ACCESS Test Bank for Finite Mathematics with Applications In the
Management Natural and Social Sciences 13th Edition Lial
INSTRUCTOR’S
SOLUTIONS MANUAL
SAL SCIANDRA
Niagara County Community College
M ATHEMATICS WITH A PPLICATIONS
I N THE M ANAGEMENT , N ATURAL , AND S OCIAL S CIENCES
THIRTEENTH EDITION
F INITE M ATHEMATICS
WITH A PPLICATIONS
I N THE M ANAGEMENT , N ATURAL , AND S OCIAL S CIENCES
THIRTEENTH EDITION
Margaret L. Lial
American River College
Thomas W. Hungerford
Saint Louis University
John P. Holcomb, Jr.
Cleveland State University
Bernadette Mullins
Birmingham-Southern College
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,ACCESS Test Bank for Finite Mathematics with Applications In the ACCESS Test Bank for Finite Mathematics with Applications In the
Management Natural and Social Sciences 13th Edition Lial Management Natural and Social Sciences 13th Edition Lial
Contents
Chapter 1 Algebra and Equations.......................................................................................1
Chapter 2 Graphs, Lines, and Inequalities .......................................................................46
Chapter 3 Functions and Graphs ......................................................................................92
Chapter 4 Exponential and Logarithmic Functions ........................................................167
Chapter 5 The Mathematics of Personal Finance ..........................................................204
Chapter 6 Systems of Linear Equations and Matrices ...................................................242
Chapter 7 Linear Programming ......................................................................................323
Copyright © 2024, 2019, 2015 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. This publication is protected by copyright, and permission should be obtained from the
publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means,
Chapter 8 Sets and Probability .......................................................................................428
electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request forms, and
the appropriate contacts within the Pearson Education Global Rights and Permissions department, please visit
www.pearsoned.com/permissions/.
Chapter 9 Counting, Probability Distributions, and
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the Further Topics in Probability ...........................................................................................459
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are for
demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship, endorsement,
authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner Chapter 10 Introduction to Statistics ..............................................................................495
and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
Chapter 11 Differential Calculus....................................................................................526
Chapter 12 Applications of the Derivative .....................................................................604
Chapter 13 Integral Calculus ..........................................................................................680
Chapter 14 Multivariate Calculus...................................................................................750
ISBN-13: 978-0-13-789213-6
Copyright © 2024 Pearson Education, Inc.
ISBN-10: 0-13-789213-6
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,ACCESS Test Bank for Finite Mathematics with Applications In the ACCESS Test Bank for Finite Mathematics with Applications In the
Management Natural and Social Sciences 13th Edition Lial Management Natural and Social Sciences 13th Edition Lial
Chapter 1 Algebra and Equations
Section 1.1 The Real Numbers For Exercises 13–16, let p = –2, q = 3 and r = –5.
1. True. This statement is true, since every integer 13. −3 ( p + 5q ) = −3[ −2 + 5(3) ] = −3 [ −2 + 15]
can be written as the ratio of the integer and 1. = −3 (13) = −39
5
For example, 5 = .
1 14. 2 ( q − r ) = 2 ( 3 + 5 ) = 2 ( 8 ) = 16
2. False. For example, 5 is a real number, and
10
5= which is not an irrational number.
2 q+r 3 + (−5) −2
15. = = = −2
q + p 3 + (−2) 1
3. Answers vary with the calculator, but
2, 508, 429, 787 3q 3(3) 9 9
is the best. 16. = = =
798, 458, 000 3 p − 2r 3(−2) − 2(−5) −6 + 10 4
4. 0 + (−7) = (−7) + 0 17. Let r = 3.8.
This illustrates the commutative property of APR = 12r = 12(3.8) = 45.6%
addition.
18. Let r = 0.8.
5. 6(t + 4) = 6t + 6 ⋅ 4 APR = 12r = 12(0.8) = 9.6%
This illustrates the distributive property.
19. Let APR = 11.
6. 3 + (–3) = (–3) + 3 APR = 12r
This illustrates the commutative property of
addition. 11 = 12r
11
=r
7. (–5) + 0 = –5 12
This illustrates the identity property of addition. r ≈ .9167%
8. (−4)( −41 ) = 1 20. Let APR = 13.2.
