Finite mathematics for managerial life and social sciences 11th

A Sampling of New Applications
Drawn from diverse fields of interest and situations that occur in the real world

Business
n

n
n
n

Online Video Advertising Use a trend line
to project spending on Web video
advertising. p. 62
Switching Broadband Service p. 438
Satellite TV Subscribers p. 62
Market Share of Motorcycles p. 120

e
economics
n
n
n
n

Recovery from the Great Recession p. 413
Existing Home Sales p. 498
Impact of Gas Prices on Consumers p. 447
Pre-Retirees’ Spending p. 510

entertainment

college life
n
n
n

Time Spent per Week on the Internet p. 471
Time Use of College Students p. 470
Brand Switching Among Female
College Students p. 359

n

n
n

e
environment

criminal justice
n
n

n
n

Corporate Fraud Use a linear equation
to estimate the number of pending corporate
fraud cases. p. 23
Detecting Shoplifters p. 447
Identity Fraud p. 496

n

n
n
n

n
n
n

U.S. Population by Age p. 485
Percent of Population Enrolled in School p. 61
Households with Someone Under 18 p. 61

California Emissions Caps p. 37
Climate Change p. 413

fi
finance
n

demographics

Concert Attendance Use a system of linear
inequalities to determine the types of ticket
holders at a concert. p. 179
Makeup of U.S. Moviegoer Audience p. 412
Academy Membership p. 511

Model Investment Portfolios p. 120
Mortgage Rates p. 120
Asset Allocation p. 238
Ability-to-Repay Rule Apply the rule to
determine if a potential homebuyer will
qualify for a mortgage. p. 323

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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.


personal finance

government
n
n
n

Gun Owners in the Senate p. 448
Federal Budget Allocation p. 359
Federal Libraries p. 497

n
n

n

Comparative Shopping p. 134
Credit Card Ownership Calculate
probabilities using survey data about

credit card ownership. p. 454
Emergency Fund Savings p. 465

health
n
n
n

Smokers in the United States p. 19
Stress Level p. 402
Diet Planning Use a system of linear
equations and linear inequalities to help
plan a meal that satisfies certain
nutritional requirements. p. 179

social media
n
n

n
n

Facebook Users p. 61
Cyber Privacy Use operations on sets to rate
companies on how they keep personal
information secure. p. 347
Social Media Accounts p. 402
Smartphone Ownership p. 466

in the news

n

n
n

Erosion of the Middle Class Use a linear
function to model the percentage of U.S.
middle-income adults. p. 38
Terrorism Poll p. 119
Who Pays Taxes? p. 471

transportation
n
n
n

on the jo
joB
n
n
n
n

Starting a New Job p. 402
On-the-Job Distractions p. 358
Work Habits p. 454
Getting Ahead at Work p. 511

Hybrid Vehicle Mileage p. 496
Flight Cancellations p. 497

Traffic Survey p. 498

travel
n
n
n

N.Y.C. Tourists p. 439
Best U.S. City for Italian Restaurants p. 351
Stay When Visiting National Parks p. 413

See the complete Index of Applications
at the back of the text to find out more ...
Businessman with Laptop: © Odua Images / Shutterstock.com; Accounting with Calculator: © Zadorozhnyi Viktor / Shutterstock.com; Gas Prices: © justasc / Shutterstock.com; Climate Change: © kwest / Shutterstock.com; College Graduates: © gui jun peng / Shutterstock.com; Businessman Stealing Money: © Maryna Pleshkun
/ Shutterstock.com; Crowd of People: © Dariush M / Shutterstock.com; Government Columns: © Ambient Ideas / Shutterstock.com; Social Media Connections: © Mathias Rosenthal / Shutterstock.com; Concert Attendance: © swinner / Shutterstock.com; U.S. Tax Form: © Robyn Mackenzie / Shutterstock.com; New York Tourism:
© upthebanner / Shutterstock.com; New Job Workplace: © Pressmaster / Shutterstock.com; Flights Cancelled: © niroworld / Shutterstock.com; Credit Card: © luchunyu / Shutterstock.com; Medical Tests: © Hero Images / Getty Images; Background Graphic: © imagotres / iStock Vectors / Getty Images

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Finite Mathematics

FOR THE MANAGERIAL, LIFE,
AND SOCIAL SCIENCES

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eDitiOn

11

Finite MatheMatics

FOR the ManaGeRiaL, LiFe,
anD sOciaL sciences

sOO t. tan
stOnehiLL cOLLeGe

Australia  •  Brazil  •  Mexico  •  Singapore  •  United Kingdom  •  United States

