frequency
1
9
time in minutes
Tally
0
A-56
2
3
4
Number of children
5. 100
6. $33,400
7. a. Timo, 98.8; Henke, 96.6; Henke has the lower mean.
b. Timo, 6.4; Henke, 10.4
c. Timo is more consistent because his standard
deviation is lower.
8. a. $1.298; $0.131 b. 78%
c. 95%
d. 100%
9. a. continuous
b. neither
c. discrete
d. neither
e. discrete
f. continuous
10. a. 45.99%
b. 45.99%
c. 91.98%
11. a. one [71, 85]; two [64, 92]; three [57, 99]
b. 68.26%; 95.44%; 99.74%
Answers to Selected Exercises Section 4.6–Chapter 4 Review
Truckee Meadows Community College Math Department
e. 0.8398392
f. yes
c.
21. a. yes
imports (billion dollars)
40
X
12.
13.
14.
15.
16.
17.
18.
19.
20.
57
64
71
85
92
78
a. 0.0475 b. 0.4972
401
a. 1.59
b. 1.645
c. 0.51
d. 2.81
a. 66.7% 2.4%
b. 66.7% 2.8%
a. 75% 2.0%
b. 75% 3.7%
a. 4.1%
b. 3.1%
81.6%
a. ŷ 3x 15
b. 63
d. 1.0
e. yes
a. yes
99
c. 2.5%
*
*
30
*
25
*
*
*
*
*
20
35
c. 14
40
45
50
55
60
exports (billion dollars)
b.
c.
d.
e.
f.
y
40
*
*
30
*
35
ŷ 20.719 0.607x
$29.631 billion
$58.845 billion
0.8979632779
yes, r is close to 1
*
*
20
Chapter 5 Finance
*
*
Section 5.1 Simple Interest
10
20
10
30
40
x
b. ŷ 20.70x 40.25
c. 29.75
d.
y
40
*
*
30
*
*
20
*
*
10
10
20
30
APPENDIX
40
G
x
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
$480
$21.26
$153.80
$4,376.48
$14,073.09
$1,474.81
$6,162.51
$17,036.82
$6,692.61
$1,039.76
$1,240.95
$2,727.27
about 313 years
$328.19
$115.02
$140.27; $2.08
$152.84; $2.73
a. $8,125
c. $8,125
e. $19,500.08
g. $156,000.08
37. a. $38,940
c. $38,940
e. $95,013.60
g. $383,169.60
b. $146,250
d. $67.71
f. $136,500
b. $311,520
d. $356.95
f. $288,156
Answers to Selected Exercises Chapter 4 Review–Section 5.1
Truckee Meadows Community College Math Department
A-57
Section 5.2 Compound Interest
1. a. 0.03
b. 0.01
c. 0.000328767
d. 0.0046153846
e. 0.005
3. a. 0.00775
b. 0.002583333
c. 0.000084932
d. 0.001192307
e. 0.001291667
5. a. 0.02425
b. 0.008083333
c. 0.000265753
d. 0.003730769
e. 0.004041667
7. a. 34 quarters
b. 102 months
c. 3,103 days
9. a. 120 quarters
b. 360 months
c. 10,950 days
11. $7,189.67
13. $9,185.46
15. $3,951.74
17. 8.30%
19. 4.34%
21. a. 10.38% b. 10.47% c. 10.52%
23. $583.49
25. $470.54
27. First National: 9.55%; Citywide: 9.45%
29. verifies
31. does not verify—true yield is 9.74%
33. a. $9,664.97
b. $51.77
35. $19,741.51
37. a. $8,108.07
b. $690.65
39. a. 1.65%
b. $1008.23 c. $8.23
d. 0.823%
e. The CD is for one half year.
41. r (1 i)n 1
43. 7.45%
45. a. 5.70%
b. 5.74%
c. 5.77%
d. 5.79%
e. 5.78%
f. 5.78%
59. a. 14.2 years
b. 167 months ≈ 13.92 years
c. 56 quarters 14 years
d. 5,061 days ≈ 13.87 years
61. 1,822 days ≈ 4.99 years
10,346 days ≈ 28.35 years
63. 2,369 days ≈ 6.49 years
9,400 days ≈ 25.75 years
a. $1,478.56
a. $5,422.51
a. $770.00
a. $1,391.45
a. $283,037.86
a. $251,035.03
$1,396.14
$726.49
$18,680.03
$51.84
$33.93
$33.63
A-58
APPENDIX
b.
b.
b.
b.
$750.00
$1,350.00
$54,600.00
$69,600.00
c.
c.
c.
c.
$20.00
$41.45
$228,437.86
$181,435.03
$10,958.76
6
7
37. P pymt
39.
41.
47.
49.
$16,784.67
11 i2 n 1
$540,071.70
$542,167.06
$544,273.08
$546,389.80
$548,517.28
4
5
$22,854.54
$29,178.58
8
9
10
$49,784.44
$57,236.17
$64,999.94
pymt
1 11 i2 n
i11 i 2
i
$1,396.14
$726.49
a. 586 months 48 years and 10 months
1,171 payments 48 years and 9.5 months
n
Section 5.4 Amortized Loans
1.
3.
5.
7.
$125.62
b. $1,029.76
$193.91
b. $1,634.60
$1,303.32 b. $314,195.20
$378.35
b. $3,658.36
Payment Principal Interest
Total
Balance
Number Portion Portion Payment
Due
0
—
—
—
$14,502.44
1
$239.37 $138.98 $378.35 $14,263.07
2
$241.66 $136.69 $378.35 $14,021.41
9. a. $1,602.91 b. $407,047.60
c. Payment Principal Interest
Total
Balance
a.
a.
a.
a.
c.
Number
0
1
2
13.
15.
17.
G
$5,367.01
$35,767.44 $42,632.21
11.
Section 5.3 Annuities
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25. a. $537,986.93
b. 1 $537,986.93 $2,734.77 $650
2 $540,071.70 $2,745.36 $650
3 $542,167.06 $2,756.02 $650
4 $544,273.08 $2,766.72 $650
5 $546,389.80 $2,777.48 $650
27. a. $175,384.62
b. $111.84
29. a. $1,484,909.47 b. $102,000
c. $1,382,909.47 d. $979,650.96
e. $643,631.10
31. $11,954.38
33. $45.82
35. a. $595.83 b. $5,367.01
c.