This illustrates the multiplicative inverse APR = 12r
property. 13.2 = 12r
13.2
9. 8 + (12 + 6) = (8 + 12) + 6 =r
12
This illustrates the associative property of r = 1.1%
addition.
21. 3 − 4 ⋅ 5 + 5 = 3 − 20 + 5 = −17 + 5 = −12
10. 1(−20) = −20
This illustrates the identity property of
22. 8 − (−4) 2 − (−12)
multiplication.
Take powers first.
11. Answers vary. One possible answer: The sum of 8 – 16 – (–12)
a number and its additive inverse is the additive Then add and subtract in order from left to right.
identity. The product of a number and its 8 – 16 + 12 = –8 + 12 = 4
multiplicative inverse is the multiplicative
identity. 23. (4 − 5) ⋅ 6 + 6 = −1 ⋅ 6 + 6 = −6 + 6 = 0
12. Answers vary. One possible answer: When using
the commutative property, the order of the
addends or multipliers is changed, while the
grouping of the addends or multipliers is
changed when using the associative property.
Copyright © 2024 Pearson Education, Inc. 1
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, ACCESS Test Bank for Finite Mathematics with Applications In the ACCESS Test Bank for Finite Mathematics with Applications In the
Management Natural and Social Sciences 13th Edition Lial Management Natural and Social Sciences 13th Edition Lial
2 CHAPTER 1 ALGEBRA AND EQUATIONS SECTION 1. 1 THE REAL NUMBERS 3
2(3 − 7) + 4(8) 32. –2 is greater than –20. 58. 6 − (−4) −4 − 6
24. –2 > –20
4(−3) + (−3)(−2) 48. [–2, 2) 10 −10
Work above and below fraction bar. Do This represents all real numbers between –2 and
33. x is greater than or equal to 5.7. 10 10
multiplications and work inside parentheses. 2, including –2, not including 2.
x ≥ 5.7 10 = 10
2(−4) + 32 −8 + 32 24 Draw a bracket at –2, a parenthesis at 2, and a
= = = = −4 heavy line segment between them.
−12 + 6 −12 + 6 −6 34. y is less than or equal to –5.
y ≤ −5 59. −2 + 8 2−8
2
25. 8 − 4 − (−12) 6 −6
35. z is at most 7.5.
Take powers first.
z ≤ 7.5
49. (−2, ∞ ) 6 6
8 – 16 – (–12)
This represents all real numbers x such that 6=6
Then add and subtract in order from left to right.
36. w is negative. x > –2. Start at –2 and draw a heavy line
8 – 16 + 12 = –8 + 12 = 4
w<0 segment to the right. Use a parenthesis at –2 60. 3 ⋅ −5 3(−5)
(
26. −(3 − 5) − ⎡ 2 − 3 2 − 13 ⎤
⎣ ⎦ ) 37. −6 < −2
since it is not part of the graph. 3 ⋅ –5 −15
Take powers first. 3⋅5 15
38. 3.14 < π
–(3 – 5) – [2 – (9 – 13)] 15 = 15
Work inside brackets and parentheses. 50. (–∞, –2]
39. 3 4 = .75 This represents all real numbers less than or
– (–2) – [2 – (–4)] = 2 – [2 + 4] 61. 3 − 5 3−5
= 2 – 6 = –4 equal to –2. Draw a bracket at –2 and a heavy
40. 1 3 > .33 ray to the left. −2 3−5
2(−3) + ( −32) − 2 2 −2
(− 16 ) 41. a lies to the right of b or is equal to b.
27. 2 > −2
64 − 1
42. b + c = a 51. −9 − −12 = 9 − (12) = −3
Work above and below fraction bar. Take roots. 62. −5 + 1 −5 + 1
2(−3) + ( −32) − ( −24) 43. c < a < b
52. 8 − −4 = 8 − (4) = 4 −4 5 +1
8 −1 44. a lies to the right of 0 4 6
Do multiplications and divisions. 53. − −4 − −1 − 14 = −(4) − −15
3 1
−6 − 2 + 2 45. (–8, –1) 4<6
= − ( 4) − 15 = −19
8 −1 This represents all real numbers between –8 and
–1, not including –8 and –1. Draw parentheses at 63. When a < 7, a – 7 is negative.