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Finite Mathematics: For the Managerial, Life, and
Social Sciences, Eleventh Edition
Soo T. Tan
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To Pat, Bill, and Michael 

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cOntents
Preface

Chapter 1

xi

straight Lines and Linear Functions
1.1
1.2
1.3
1.4
1.5

1

the cartesian coordinate system 2
Straight Lines 10
Using Technology: Graphing a Straight Line 25
Linear Functions and Mathematical Models 29
Using Technology: Evaluating a Function 40
Intersection of Straight Lines 43
Using Technology: Finding the Point(s) of Intersection of Two Graphs 53
The Method of Least Squares 55
PorTFoLIo: MeLISSa rIch 56

Using Technology: Finding an Equation of a Least-Squares Line 64
Chapter 1 Summary of Principal Formulas and Terms 68
Chapter 1 Concept Review Questions 68
Chapter 1 Review Exercises 69
Chapter 1 Before Moving On 71

Chapter 2

systems of Linear equations and Matrices 73
2.1
2.2
2.3

2.4
2.5
2.6
2.7

Chapter 3

Systems of Linear equations: an Introduction 74
Systems of Linear equations: Unique Solutions 83
Using Technology: Systems of Linear Equations: Unique Solutions 97
Systems of Linear equations: Underdetermined and overdetermined Systems 99
Using Technology: Systems of Linear Equations: Underdetermined and
Overdetermined Systems 109
Matrices 111
Using Technology: Matrix Operations 122
Multiplication of Matrices 125
Using Technology: Matrix Multiplication 138
The Inverse of a Square Matrix 140
Using Technology: Finding the Inverse of a Square Matrix 153
Leontief Input–output Model 155
Using Technology: The Leontief Input–Output Model 162
Chapter 2 Summary of Principal Formulas and Terms 165
Chapter 2 Concept Review Questions 165
Chapter 2 Review Exercises 166
Chapter 2 Before Moving On 168

Linear Programming: a Geometric approach
3.1
3.2
3.3

169

Graphing Systems of Linear Inequalities in Two Variables 170
Linear Programming Problems 181
Graphical Solution of Linear Programming Problems 189

vii
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.


viii

cOntents

3.4

Chapter 4

Sensitivity analysis 202
Chapter 3 Summary of Principal Terms 215
Chapter 3 Concept Review Questions 215
Chapter 3 Review Exercises 216
Chapter 3 Before Moving On 217

Linear Programming: an algebraic approach
4.1
4.2

219

The Simplex Method: Standard Maximization Problems 220
Using Technology: The Simplex Method: Solving Maximization Problems 241
The Simplex Method: Standard Minimization Problems 246
PorTFoLIo: chad SMITh 248

4.3

Chapter 5

Mathematics of Finance 281
5.1

5.2
5.3
5.4

Chapter 6

Using Technology: The Simplex Method: Solving Minimization Problems 260
the simplex Method: nonstandard Problems 264
Chapter 4 Summary of Principal Terms 276
Chapter 4 Concept Review Questions 276
Chapter 4 Review Exercises 277
Chapter 4 Before Moving On 278

compound Interest 282
Using Technology: Finding the Accumulated Amount of an Investment, the
Effective Rate of Interest, and the Present Value of an Investment 298
annuities 301
Using Technology: Finding the Amount of an Annuity 310
amortization and Sinking Funds 312
Using Technology: Amortizing a Loan 324
arithmetic and Geometric Progressions 327
Chapter 5 Summary of Principal Formulas and Terms 336
Chapter 5 Concept Review Questions 336

Chapter 5 Review Exercises 337
Chapter 5 Before Moving On 339

sets and counting 341
6.1
6.2
6.3
6.4

Sets and Set operations 342
The Number of elements in a Finite Set
The Multiplication Principle 362
Permutations and combinations 368

352

PorTFoLIo: Lara SoLaNkI 372

Using Technology: Evaluating n!, P(n, r), and C(n, r) 382
Chapter 6 Summary of Principal Formulas and Terms 383
Chapter 6 Concept Review Questions 383
Chapter 6 Review Exercises 384
Chapter 6 Before Moving On 386

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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.