1
2
3
Portion
—
$62.28
$62.85
Portion
—
$1,540.63
$1,540.06
Payment
Due
—
$170,000.00
$1,602.91 $169,937.72
$1,602.91 $169,874.87
d. $4,218.18 per month (assuming only home loan
payment)
a. $18,950
b. $151,600
c. $18,950
d. $1,501.28
e. $189.50
f. $271.61
g. $1,962.39 h. $1,501.28
a. $404.72; $353.68
b. $4,597.24; $2,730.25
c. simple interest loan (why?)
a. $354.29; $1,754.44
b. $278.33; $2,359.84
c. $233.04; $2,982.40
a. $599.55; $115,838.00
b. $665.30; $139,508.00
c. $733.76; $164,153.60 d. $804.62; $189,663.20
e. $877.57; $215,925.20 f. $952.32; $242,835.20
Answers to Selected Exercises Section 5.2–Section 5.4
Truckee Meadows Community College Math Department
19. Both verify, but not exactly. Their computations
are actually more accurate than ours, since they are using
more accurate round-off rules than we do.
21. a. $877.57; $215,925.20
b. $404.89; $215,814.20
23. a. $24,535.12
Principal
Interest
Total
Amount Due
b. Payment
Number
0
1
2
3
4
5
Portion
—
$23,647.62
$23,822.51
$23,998.70
$24,176.19
$24,354.98
25. a. $12,232.14
b. Payment
Principal
Number
Portion
Portion
—
$887.50
$712.61
$536.42
$358.93
$180.13
Payment
—
$24,535.12
$24,535.12
$24,535.12
$24,535.12
$24,535.11
after Payment
$120,000.00
$96,352.38
$72,529.87
$48,531.17
$24,354.98
$0.00
Interest
Total
Amount Due
Portion
Payment
after Payment
37. a. $1,718.80
b. $172,157.40 c. $240,354.60
d. $573,981.98 e. $1,200,543.86
f. The decision is between saving more for retirement
or increasing their standard of living now. (Why?)
49. b. $1,511.44
c. $4,269.82
e. $270.64
51. b. $18,449.10 c. $18,156.11
e. $1,087.63
53. b. $50,702.84 c. $47,587.04
e. $3,818.14
55. b. $735.77
c. $2,353.64
e. $101.61
57.
Total
Payment Principal Interest Payment
Balance
0
$32,440.00
1
$2,638.90 $141.93 $2,780.82 $29,801.11
2
$2,650.44 $130.38 $2,780.82 $27,150.66
0
—
—
—
$48,000.00
1
$11,862.14
$370.00
$12,232.14
$36,137.86
2
$11,953.58
$278.56
$12,232.14
$24,184.28
3
$2,662.04 $118.78 $2,780.82 $24,488.63
3
$12,045.72
$186.42
$12,232.14
$12,138.56
4
$2,673.68 $107.14 $2,780.82 $21,814.95
4
$12,138.56
$93.57
$12,232.13
$0.00
5
$2,685.38
$95.44 $2,780.82 $19,129.57
6
$2,697.13
$83.69 $2,780.82 $16,432.44
Balance
7
$2,708.93
$71.89 $2,780.82 $13,723.51
$10288.00
8
$2,720.78
$60.04 $2,780.82 $11,002.73
27. a. $35.37
c.
b. $1735.36
Total
Payment Principal Interest Payment
0
1
$1699.99
$35.37
$1735.36
$8588.01
9
$2,732.68
$48.14 $2,780.82
$8,270.05
2
$1705.84
$29.52
$1735.36
$6882.17
10
$2,744.64
$36.18 $2,780.82
$5,525.41
3
$1711.70
$23.66
$1735.36
$5170.47
11
$2,756.65
$24.17 $2,780.82
$2,768.76
4
$1717.59
$17.77
$1735.36
$3452.88
12
$2,768.76
$12.11 $2,780.87
$0.00
5
$1723.67
$11.87
$1735.36
$1729.39
6
$1729.39
$5.94
$1735.33
$0
Principal
Portion
—
$308.95
$308.95
$308.95
Interest
Portion
—
$95.77
$95.77
$95.77
Total
Payment
—
$404.72
$404.72
$404.72
Amount
Due after
Payment
$14,829.32
$14,520.37
$14,211.42
$13,902.47
Section 5.5
1.
3.
5.
7.
9.
11.
14.6%
11.2%
a. $126.50
b. verifies
a. $228.77
b. does not verify
Either one could be less expensive, depending on the A.P.R.
Really Friendly S and L will have lower payments but
higher fees and/or more points.
13. $8,109.54
15. a. $819.38
b. $801.40
c. $8,009.75
d. $9,496.12
d. $124.13
29. add-on:
Payment
Number
0
1
2
3
simple interest:
Section 5.6
Amount
Due after
Payment
$14,246.39
$13,998.07
$13,747.92
$13,495.92
Payment Principal Interest
Total
Number
Portion Portion Payment
0
—
—
—
1
$248.32 $105.36 $353.68
2
$250.15 $103.53 $353.68
3
$252.00 $101.68 $353.68
31. $3,591.73
33. $160,234.64
35. a. $1,735.74
b. $151,437.74 c. $1,204.91
d. $472,016.40 e. $343,404.24 f. yes (why?)
APPENDIX
1. a.
b.
3. a.
b.
5. a.
b.
$143,465.15
$288,000.00
$179,055.64
$390,000.00
$96.26
$34,653.60; she receives $253,346.40 more than
she paid
7. a. $138.30
b. $331.39
9. a. $185,464.46 b. $14,000.00
c. $14,560.00
d. $29,495.89
G
Answers to Selected Exercises Section 5.4–5.6
Truckee Meadows Community College Math Department
A-59
11. a. $36,488.32
d. $1,079.79
13. a. $12,565.57
d. $61.48
15. a. $17,502.53
d. $372.99
17. $490,907.37
b. 576,352.60
c. $454.10
b. 10.4713067%
c. $138,977.90
b. 0.0927217
c. $245,973.09
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
$8,730.15
$15,547.72
$4,067.71
$4,104.26
about 1.9 years
$3,443.70; $57.03
a. $308.25 b. $70,692.00 c. $235,092.00
Bank of the South at 7.88% is better than Extremely
Trustworthy Savings at 7.63%.
a. $4,580.78
b. $2,109.38
$37,546.62
$19,173.84
$37,738.26
a. $189,090.91
b. $88.22
a. $263.17
b. $3,651.62
c. Period
Amount
Number Principal Interest
Total Outstanding
0
—
—
—
$12,138.58
1
$153.16 $110.01 $263.17 $11,985.42
2
$154.55 $108.62 $263.17 $11,830.87
d. does not verify e. $6,885.51
a. $174.50
b. does not verify
a. $1,217.96
b. $7,299.98
a. $261,366.36
b. 255.25
c. payments $91,890.00; receipts $510,000.00
a. $58,409.10
b. $881,764.23
c. $556.55
Chapter 6 Geometry
Section 6.1 Perimeter and Area
16.1 cm2
12.5 in.2
21.7 ft2
176 m2
a. 33.2 in.2
a. 30 m2
a. 27.7 m2
a. 80 ft2
a. 3,927.0 yd2
a. 54 yd2
a. 49.8 ft2
a. 1,963.5 ft2
c. 3,572.6 ft2
25. a. 3,136 in.2
27. 8.0 ft2
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
A-60
APPENDIX
3.9 mi
8 ft
a. 5,256.6 yd2
seven
large
b. 325.7 yd
Section 6.2 Volume and Surface Area
Chapter 5 Review
1.