Add and subtract. 54. − 6 − −12 − 4 = − (6) − −16 = −6 − (16) = −22 So a − 7 = −(a − 7) = 7 − a .
–8 and –1 and a heavy line segment between
− 12
2
− 32 + 12 − 14 −7 them. The parentheses at –8 and –1 show that
= 2 = = −1
7 7 7 neither of these points belongs to the graph. 55. 5 −5 64. When b ≥ c, b – c is positive.
5 __ 5 So b − c = b − c .
2
6 − 3 25
28. 5=5
6 2 + 13 Answers will vary for exercises 65–67. Sample answers
46. [–1, 10]
Take powers and roots. are given.
This represents all real numbers between –1 and 56. − −4 4
36 − 3(5) 36 − 15 21 10, including –1 and 10. Draw brackets at –1 and 65. No, it is not always true that a + b = a + b . For
= = =3 10 and a heavy line segment between them. −4 4
36 + 13 49 7 example, let a = 1 and b = –1. Then,
−4<4
a + b = 1 + (−1) = 0 = 0 , but
2040 189 4587
29. , , 27, , 6.735, 47 57. 10 − 3 3 − 10 a + b = 1 + (−1) = 1 + 1 = 2 .
523 37 691 47. (−2, 3] 7 −7
187 385 This represents all real numbers x such that 66. Yes, if a and b are any two real numbers, it is
30. , 2.9884, 85 , π , 10, 7 7
63 117
–2 < x ≤ 3. Draw a heavy line segment from –2 always true that a − b = b − a . In general,
to 3. Use a parenthesis at –2 since it is not part of 7=7
a – b = –(b – a). When we take the absolute
31. 12 is less than 18.5. the graph. Use a bracket at 3 since it is part of value of each side, we get
12 < 18.5 the graph.
a − b = −(b − a ) = b − a .
Copyright © 2024 Pearson Education, Inc.
Copyright © 2024 Pearson Education, Inc.
mynursytest.store mynursytest.store
Management Natural and Social Sciences 13th Edition Lial
INSTRUCTOR’S
SOLUTIONS MANUAL
SAL SCIANDRA
Niagara County Community College
M ATHEMATICS WITH A PPLICATIONS
I N THE M ANAGEMENT , N ATURAL , AND S OCIAL S CIENCES
THIRTEENTH EDITION
F INITE M ATHEMATICS
WITH A PPLICATIONS
I N THE M ANAGEMENT , N ATURAL , AND S OCIAL S CIENCES
THIRTEENTH EDITION
Margaret L. Lial
American River College
Thomas W. Hungerford
Saint Louis University
John P. Holcomb, Jr.
Cleveland State University
Bernadette Mullins
Birmingham-Southern College
mynursytest.store
,ACCESS Test Bank for Finite Mathematics with Applications In the ACCESS Test Bank for Finite Mathematics with Applications In the
Management Natural and Social Sciences 13th Edition Lial Management Natural and Social Sciences 13th Edition Lial
Contents
Chapter 1 Algebra and Equations.......................................................................................1
Chapter 2 Graphs, Lines, and Inequalities .......................................................................46
Chapter 3 Functions and Graphs ......................................................................................92
Chapter 4 Exponential and Logarithmic Functions ........................................................167
Chapter 5 The Mathematics of Personal Finance ..........................................................204
Chapter 6 Systems of Linear Equations and Matrices ...................................................242
Chapter 7 Linear Programming ......................................................................................323
Copyright © 2024, 2019, 2015 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. This publication is protected by copyright, and permission should be obtained from the
publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means,
Chapter 8 Sets and Probability .......................................................................................428
electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request forms, and
the appropriate contacts within the Pearson Education Global Rights and Permissions department, please visit
www.pearsoned.com/permissions/.