cOntents

Chapter 7

Probability
7.1
7.2
7.3
7.4
7.5
7.6

Chapter 8

387

experiments, Sample Spaces, and events 388
definition of Probability 396
rules of Probability 407
Use of counting Techniques in Probability 417
conditional Probability and Independent events 424
Bayes’ Theorem 441
Chapter 7 Summary of Principal Formulas and Terms 451
Chapter 7 Concept Review Questions 452
Chapter 7 Review Exercises 452
Chapter 7 Before Moving On 456

Probability Distributions and statistics
8.1
8.2

457

distributions of random Variables 458
Using Technology: Graphing a Histogram 467
expected Value 472
PorTFoLIo: roBerT h. MaSoN 480

8.3
8.4
8.5
8.6

Chapter 9

Variance and Standard deviation 487
Using Technology: Finding the Mean and Standard Deviation 499
The Binomial distribution 501
The Normal distribution 513
applications of the Normal distribution 522
Chapter 8 Summary of Principal Formulas and Terms 530
Chapter 8 Concept Review Questions 531
Chapter 8 Review Exercises 531
Chapter 8 Before Moving On 533

Markov chains and the theory of Games
9.1
9.2
9.3
9.4

535

Markov chains 536
Using Technology: Finding Distribution Vectors 545
regular Markov chains 546
Using Technology: Finding the Long-Term Distribution Vector 555
absorbing Markov chains 557
Game Theory and Strictly determined Games 564
PorTFoLIo: chrISTIaN derrIck 566

9.5

Games with Mixed Strategies 574
Chapter 9 Summary of Principal Formulas and Terms 585
Chapter 9 Concept Review Questions 586
Chapter 9 Review Exercises 587
Chapter 9 Before Moving On 589

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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

ix


x

coNTeNTS

Appendix A

Introduction to Logic 591

A.1
A.2
A.3
A.4
A.5
A.6

Propositions and Connectives 592
Truth Tables 596
The Conditional and Biconditional Connectives 598
Laws of Logic 603
Arguments 607
Applications of Logic to Switching Networks 612

Appendix B

The System of Real Numbers

Appendix C

Review of Logarithms

Appendix d

Tables

617

621

627

Table 1: Binomial Probabilities 628
Table 2: The Standard Normal Distribution

Answers
Index

631

633

667

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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.


PReFace
Math plays a vital role in our increasingly complex daily life. Finite Mathematics
for the Managerial, Life, and Social Sciences attempts to illustrate this point with its
applied approach to mathematics. Students have a much greater appreciation of the
material if the applications are drawn from their fields of interest and from situations
that occur in the real world. This is one reason you will see so many exercises in my
texts that are modeled on data gathered from newspapers, magazines, journals, and
other media. In addition, many students come into this course with some degree of
apprehension. For this reason, I have adopted an intuitive approach in which I try
to introduce each abstract mathematical concept through an example drawn from a
common life experience. Once the idea has been conveyed, I then proceed to make it
precise, thereby ensuring that no mathematical rigor is lost in this intuitive treatment

of the subject.
The only prerequisite for understanding this text is one to two years, or the equivalent, of high school algebra. This text offers more than enough material for a onesemester or two-quarter course. The following chapter dependency chart is provided
to help the instructor design a course that is most suitable for the intended audience.

1

6

straight Lines
and Linear
Functions

2

systems
of Linear
equations
and Matrices

3

Linear
Programming:
a Geometric
approach

sets and
counting

9

Markov chains
and the theory
of Games

5

Mathematics
of Finance

7

Probability

8

Probability
Distributions
and statistics

4

Linear
Programming:
an algebraic
approach

Unless otherwise noted, all content on this page is © Cengage Learning.

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

xi

xi


xii

PReFace

the approach
Presentation
Consistent with my intuitive approach, I state the results informally. However, I have
taken special care to ensure that mathematical precision and accuracy are not compromised.

Motivation
Illustrating the practical value of mathematics in applied areas is an objective of my
approach. Concepts are introduced with concrete, real-life examples wherever appropriate. These examples and other applications have been chosen from current topics
and issues in the media and serve to answer a question often posed by students: “What
will I ever use this for?”

Problem-solving emphasis
Special emphasis is placed on helping students formulate, solve, and interpret the
results of applied problems. Because students often have difficulty setting up and solving word problems, extra care has been taken to help them master these skills:
■
■
■

Very early on in the text, students are given practice in solving word problems.

Guidelines are given to help students formulate and solve word problems.
One entire section is devoted to modeling and setting up linear programming
problems.