2.
3.
4.
5.
6.
7.
8.
29.
31.
33.
35.
37.
b.
b.
b.
b.
b.
b.
b.
b.
20.4 in.
30 m
24 m
44 ft
257.1 yd
30 yd
28.9 ft
863.9 ft2
b. 21.8 ft2
G
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
a. 38.22 m3
b. 72.94 m2
3
a. 785.40 in.
b. 471.24 in.2
3
a. 2.81 in.
b. 9.62 in.2
16.76 ft3
21.33 ft3
36 ft3
47.12 ft3
a. 136.5 in.3
b. 151 in.2
3
17,802.36 ft
a. hardball, 12.31 in.3; softball, 29.18 in.3; volume of
softball is 137% more than that of hardball
b. hardball, 25.78 in.2; softball, 45.83 in.2; surface area
of softball is 78% more than that of hardball
49
147
no; should have paid $118.75
36.82 in.3
$175.20
91,445.760 ft3
301.59 ft3
Section 6.3
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
a right triangle
not a right triangle
a. the regular pyramid (2,025 khar . 1,554 khar)
36; 18; 9; 36; 18; 9; 63; 9; 3; 63; 189; 189
a square with sides of 21 units
49
16
a. 28.4444 palms2 b. 28.2743 palms2
c. 0.6%
a. 113.7778 palms3
b. 113.0973 palms3 c. 0.6%
11 cubits
the khar (1 khar 5887 in.3 1 ft3 1,728 in.3)
1.5 setats
a. 2 khet
b. 200 cubits
a. 960 khar
b. 954.2588 khar
c. 0.6%
Section 6.4 The Greeks
x 5; y 60
x 64.6; y 2.5
36 ft
5.3 ft (rounded down so the object will fit)
7.5 in.
a. 3.061467459
b. 3.313708499
21. a. 3.121445152
b. 3.182597878
1.
3.
5.
9.
11.
19.
Answers to Selected Exercises Section 5.6–Section 6.4
Truckee Meadows Community College Math Department
5. center (5, 2); radius 4
y
Section 6.5 Right Triangle Trigonometry
1.
3.
5.
7.
9.
11.
13.
14.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
60°; x 3; y 3 13
30°; x 14; y 7 13
45°; x 3; y 3 12
7 22
45°; x 7 22
2 ;y 2
B 53°; b 15.9; c 19.9
B 35.7°; a 7.8; c 9.6
A 40.1°; a 0.59; b 0.70
a .081; b .028; A 71.3°
A 80.85°; b 249; c 1,556
B 36.875°; a 43.52; b 32.64
A 85.00°; a 11.453; c 11.497
A 40.7°; B 49.3°; b 17.4
A 40.6°; B 49.4°; c 9.2
A 74.4°; B 15.6°; a 0.439
a. 64.0 ft
b. 92.3 ft
150 ft
18.4°
a. 176.1 ft
b. 26.7 ft
26.2 ft 37.167 ft
167 ft
630 ft
1,454 ft
24.6 ft
•
x
•
•
•
•
7. center (5, 5); radius 5
y
•
•
•
•
•
Section 6.6
x
1. center (0, 0); radius 1
y
9. focus (0, 14)
1
y
•
-1
•
x
1
•
-1
3. center (2, 0); radius 3
y
11. focus (0, 12)
•
•
•
y
•
•
•
•
x
•
x
• • •
•
APPENDIX
G
x
Answers to Selected Exercises Section 6.5–6.6
Truckee Meadows Community College Math Department
A-61
13. 2.9 ft above the bottom of the dish
15. 169 inch above the bottom of the reflector
23. foci (1, 2 13) and (1, 2 13)
y
17. foci ( 15, 0) and ( 15, 0)
y
•
•
•
•
x
•
•
•
•
x
19. foci (0, 121) and (0, 121)
y
•
•
25. They should stand at the foci, which are located 9 ft from
the center, in the long direction.
•
x
9 ft
•
9 ft
•
•
•
27.
y
x
1
2
92.955
92.9422
21. foci (0, 17) and (0, 17)
y
29. a. foci ( 12, 0) and ( 12, 0)
y
•
•
•
x
•
•
•
A-62
APPENDIX
G
Answers to Selected Exercises
Section 6.6
Truckee Meadows Community College Math Department
x
b. foci (0, 12) and (0, 12)
Section 6.7
y
1.
5.
9.
13.
17.
one
zero or one
zero, one, two, or three
infinitely many
zero or one
3.
7.
11.
15.
zero or one
none
two
zero or one
•
x
•
Section 6.8 Fractal Geometry
1. b.
31. foci ( 113, 0) and ( 113, 0)
y
•
•
x
33. foci (0, 129) and (0, 129)
5.
7.
9.
11.
13.
15.
17.
y
•
d2
d 31
d 1.6 It’s not 2-dimensional, as a regular triangle is.
d 1.6 It’s not 2-dimensional, as a regular triangle is.
d 1.5 It’s not 2-dimensional.
d 3, the same dimension that we observed before.
d2
x
•
Section 6.9 The Perimeter and Area of
a Fractal
1. a. In step 1, there is only one triangle. If each side
is 1 ft. in length, then the perimeter is 3 ft. In
step 2, the original triangle is modified by removing
a center triangle. This results in three smaller
triangles. Each side of the original triangle now has
two triangles with sides of length 12 ft. Thus, the
perimeter of one of these smaller triangles is
1
21212 3 · 12 32 ft. Since
there are three such triangles, the total perimeter
is 3 · 32 92 ft.
35. foci (3 15, 0) and (3 15, 0)
y
•
•
x
APPENDIX
G
Answers to Selected Exercises Section 6.6–6.9
Truckee Meadows Community College Math Department
A-63
1. b.
g.
Number Length of
of
each side
Step Triangles (in feet)
1
Perimeter
Total
of one
Perimeter of
triangle all triangles
(in feet)
(in feet)
1
1
3
3
3
1
2
3
2
9
3
9
1
4
3
4
27
4
27
1
8
3
8
81
5
81
1
16
3
16
243
243
1
32
3
32
729
2
6
c.
d.
e.
f.
g.
h.
2
4
8
16
32
3
2
1
2
3
2
31 32 2 n1
The perimeter is infinite. The numbers get larger and
larger without bound.