Chapter 9 Counting, Probability Distributions, and
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the Further Topics in Probability ...........................................................................................459
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are for
demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship, endorsement,
authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner Chapter 10 Introduction to Statistics ..............................................................................495
and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
Chapter 11 Differential Calculus....................................................................................526
Chapter 12 Applications of the Derivative .....................................................................604
Chapter 13 Integral Calculus ..........................................................................................680
Chapter 14 Multivariate Calculus...................................................................................750
ISBN-13: 978-0-13-789213-6
Copyright © 2024 Pearson Education, Inc.
ISBN-10: 0-13-789213-6
mynursytest.store mynursytest.store
,ACCESS Test Bank for Finite Mathematics with Applications In the ACCESS Test Bank for Finite Mathematics with Applications In the
Management Natural and Social Sciences 13th Edition Lial Management Natural and Social Sciences 13th Edition Lial
Chapter 1 Algebra and Equations
Section 1.1 The Real Numbers For Exercises 13–16, let p = –2, q = 3 and r = –5.
1. True. This statement is true, since every integer 13. −3 ( p + 5q ) = −3[ −2 + 5(3) ] = −3 [ −2 + 15]
can be written as the ratio of the integer and 1. = −3 (13) = −39
5
For example, 5 = .
1 14. 2 ( q − r ) = 2 ( 3 + 5 ) = 2 ( 8 ) = 16
2. False. For example, 5 is a real number, and
10
5= which is not an irrational number.
2 q+r 3 + (−5) −2
15. = = = −2
q + p 3 + (−2) 1
3. Answers vary with the calculator, but
2, 508, 429, 787 3q 3(3) 9 9
is the best. 16. = = =
798, 458, 000 3 p − 2r 3(−2) − 2(−5) −6 + 10 4
4. 0 + (−7) = (−7) + 0 17. Let r = 3.8.
This illustrates the commutative property of APR = 12r = 12(3.8) = 45.6%
addition.
18. Let r = 0.8.
5. 6(t + 4) = 6t + 6 ⋅ 4 APR = 12r = 12(0.8) = 9.6%
This illustrates the distributive property.
19. Let APR = 11.
6. 3 + (–3) = (–3) + 3 APR = 12r
This illustrates the commutative property of
addition. 11 = 12r
11
=r
7. (–5) + 0 = –5 12
This illustrates the identity property of addition. r ≈ .9167%
8. (−4)( −41 ) = 1 20. Let APR = 13.2.
This illustrates the multiplicative inverse APR = 12r
property. 13.2 = 12r
13.2
9. 8 + (12 + 6) = (8 + 12) + 6 =r
12
This illustrates the associative property of r = 1.1%
addition.
21. 3 − 4 ⋅ 5 + 5 = 3 − 20 + 5 = −17 + 5 = −12
10. 1(−20) = −20
This illustrates the identity property of
22. 8 − (−4) 2 − (−12)
multiplication.
Take powers first.
11. Answers vary. One possible answer: The sum of 8 – 16 – (–12)
a number and its additive inverse is the additive Then add and subtract in order from left to right.
identity. The product of a number and its 8 – 16 + 12 = –8 + 12 = 4
multiplicative inverse is the multiplicative
identity. 23. (4 − 5) ⋅ 6 + 6 = −1 ⋅ 6 + 6 = −6 + 6 = 0
12. Answers vary. One possible answer: When using
the commutative property, the order of the
addends or multipliers is changed, while the
grouping of the addends or multipliers is
changed when using the associative property.
Copyright © 2024 Pearson Education, Inc. 1
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, ACCESS Test Bank for Finite Mathematics with Applications In the ACCESS Test Bank for Finite Mathematics with Applications In the
Management Natural and Social Sciences 13th Edition Lial Management Natural and Social Sciences 13th Edition Lial
2 CHAPTER 1 ALGEBRA AND EQUATIONS SECTION 1. 1 THE REAL NUMBERS 3
2(3 − 7) + 4(8) 32. –2 is greater than –20. 58. 6 − (−4) −4 − 6
24. –2 > –20
4(−3) + (−3)(−2) 48. [–2, 2) 10 −10
Work above and below fraction bar. Do This represents all real numbers between –2 and
33. x is greater than or equal to 5.7. 10 10
multiplications and work inside parentheses. 2, including –2, not including 2.
x ≥ 5.7 10 = 10
2(−4) + 32 −8 + 32 24 Draw a bracket at –2, a parenthesis at 2, and a
= = = = −4 heavy line segment between them.
