Mathema�cs with
Applica�ons In the
Management, Natural,
and Social Sciences,
13e Margaret, Thomas,
John, Bernadete
(Solu�ons Manual All
Chapters, 100%
Original Verified, A+
Grade)
, 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
Chapter 8 Sets and Probability .......................................................................................428
Chapter 9 Counting, Probability Distributions, and
Further Topics in Probability ...........................................................................................459
Chapter 10 Introduction to Statistics ..............................................................................495
Chapter 11 Differential Calculus ....................................................................................526
Chapter 12 Applications of the Derivative .....................................................................604
Chapter 13 Integral Calculus ..........................................................................................680
Chapter 14 Multivariate Calculus...................................................................................750
Copyright © 2024 Pearson Education, Inc.
, 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
, 2 CHAPTER 1 ALGEBRA AND EQUATIONS
2(3 − 7) + 4(8) 32. –2 is greater than –20.
24. –2 > –20
4(−3) + (−3)(−2)
Work above and below fraction bar. Do 33. x is greater than or equal to 5.7.
multiplications and work inside parentheses. x ≥ 5.7
2(−4) + 32 −8 + 32 24
= = = = −4
−12 + 6 −12 + 6 −6 34. y is less than or equal to –5.
y ≤ −5
25. 8 − 4 2 − (−12)
35. z is at most 7.5.
Take powers first.
z ≤ 7.5
8 – 16 – (–12)
Then add and subtract in order from left to right.
36. w is negative.
8 – 16 + 12 = –8 + 12 = 4
w<0
⎣ (
26. −(3 − 5) − ⎡ 2 − 3 2 − 13 ⎤
⎦ ) 37. −6 < −2
Take powers first.
38. 3.14 < π
–(3 – 5) – [2 – (9 – 13)]
Work inside brackets and parentheses.
39. 3 4 = .75
– (–2) – [2 – (–4)] = 2 – [2 + 4]
= 2 – 6 = –4
40. 1 3 > .33
3 2
2(−3) + −
27.
( −2) ( − 16 ) 41. a lies to the right of b or is equal to b.
64 − 1
42. b + c = a
Work above and below fraction bar. Take roots.
2(−3) + ( −32) − ( −24) 43. c < a < b
8 −1 44. a lies to the right of 0
Do multiplications and divisions.
−6 − 32 + 12 45. (–8, –1)
8 −1 This represents all real numbers between –8 and
Add and subtract. –1, not including –8 and –1. Draw parentheses at
–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.
6 2 − 3 25
28.
6 2 + 13 46. [–1, 10]
Take powers and roots. This represents all real numbers between –1 and
36 − 3(5) 36 − 15 21 10, including –1 and 10. Draw brackets at –1 and
= = =3 10 and a heavy line segment between them.
36 + 13 49 7
2040 189 4587
29. , , 27, , 6.735, 47
523 37 691 47. (−2, 3]
187 385 This represents all real numbers x such that
30. , 2.9884, 85 , π , 10, –2 < x ≤ 3. Draw a heavy line segment from –2
63 117
to 3. Use a parenthesis at –2 since it is not part of
31. 12 is less than 18.5. the graph. Use a bracket at 3 since it is part of
12 < 18.5 the graph.
Copyright © 2024 Pearson Education, Inc.
Applica�ons In the
Management, Natural,
and Social Sciences,
13e Margaret, Thomas,
John, Bernadete
(Solu�ons Manual All
Chapters, 100%
Original Verified, A+
Grade)
, 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
Chapter 8 Sets and Probability .......................................................................................428
Chapter 9 Counting, Probability Distributions, and
Further Topics in Probability ...........................................................................................459
Chapter 10 Introduction to Statistics ..............................................................................495
Chapter 11 Differential Calculus ....................................................................................526
Chapter 12 Applications of the Derivative .....................................................................604
Chapter 13 Integral Calculus ..........................................................................................680
Chapter 14 Multivariate Calculus...................................................................................750
Copyright © 2024 Pearson Education, Inc.
, 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
, 2 CHAPTER 1 ALGEBRA AND EQUATIONS
2(3 − 7) + 4(8) 32. –2 is greater than –20.
24. –2 > –20
4(−3) + (−3)(−2)
Work above and below fraction bar. Do 33. x is greater than or equal to 5.7.
multiplications and work inside parentheses. x ≥ 5.7
2(−4) + 32 −8 + 32 24
= = = = −4
−12 + 6 −12 + 6 −6 34. y is less than or equal to –5.
y ≤ −5
25. 8 − 4 2 − (−12)
35. z is at most 7.5.
Take powers first.
z ≤ 7.5
8 – 16 – (–12)
Then add and subtract in order from left to right.
36. w is negative.
8 – 16 + 12 = –8 + 12 = 4
w<0
⎣ (
26. −(3 − 5) − ⎡ 2 − 3 2 − 13 ⎤
⎦ ) 37. −6 < −2
Take powers first.
38. 3.14 < π
–(3 – 5) – [2 – (9 – 13)]
Work inside brackets and parentheses.
39. 3 4 = .75
– (–2) – [2 – (–4)] = 2 – [2 + 4]
= 2 – 6 = –4
40. 1 3 > .33
3 2
2(−3) + −
27.
( −2) ( − 16 ) 41. a lies to the right of b or is equal to b.
64 − 1
42. b + c = a
Work above and below fraction bar. Take roots.
2(−3) + ( −32) − ( −24) 43. c < a < b
8 −1 44. a lies to the right of 0
Do multiplications and divisions.
−6 − 32 + 12 45. (–8, –1)
8 −1 This represents all real numbers between –8 and
Add and subtract. –1, not including –8 and –1. Draw parentheses at
–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.
6 2 − 3 25
28.
6 2 + 13 46. [–1, 10]
Take powers and roots. This represents all real numbers between –1 and
36 − 3(5) 36 − 15 21 10, including –1 and 10. Draw brackets at –1 and
= = =3 10 and a heavy line segment between them.
36 + 13 49 7
2040 189 4587
29. , , 27, , 6.735, 47
523 37 691 47. (−2, 3]
187 385 This represents all real numbers x such that
30. , 2.9884, 85 , π , 10, –2 < x ≤ 3. Draw a heavy line segment from –2
63 117
to 3. Use a parenthesis at –2 since it is not part of
31. 12 is less than 18.5. the graph. Use a bracket at 3 since it is part of
12 < 18.5 the graph.
Copyright © 2024 Pearson Education, Inc.