1
3. a. In step 1, there is only one square. If each side is 1 ft. in
length, then the perimeter is 4 ft. In step 2, the original
square is divided into nine smaller squares and modified
by removing the center square. The removed square
contributes to the perimeter. It has sides of length 13 ft.
Thus, the perimeter of this smaller square is 4 · 13 43
ft. The total perimeter is the sum of the previous
perimeter and the new contribution: 443 ft.
8 n2
4
· a b , valid for n>1
3
3
h. The total perimeter is infinite. The numbers increase
without bound.
2 n1 23
5. a. 3 · 2n1
b. c. a b
d. 0
3
4
Chapter 6 Review
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Area x(x 2) square feet. Perimeter 4x 4 feet.
114 ft2, 42 ft
73.5 in.2; 41 in.
36 cm2; 28 cm
69 yd2; 37.4 yd
2,789.7 ft3
72.8 cm3; 153.9 cm2
254.5 yd3; 216.8 yd2
1,056 in.3; 664 in.2
4.1 mi
nine
672.1 yd2
a. 224 in.3
b. 200 in.2
a. hardball, 12.3 in.3; tennis ball, 8.2 in.3; volume of
hardball is 50% more than that of tennis ball
b. hardball, 25.8 in.2; tennis ball, 19.6 in.2; surface area
of hardball is 32% more than that of tennis ball
a. 450.7 ft3
b. 268.0 ft2
a. 3.1605 cubits2 b. 3.1416 cubits2 c. 0.6%
a. 4.2140 cubits3
b. 4.1888 cubits3 c. 0.6%
the regular pyramid (40,000 khar . 28,140 khar)
a square with sides of 16 units
3. b.
Total
Perimeter perimeter of
Number Length of of one new
all new
of new each side
square
squares (in
Step squares (in feet)
(in feet)
feet)
Total perimeter of all squares
(in feet)
1
1
1
4
4
4
2
1
1
3
4
3
4
3
443
3
8
1
9
4
9
32
9
443329
4
64
1
27
4
27
256
27
443 32925627
5
512
1
81
4
81
2048
81
44332925627204881
6
4096
1
243
4
243
16384
243
4 433292562720488116384243
c.
d.
e.
f.
A-64
8
3
1
3
8
3
1
APPENDIX
G
Answers to Selected Exercises Section 6.9–Chapter 6 Review
Truckee Meadows Community College Math Department
20.
21.
22.
26.
27.
28.
31. foci (0, 15) and (0, 15)
y
256
81
6.5 ft (rounded down so the object will fit)
4.7 ft
3.313708499
3.105828541
center (1, 1); radius 1
•
y
•
•
• • •
•
•
x
•
x
32. They should stand at the foci, which are located 17.3 ft
from the center of the room, in the long direction.
29. a. foci ( 113, 0) and ( 113, 0)
y
17.3 ft
•
•
•
17.3 ft
•
•
B 64.6°; a 24.1 ft; b 50.7 ft
A 33.7°; B 56.3°; c 81.5 cm
213.2 ft
983 ft
a. Given a line and a point not on that line, there is one
and only one line through the point parallel to the
original line.
b. 1. Given a line and a point not on that line, there are
no lines through the point parallel to the original line
(parallels don’t exist).
2. Given a line and a point not on that line, there are
at least two lines through the point parallel to the
original line.
c. 1. a sphere (Riemannian geometry)
2. a Poincaré disk (Lobachevskian geometry)
d. see page 412, Figure 6.57
38. a. one
b. more than one c. none
39. a. sum 180° b. sum 180°
c. sum 180°
40.
500 2500
b. The total perimeter in steps 1–5: 4, 203 , 100
9 , 27 , 81
5 n1
c. 4 · a b
3
d. The perimeter is infinite.
5 n1
e. a b
9
f. 0
g. d 1.465
33.
34.
35.
36.
37.
x
b. foci (0, 113) and (0, 113)
y
•
x
•
30. 2 ft above the bottom of the reflector
APPENDIX
G
Answers to Selected Exercises Chapter 6 Review
Truckee Meadows Community College Math Department
A-65
h. If we focus in on any smaller square it will look like
the entire box fractal.
i. For any square that is not removed, the recursive rule
is to remove the same four squares in the middle of
the edges.
Chapter 7 Matrices and Markov
Chains
Section 7.0 Review of Matrices
a. 3 2
a. 2 1
a. 1 2
a. 3 3
a. 3 1
22
41
3
11
115
3
a. AC C 383 S
783
23. a. AD does not exist.
25. a. CG does not exist.
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
27. a. JB does not exist.
10
29. a. AF C 56
0
b.
b.
b.
b.
b.
b. CA does not exist.
b. DA does not exist.
b. GC does not exist.
2,243
b. BJ C 1,056 S
52
31. $130 on sale, $170 regular price
33. [3.45 3.70]
35. 3.07; 3; 3.50
106
d
68
41. does not exist
19
43. C 74
13
7
0
2
c
39.
3
34
2
d
0
1. a. p(current purchase is KickKola) 0.14;
p(current purchase is not KickKola) 0.86
b. P [0.14 0.86]
3. a. p(currently own) 0.32; p(currently rent) 0.68
b. P [0.32 0.68]
5. a. p(Silver’s) 0.48; p(Fitness Lab) 0.37;
p(ThinNFit) 0.15
b. P [0.48 0.37 0.15]
APPENDIX
G
0.63 0.37
d
0.12 0.88
9. a. p(buy next residence currently rent) 0.12;
p(rent next residence currently own) 0.03;
p(rent next residence currently rent) 0.88;
p(buy next residence currently own) 0.97
0.97 0.03
d
0.12 0.88
11. a. p(Silver’s next currently Silver’s) 0.71;
p(Fitness Lab next currently Silver’s) 0.12;
p(ThinNFit next currently Silver’s) 0.17;
p(Silver’s next currently Fitness Lab) 0.32;
p(Fitness Lab next currently Fitness Lab) 0.34;
p(ThinNFit next currently Fitness Lab) 0.34;
p(Silver’s next currently ThinNFit) 0.02;
p(Fitness Lab next currently ThinNFit) 0.02;
p(ThinNFit next currently ThinNFit) 0.96
0.71 0.12 0.17
b. C 0.32 0.34 0.34 S
0.02 0.02 0.96
13. a. 19%
b. 22%
15. a. 46%; 19%; 35%
c. 39%; 13%; 48%
d. 33%; 10%; 57%
17. 27%
Section 7.2 Systems of Linear Equations
1.
3.
5.
7.
9.
11.
13.
15.
17.