−12 + 6 −12 + 6 −6 34. y is less than or equal to –5.
y ≤ −5 59. −2 + 8 2−8
2
25. 8 − 4 − (−12) 6 −6
35. z is at most 7.5.
Take powers first.
z ≤ 7.5
49. (−2, ∞ ) 6 6
8 – 16 – (–12)
This represents all real numbers x such that 6=6
Then add and subtract in order from left to right.
36. w is negative. x > –2. Start at –2 and draw a heavy line
8 – 16 + 12 = –8 + 12 = 4
w<0 segment to the right. Use a parenthesis at –2 60. 3 ⋅ −5 3(−5)
(
26. −(3 − 5) − ⎡ 2 − 3 2 − 13 ⎤
⎣ ⎦ ) 37. −6 < −2
since it is not part of the graph. 3 ⋅ –5 −15
Take powers first. 3⋅5 15
38. 3.14 < π
–(3 – 5) – [2 – (9 – 13)] 15 = 15
Work inside brackets and parentheses. 50. (–∞, –2]
39. 3 4 = .75 This represents all real numbers less than or
– (–2) – [2 – (–4)] = 2 – [2 + 4] 61. 3 − 5 3−5
= 2 – 6 = –4 equal to –2. Draw a bracket at –2 and a heavy
40. 1 3 > .33 ray to the left. −2 3−5
2(−3) + ( −32) − 2 2 −2
(− 16 ) 41. a lies to the right of b or is equal to b.
27. 2 > −2
64 − 1
42. b + c = a 51. −9 − −12 = 9 − (12) = −3
Work above and below fraction bar. Take roots. 62. −5 + 1 −5 + 1
2(−3) + ( −32) − ( −24) 43. c < a < b
52. 8 − −4 = 8 − (4) = 4 −4 5 +1
8 −1 44. a lies to the right of 0 4 6
Do multiplications and divisions. 53. − −4 − −1 − 14 = −(4) − −15
3 1
−6 − 2 + 2 45. (–8, –1) 4<6
= − ( 4) − 15 = −19
8 −1 This represents all real numbers between –8 and
–1, not including –8 and –1. Draw parentheses at 63. When a < 7, a – 7 is negative.
Add and subtract. 54. − 6 − −12 − 4 = − (6) − −16 = −6 − (16) = −22 So a − 7 = −(a − 7) = 7 − a .
–8 and –1 and a heavy line segment between
− 12
2
− 32 + 12 − 14 −7 them. The parentheses at –8 and –1 show that
= 2 = = −1
7 7 7 neither of these points belongs to the graph. 55. 5 −5 64. When b ≥ c, b – c is positive.
5 __ 5 So b − c = b − c .
2
6 − 3 25
28. 5=5
6 2 + 13 Answers will vary for exercises 65–67. Sample answers
46. [–1, 10]
Take powers and roots. are given.
This represents all real numbers between –1 and 56. − −4 4
36 − 3(5) 36 − 15 21 10, including –1 and 10. Draw brackets at –1 and 65. No, it is not always true that a + b = a + b . For
= = =3 10 and a heavy line segment between them. −4 4
36 + 13 49 7 example, let a = 1 and b = –1. Then,
−4<4
a + b = 1 + (−1) = 0 = 0 , but
2040 189 4587
29. , , 27, , 6.735, 47 57. 10 − 3 3 − 10 a + b = 1 + (−1) = 1 + 1 = 2 .
523 37 691 47. (−2, 3] 7 −7
187 385 This represents all real numbers x such that 66. Yes, if a and b are any two real numbers, it is
30. , 2.9884, 85 , π , 10, 7 7
63 117
–2 < x ≤ 3. Draw a heavy line segment from –2 always true that a − b = b − a . In general,
to 3. Use a parenthesis at –2 since it is not part of 7=7
a – b = –(b – a). When we take the absolute
31. 12 is less than 18.5. the graph. Use a bracket at 3 since it is part of value of each side, we get
12 < 18.5 the graph.
a − b = −(b − a ) = b − a .
Copyright © 2024 Pearson Education, Inc.
Copyright © 2024 Pearson Education, Inc.
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