34
11 S
44
Section 7.1 Markov Chains
A-66
b. c
b. c
none
column
row
square
column
50
229 S b. FA does not exist.
153
37. c
7. a. p(next purchase is KickKola current purchase is not
Kick Kola) 0.12; p(next purchase is KickKola current purchase is KickKola) 0.63;
p(next purchase is not KickKola current purchase is
not KickKola) 0.88; p(next purchase is not
KickKola current purchase is KickKola) 0.37
yes
no
no
72
a. 25, 2; 196 ,19
4
4
a. 3, 4; 3, 4
a. 1, 7; 32, 4; 1, 7
yes
no
no
b. one solution
b. infinite number of solutions
b. one solution
Section 7.3 Long-Range Predictions with
Markov Chains
30.1818 0.8182 4
L 3 158 157 4
24%
80%; 20%; current trends continue, and residents’
moving plans are realized
9. Sierra Cruiser will eventually control 26% of the
market.
1.
3.
5.
7.
Answers to Selected Exercises Chapter 6 Review–Section 7.3
Truckee Meadows Community College Math Department
Section 7.4 Solving Larger Systems of
Equations
1. x 4, y 2, z 1
3. x 2, y 5, z 7
5. x 5, y 10, z 2
2
7 11
7. c
d
3 2 15
2
11. C 5
1
3
2
1
15. c
3
7
1
0
1
19. C0
0
21.
23.
37.
39.
7
12
1
53
19 S
55
5
d
14
1
3
1
2
0
11
9. c
1
1
2
3
5
13. C 3
2
0
1
2
17. c
0
1
1
0
b. If current trends continue, the percentages will be
17.6%, 23.9%, and 58.5%. Thus, significantly
fewer apartments will be needed, and significantly
more condominiums and townhouses will be
needed.
c. emigration and immigration
5
d
41
1
0
2
Chapter 8 Linear Programming
2
15 S
53
Section 8.0 Review of Linear Inequalities
1.
39
5
7d
5
y
6
9 S
4
x
(9, 2)
(0.5281, 0.6205, 0)
no solution
(4, 0, 7)
Section 7.5 More on Markov Chains
y
3.
1. 3 0.2115 0.5577 0.2308 4
3. 10.8%; 4.5%; 84.6%
5. 48.6%; 37.6%; 13.8%
Chapter 7 Review
1.
2.
3.
4.
x
neither; 3 2
square; 3 3
column; 4 1
row; 1 4
5. c
23
24
24
d
28
6. does not exist
7. c
18
0
8. c
35
12
3
10
19
34
5.
15
d
25
72
51
y
24
d
24
9.
10.
11.
17.
does not exist
$43,000; $41,300
no; yes
a. 21.5%
b. 25.9% c. 29.6%
d. Current trends continue, and the survey accurately
reflects future purchases.
18. a. If current trends continue, the percentages will be
22.1%, 19.6%, and 58.3%. Thus, more
condominiums and townhouses will be needed.
APPENDIX
G
x
Answers to Selected Exercises Section 7.4–Section 8.0
Truckee Meadows Community College Math Department
A-67
y
7.
b. unbounded
c. (331, 323)
15. a.
y
70
60
50
40
30
20
10
x
x
10 20 30 40 50
y
9. a.
b. bounded
c. (0, 0), (0, 14), (10, 10), (12, 0)
y
17. a.
x
50
40
30
20
10
b. unbounded
x
c. (1, 3)
10 20 30 40 50
y
11. a.
b. bounded
c. (0, 10), (0, 23112 ), (12, 15), (1717, 0), (10, 0)
x
19. a.
b. unbounded
y
c. (1, 5)
13. a.
y
x
x
A-68
APPENDIX
G
Answers to Selected Exercises
b. bounded
c. (0, 0), (0, 1.7), (1.3, 1.2), (1.5, 0)
Section 8.0
Truckee Meadows Community College Math Department
y
21. a.
7. a. 5x1 4x2 480
b. 5x1 4x2 s1 480
c. x1 feet of pipe, x2 number of elbows,
s1 unused time in minutes
9. a. 24x1 36x2 56x3 72x4 50,000
b. 24x1 36x2 56x3 72x4 s1 50,000
c. x1 number of twin beds, x2 number of double beds,
x3 number of queen-size beds, x4 number of kingsize beds, s1 unused space in cubic feet
11. (x1, x2, s1, s2) (0, 19, 0, 12), z 22
13. (x1, x2, s1, s2, s3) (0, 0, 7.8, 9.3, 0.5), z 9.6
15. (x1, x2, s1, s2, s3, s4) (25, 73, 0, 32, 46, 0), z 63
35
30
25
20
15
10
5
x
5 10 15 20 25
3
17. £ 4
2
b. bounded
c. (0, 0), (0, 8), (4, 10), (8, 6), (10, 0)
Section 8.1 The Geometry of Linear
Programming
1. x number of shrubs, y number of trees; 1x 3y 100
3. x number of hardbacks, y number of paperbacks;
4.50x 1.25y 5,000
5. x number of refrigerators, y number of dishwashers;
63x 41y 1,650
7. no floor lamps and 45 table lamps, for a profit
of $1,485
9. 60 pounds of Morning Blend and 120 pounds of South
American Blend each day for a profit of $480
11. 15,000 loaves to Shopgood and 20,000 loaves to Rollie’s
each week for shipping costs of $3,000
13. Global has many choices, including the following:
15 Orvilles and 30 Wilburs
18 Orvilles and 28 Wilburs
21 Orvilles and 26 Wilburs
Each of these generates a cost of $720,000.
15. a. 20 large and 30 small, for a profit of $9,500
b. 40 large and no small, for a profit of $10,000
c. 40
17. 0 Mexican; 0 Colombian
19. 150 minutes; $0
21. a. no maximum b. no maximum c. (6, 0) d. 12
23. 3 weeks at Detroit and 6 weeks at Los Angeles, for
a minimum cost of $3,780,000
Section 8.2 Introduction to the Simplex
Method
1. 3x1 2x2 s1 5
3. 3.41x1 9.20x2 6.16x3 s1 45.22
5. a. 6.99x1 3.15x2 1.98x3 42.15
b. 6.99x1 3.15x2 1.98x3 s1 42.15
c. x1 pounds of meat, x2 pounds of cheese,
x3 loaves of bread, s1 unused money
APPENDIX
4
7
4
1
0
0
0
1
0
0
0
1
40
50 §
0
(x1, x2, s1, s2) (0, 0, 40, 50), z 0
112
3 1 0 0 0 370
1
1 0 1 0 0
70
19. ≥
¥
47
19 0 0 1 0 512
12.10 43.86 0 0 0 1
0
(x1, x2, s1, s2, s3) (0, 0, 370, 70, 512), z 0
5
3
9 1 0 0 0 10
12
34 100 0 1 0 0 10
¥
21. ≥
52
7
12 0 0 1 0 10
4 7 9 0 0 0 1
0
(x1, x2, x3, s1, s2, s3) (0, 0, 0, 10, 10, 10), z 0
50
30 1 0 0 2,400
23. £ 0.90 1.50 0 1 0
190 §
1.2
4 0 0 1
0
(x1, x2, s1, s2) (0, 0, 2400, 190), z 0
1
2
1
2
1
4
3
4
1 0 0 200
0 1 0 330 §
3.5 4 0 0 1
0
(x1, x2, s1, s2) (0, 0, 200, 330), z 0
25. £
Section 8.3 The Simplex Method: Complete
Problems
1. pivot on 19
3. pivot on 19
5. a. pivot on 4
0
b. £ 1
0
7
4
1
4
52
1
0
0
14
1
4
3
2
0
0
1
5
2
1
2§
3
c. (x1, x2, s1, s2) (1/2, 0,
0), z 3
7. a. pivot on 1 (row 1, column 1)
212,
1
1
5 0 0
3
b. £ 0 3 14 1 0
3§
0
6
28 0 1 24
c. (x1, x2, s1, s2) (3, 0, 0, 3), z 24
G
Answers to Selected Exercises Section 8.0–Section 8.3
Truckee Meadows Community College Math Department
A-69
9. Each day, make no bread and 80 cakes, for a profit of
$320. This uses all available time and leaves $70
unspent.
11. Each week, make 15 sofas and 40 chairs, for
a profit of $21,750. This leaves no extra time in
either shop.
13. Prepare 20,000 liters of House White, no Premium
White, and 5,000 liters of Sauvignon Blanc, for a profit
of $30,000. This uses all the grapes.
15. Prepare 300 pounds of Smooth Sipper and no Kona
Blend, for a profit of $900. This leaves 100 pounds each
of Colombian and Arabian beans.
25. (4.304, 2.956, 0, 0, 9.173, 0, 0), z 264.304
27. (3.694, 0, 1.117, 0, 0, 30.359, 0, 0); z 195.884
29. 13.2 modern coffee tables, 14.2 modern end tables; profit
$9,228.79; no slack
31. 427 dozen blueberry muffins, 1013 dozen apple-cin.
muffins; profit $21,461.33; no slack
33. 57.3 sofas, 21.8 recliners; $36,140 profit; 15.5 slack
coating hours
3.
y
x
4.
y
x
Chapter 8 Review
y
1.
5. (32, 12)
y
x
x
y
2.
10
6. (217
, 15
17 )
y
x
x
A-70
APPENDIX
G
Answers to Selected Exercises Section 8.3–Chapter 8 Review
Truckee Meadows Community College Math Department
7. (3, 23)
14. Make 24 model 110s, 16 model 220s, and 50 model
330s, with no tweeters, midrange speakers, or
woofers left over. This gives a maximum income
of $26,780.
y
5
Chapter 9 Exponential and
Logarithmic Functions
x
–5
5
–5
Section 9.0 A Review of Exponentials
and Logarithms
8. (112, 4)
y
x
9. no solution
10. (0, 5), (3, 0), (4, 0)
y
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
v3
v 22
u 251
u1
b3
b 13
bk H
b(G 5) F E
T logb S
MN logb(P Q)
a. 3.320116923
a. 2.166574135
a. 0.2231301601
a. 3.146511444
a. 0.335160023
a. 0.7654678421
a. 0.5447271754
a. 3.4
a. 1.406294361
a. 3.6
a. 25
a. 2
a. 5.68738518
log 2.8, ln 2.8, e2.8, 102.8
b.
b.
b.
b.
b.
b.
b.
b.
b.
b.
b.
b.
b.
15.84893192
2.404528869
0.0316227766
2.301759749
0.1990535853
0.3324384599
0.2365720064
3.4
0.622059913
3.6
25
0.8685889638
2.47
Section 9.0 B Review of Properties of
Logarithms
x
11. 30 of each assembly for a maximum income of $16,500
12. 750 Sunnys and 375 Iwas for a maximum profit of
$240,000
13. Make 30 of each assembly, with no tweeters or midrange
speakers left over and 14 woofers left over. This gives
a maximum income of $16,500.
APPENDIX
G
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
7.5x
0.058x
3x 1
8x
log x log 5
ln 1.4 ln x
x log 1.0625
log 4 3 log x
ln 2 ln x ln 3
log2x
ln(10x)
log(2x)
ln(x2)
0
a. 1.386294361
a. 18.24071528
b. 0.602059991
b. 7.921841991
Answers to Selected Exercises Chapter 8 Review–Section 9.0
Truckee Meadows Community College Math Department
A-71
33.
35.
37.
39.
41.
43.
45.
47.
53.
55.
57.
59.
61.
63.
65.
67.
69.
a. 45.05167868
b. 19.56569545
a. 46.20981204
b. 20.06866638
a. 139.4647196
b. 60.56875813
a. 1.318256739
b. 1.127496852
a. 70.79457844
b. 6.359819523
a. 2.5
b. 10.87312731
a. 227.144644
b. 1.680457629
a. 1.892872033
b. 1.85461744
3.5; acid
7.4; base
4.9
107 moles per liter
a. yes; pH 6.5 is acceptable
b. no; pH 3.5 is not acceptable
from 3.16 109 to 107 moles per liter
log 3
a.
b. 1.58
log 2
log 6
a.
b. 1.63
log 3
log 8
a.
b. 1.50
log 4
Section 9.1 Exponential Growth
1. 32,473
3. July 2011
5. a. (0, 8240) and (10, 9258)
b. 10 years
c. 1,018 thousand people
d. 101.8 thousand people per year
e. 1.2% per year
7. a. (0, 19342) and (10, 21200)
b. 10 years
c. 1,858 thousand people
d. 185.8 thousand people per year
e. 1.0% per year
9. a. p(t) 8,240e.0116487699t (in thousands)
b. 9,813.2 thousand
c. 10,401.8 thousand
d. Halfway through 2049
11. a. p(t) 19,342e.0091722284t in thousands
b. 21,791.5 thousand
c. 23,236.5 thousand
d. early in 2034
13. a. p 2,510e0.2541352t b. 14,870
c. 2.7 days
15. a. p(t) 230,000e.0497488314t
b. October 2001
c. $417,826
d. $15,652 per month
17. a. p(t) 90.9e.0159798794t
b. 98.5 quadrillion BTU’s
19. a. p(t) 6,343e.0771316418t
b. $10,076 billion
A-72
APPENDIX
G
21. a. p(t) 3,929,214e.0300866701t
b. 1810
c. In 1810: 7,171,916. In 2000: 2,179,040,956
23. Africa, 26 years; North America, 73 years;
Europe, 138 years
25. 40 years
27. a. because it will not increase by the same amount
each year
b. approximately 4.25 years
29. p(t) 19,342(1.009214422)t thousand people
31. p(t) 8,240(1.011716881)t thousand people
33. 8,240e.0116487699t 8,240(e.0116487699)t
8,240(1.011716881)t
35. 5,060.3 days 13.86 years
37. 586 months 48 years and 10 months
Section 9.2 Exponential Decay
1. 3.2 g
3. 7.4 g
5. a. Q 50e0.266595069t (t in hours)
b. 38.3 mg
c. 0.08 mg
d. 11.7 mg per hour
e. 23.4% per hour
f. 2.1 mg per hour
g. 4.2% per hour
h. Radioactive substances decay faster when there
is more substance present. The rate of decay is
proportional to the amount present.
7. a. 21.0 hr
b. 42.0 hr
c. 63.0 hr
9. 30.2 years
11. 50.3 years
13. 81,055 years
15. 99.7 sec
17. 53% of the amount expected in a living organism
19. 63.5 days
21. 1,441 years
23. 14,648 years
25. 2,949 years
27. 93% of the amount expected in a living organism;
79% of the amount expected in a living organism
29. 50% of the amount expected in a living organism
31. The claim is not justified. (62% remaining carbon-14
would indicate approximately 3,950 years.)
33. approximately 8,300 years old
Section 9.3 Logarithmic Scales
1. 7.6
3. 5.2
Answers to Selected Exercises Section 9.0–Section 9.3
Truckee Meadows Community College Math Department
5. a. 16 times as much earth movement
b. 55 times as much energy released
7. a. 32 times as much earth movement
b. 150 times as much energy released
9. a. 1.3 times as much earth movement
b. 1.4 times as much energy released
11. a. 158 times as much earth movement
b. 1,549 times as much energy released
13. a. 26%
b. 40%
15. Energy released is magnified by a factor of 28.
17. 70 dB
19. 74 dB
21. 10 dB
23. 9.1 dB
25. four joined (five total)
27. one joined (two total)
29. five joined (six total)
31. a gain of 3 dB
33. The new sound would be 0.003% as intense as the old
sound, so the energy hitting the buildings would be
0.003% as strong.
23. 102 dB
24. 9 dB gained
25. Three trumpets have joined in.
Chapter 9 Review
23. a.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
x4
x4
x 3,125
log(10x ) x and 10log x x
ln(ex ) x and eln x x
log( AB) log A log B
ln( AB) ln A ln B
log(An) n(log A)
ln(An) n(ln A)
log(AB) log A log B
ln(AB) ln A ln B
21x3
log a
b
4
log(x 2)
log x log 2
11.30719075
8
447,213.6
a. P 10,000e0.458145365t (t in hours)
b. 38,147,000 c. 130 p.m.
d. The growth conditions are unlimited, and the
culture grows at a rate proportional to the
population size.
a. Q 300e0.130782486t (t in years)
b. 1.5 g c. 263.2 g d. 17.6 years
2,600 years old
3.1 on the Richter scale
a. 40 times more earth movement
b. 209 times more energy
APPENDIX
G
Chapter 10 Calculus
Section 10.0
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
a 5/2, b 7/2
x 16.5, y 19.5
x 12, y 5
x 1.5, y 6.25
a. 15 students/1 teacher
b. 362 teachers
a. 9/100
a. 32.1 mph
a. 76.9 mph
a. 24.6 mpg
c. 369 mi
4g
480 ft
b.
b.
b.
b.
9%
128.4 mi
307.7 mi
369 mi
y
•
•
•
x
b. x 0
c. (0, 4)
y
25. a.
•• •
•
•
•
b. x 2
•
x
c. (2, 7)
Answers to Selected Exercises Section 9.3–Section 10.0
Truckee Meadows Community College Math Department
A-73
27. a.
b. x 1
c. (1, 2)
y
33. a. 12
y
b.
•
•
•
x
• •
•
•
• •
•
x
b. x 4
c. (4, 2)
y
29. a.
• ••
•
•
x
•
•
35. a. 0
y
b.
•
•
•
31. a.
y
•
37. 21
41. 8x 13
45. 8x 8x 11
• •
y
1. a
•
APPENDIX
•
G
39. 6
43. x2 14x 46
47. x2 2xx (x)2 3
Section 10.1
•
•
A-74
x
b. x 3
c. (3, 18)
x
L2
L1
• •
Answers to Selected Exercises Section 10.0–Section 10.1
Truckee Meadows Community College Math Department
•
x
b. L1 14, L2 1, A1 1, A2 4
c. 14, 14
d. L3 94, L4 4, A3 9, A4 16
e. 169 , 169
3.a.
7. a.
•
•
•
•
y
•
•
•
•
• ••
9.
11.
13.
15.
•
y
•
x
b. L1 4, L2 9, A1 4, A2 9
c. 49, 49
area of the square is 9
area of the square is 1
area of the square is 64
b2
b2
a. c b. c 4
4
17. x b ; 2 b2 4ac
2a
10.2 Four Problems
•
x
1. a. 20 ft
b. 6 ft/sec
c. 45 ft
d. 3 ft/sec
3. a. 40 ft/min b. 56 ft/min c. 196 ft. d. 28 ft/min
5. The last three entries under “total distance traveled” are
16, 25, and 36.
7. 128 ft
9. 3.5 oz
11. 2,304 ft
13. 16 ft
15. 30 ft
17. m 12; y 12x 18
19. m 27; y 27x 54
21. m 4; y 4x 8
23. m 4; y 4x 10
25. m 4; y 4x 6
b. L1 3, L2 12, A1 1, A2 4
c. 14, 41
d. L3 27, L4 48, A3 9, A4 16
e. 169 , 169
5. a.
y
Section 10.3 Newton and Tangent Lines
•
1. m 24; y 24x 48
5. m 23; y 23x 97
9. m 1; y x 1
•
Section 10.4 Newton on Falling Objects
and the Derivative
•
•
3. m 6; y 6x 7
7. m 12; y 12x 16
1.
3.
5.
7.
9.
11.
13.
19.
21.
• •
•
x
b. L1 1, L2 4, A1 1, A2 4
c. 14, 14
APPENDIX
G
a. 16 ft
b. 32 ft/sec
a. 400 ft
b. 160 ft/sec
a. 1,024 ft
b. 256 ft/sec
a. 2 sec
b. 64 ft/sec
The derivative is ds
dt 32.
2
7
22x
6x
c.
c.
c.
c.
16 ft/sec
80 ft/sec
128 ft/sec
32 ft/sec
Answers to Selected Exercises Section 10.1–Section 10.4
Truckee Meadows Community College Math Department
A-75
23. 6x 2
31. a. f(x) 2x 4
b. Slope at x 1 is 6. Slope at x 2 is 8.
c.
53. a. average growth rate in thousands of people per year
b. instantaneous growth rate in thousands of people
per year
40
Section 10.5 The Trajectory of a Cannonball
35
1. a.
c.
3. a.
c.
5. a.
c.
7. a.
c.
9. a.
c.
11. a.
c.
13. a.
15. a.
17. a.
b.
c.
d.
19. a.
b.
c.
21. a.
c.
d.
e.
30
25
rise = 8
20
run = 1
15
10
5
rise = 6
run = 1
−1
1
2
3
4
33. a. f(x) 2x 2
b. Slope at x 1 is 0. Slope at x 2 is 2.
c.
10
8
6
23.
rise = 2
4
25.
27.
29.
run = 1
2
−1
1
2
−2
3
4
31.
y 0.0003x2 0.5774x 4 b. 1,932 ft
282 ft
d. no
y 0.0004x2 x 4
b. 2,504 ft
629 ft
d. yes
y 0.0006x2 1.7321x 5 b. 2,890 ft
1,225 ft
d. yes
y 0.0005x2 0.5774x 5 b. 1,163 ft
172 ft
d. no
y 0.0005x2 x 4
b. 2,004 ft
504 ft
d. yes
y 0.0007x2 1.7321x 3 b. 2,476 ft
1,074 ft
d. yes
y 0.0006x2 x 4
b. 1,651 ft
y 0.0002x2 0.5774x 4 b. 2,859 ft
123 ft/sec
y 0.0014x2 0.5774x 3
63 ft
114 ft/sec
y 0.0040x2 x 106
330 ft
5.2 sec
60° b. 60°, 60°, 60°
2
2 and 2
13
64
y 2 x2 13x C
s
3.9 secs
17.8 secs
a. y 0.0005x2 0.3640x 5 b. 741 ft
c. 71 ft
a. y 0.0034x2 2.7475x 5 b. 810 ft
c. 560 ft
Section 10.6 Newton and Areas
1. a. A(x) 2x
b.
3x2
9x2 4
40x4
20x3 6x 2
a. average speed in mi/sec
b. instantaneous speed in mi/sec
49. a. average flow rate in gal/hr
b. instantaneous flow rate in gal/hr
51. a. average growth rate in cm/yr
b. instantaneous growth rate in cm/yr
4
35.
37.
43.
45.
47.
A-76
APPENDIX
G
2
−1
x
−2
Answers to Selected Exercises Section 10.4–Section 10.6
Truckee Meadows Community College Math Department
c. A(3) 6
c. A(3) 9
10
4
8
2
6
4
−1
1
2
3
4
5
2
6
−1
−2
1
2
3
4
5
6
1
2
3
4
5
6
2
3
4
5
6
−2
d. A(4) 8
4
2
d. A(4) 16
−1
1
2
3
4
5
10
6
8
−2
6
e. A(4) A(3) 2
4
4
2
−1
2
−2
−1
1
2
3
4
5
6
−2
3. a. A(x) x2
b.
10
e. A(4) A(3) 7
10
8
8
6
6
4
4
2
2
−1
x
−2
1
−2
APPENDIX
G
Answers to Selected Exercises
Truckee Meadows Community College Math Department
Section 10.6
A-77
e. A(4) A(3) 5.5
5. a. A(x) 2x 12x2
b.
10
10
8
8
6
6
4
4
2
2
−1
2
x
1
2
3
4
5
6
−2
−2
7. a. A(x) 3x x2
b.
14
c. A(3) 10.5
10
12
8
10
6
8
4
6
4
2
2
−1
1
2
3
4
5
6
1.5
−2
−2
x
c. A(3) 18
d. A(4) 16
14
10
12
8
10
8
6
6
4
4
2
−1
2
1
2
3
4
5
6
−1
−2
A-78
APPENDIX
G
Answers to Selected Exercises
−2
1
2
Section 10.6
Truckee Meadows Community College Math Department
3
4
5
6
d. A(4) 28
Chapter 10 Review
14
12
10
8
6
4
2
−1
−2
1
2
3
4
5
6
2. a 4.5, b 5.25
3. a. about 30.4 mpg
b. 456 mi
4. a. 65
b. 8x2 16x(x) 8(x)2 7
5. a. 120 ft
b. about 6.7 ft/sec
c. 83.3 ft
d. 3.3 ft/sec
6. 400 ft
7. a.
y
e. A(4) A(3) 10
•
14
12
10
8
6
4
•
2
−1
9.
11.
13.
15.
17.
19.
21.
23.
−2
1
2
5x c
3x2 4x c
area 25
area 95
4x2 7x c
x3 x2 5x c
249
329
25. a. 1
27. a. 0
29. a. 8
31. a. 15x4
33.
35.
37.
39.
41.
43.
45.
47.
a. 63
a. 432
a. 576,551.14
a. 1,463,217
4x2 7x c
x3 x2 5x c
5 7
3
7 x x 13x c
18
x c
3
4
5
6
•
x
b. L1 2, L2 8, A1 1, A2 4
c. 14, 41
d. L3 18, L4 32, A3 9, A4 16
e. 169 , 169
8. The root is 1, and the area of the square is 1.
9. a. and g.
x2
c
2
b. 5x c
b. 4x2 c
x2
b.
4x c
6
b. 999,973
b. 9,624
b. 7,141,316
b. 1,763
y
•
b.
•
•
•••
x
APPENDIX
G
Answers to Selected Exercises Section 10.6–Chapter 10 Review
Truckee Meadows Community College Math Department
A-79
b. x 21
d. 7
f. y 6x 10
10. slope 12;
y 12x 13
c. (2, 7)
e. 6
11.
12.
13.
14.
15.
18.
19.
a. 100 feet b. 80 ft/sec c. 40 ft/sec
0
2
2x 3
a. average rate of weight loss in pounds/week
b. instantaneous rate of weight loss in pounds/week
a. average growth rate in bass/week
b. instantaneous growth rate in bass/week
a. y 0.0005x2 0.5774x 4.5 b. 1,163 ft
c. 171 ft d. yes
3 2
2 x 2x c
152
13.
15.
17.
19.
21.
a. 88 ft/sec b. 0.9 sec
a. 81 mph b. 16 mi
a. 0.0157534247
a. 1.83 m
b. 76.7 kg
164.56 gals
y
16.
•
• •
17.
••
•
x
•
Appendix E
1. a. 4 yd
3. a. 52,800 ft
5. 126,720 in.
7. a. 50,000 m
9. a. 0.02 liters
11. a. 454 g
A-80
b. 36 ft
b. 0.0019 mi
b. 0.05 km
b. 200 cl
b. 3.6 kg
APPENDIX
G
Answers to Selected Exercises Chapter 10 Review–Appendix E
Truckee Meadows Community College Math Department
b. $47.26
c. 23; no
c. $48.84
d. 28; yes