Modeling
One important skill that every student should acquire is the ability to translate a
real-life problem into a mathematical model. In Section 1.3, the modeling process is
discussed, and students are asked to use models (functions) constructed from real-life
data to answer questions. Additionally, students get hands-on experience constructing
these models in the Using Technology sections.

new to this edition
The focus of this revision has been the continued emphasis on illustrating the mathematical concepts in Finite Mathematics by using more real-life applications that are
relevant to the everyday life of students and to their fields of study in the managerial,
life, and social sciences. A sampling of these new applications is provided on the
inside front cover pages.
Many of the exercise sets have been revamped. In particular, the exercise sets
were restructured to follow more closely the order of the presentation of the material
in each section and to progress more evenly from easier to more difficult problems in
both the rote and applied sections of each exercise set. Additional concept questions,
rote exercises, and true-or-false questions were also included.

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.


preface 

xiii

More Specific Content Changes
Chapter 1  In Section 1.2, parts (b) and (c) of Example 12 illustrate how to determine whether a point lies on a line. A new application, Smokers in the United States,
has been added to the self-check exercises. In Section 1.3, new data have been used
for the U.S. Health-Care Expenditures application, and students are shown how the
new model for this application is constructed in Section 1.5 using the least-squares
method. Also, in Using Technology Section 1.3, Applied Examples 2 and 4, Drinking
and Driving Among High School Students have been added for the graphing calculator
and Excel applications.
Chapters 2–4  A wealth of new application exercises has been added, and many
examples and exercises have been updated. Also, in Section 3.1, newly added Example
6 illustrates how to determine whether a point lies in a feasible set of inequalities. This
is followed by a new application, Applied Example 7, A Production Problem, in which
students are shown how they can use a solution set for a given system of inequalities (restrictions) to determine whether certain production goals can be met. Also, in
Section 3.1, Exercise 44, we see how the solution of a system of linear equations is
obtained by looking at a system of inequalities.
Chapter 5  Interest rate problems throughout the entire chapter were revised to
reflect the current interest rate environment. Also, in Section 5.3, two new exercises
were added illustrating the new Ability-to-Repay Rules for Mortgages adopted by the
Consumer Financial Protection Bureau in response to the recent financial crisis.
Chapters 6–8  In the probability and statistics chapters of the text, the emphasis is
again placed on providing new real-life application exercises. These chapters deal with
the calculations of probabilities and data analysis and the emphasis here was placed on
providing data from marketing, economic, consumer, and scientific surveys that was
relevant, current, and of interest to students to motivate the mathematical concepts
presented. Some of these surveys involve the following questions:
What is the greatest challenge upon starting a new job?
How many years will it take you to fully recover from the Great Recession?
What is the most common cause of on-the-job distraction?

How do workers get ahead on the job?
How many social media accounts do you have?
Have gas prices caused you any financial hardship?
Also, several new examples were added in these chapters: In Section 6.1, Applied
Example 13, Cyber Privacy, illustrates set operations. In Section 6.2, Example 5 illustrates how the solution of a system of linear equations can sometimes be used to help
draw a Venn diagram. In Section 7.5, Example 8 illustrates the difference between
mutually exclusive and independent events. Also, Applied Example 12, Predicting
Travel Weather, illustrates the calculation of the probability of independent events.
In Section 8.2, Applied Example 8, Commuting Times, illustrates the calculation of
expected value for grouped data; and in Section 8.3, Applied Example 4, Married
Men, illustrates the calculation of standard deviation for grouped data. Using Technology Section 8.1 was expanded to include an example (Applied Example 3, Time
Use of College Students) and exercises illustrating how Excel can be used to create
pie charts.

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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.


xiv

PReFace

Features

6.1 SetS and Set OperatiOnS

345

addition and multiplication enable us to combine numbers to obtain other numbers. In
6.1 SetS and Set OperatiOnS

Real-World connections
what follows, all sets are assumed to be subsets of a given universal set U.

Motivating applications
Many new applied examples
and exercises have been
added in the Eleventh Edition.
Among the topics of the new
applications are Facebook
users, satellite TV subscribers,
U
criminal justice, cyber privacy,
brand switching
among
A
B
U
college students, social media
accounts, detecting shoplifters,
and smartphone ownership.
FigUre 2

Set union A < B

Set
$ Union
APPLIED EXAMPLE 13 Cyber privacy In a poll surveying 1500 registered

Let Avoters
and B in

be California,
sets. The union
A and B, written
< B,to
is rank
the setthe
of following
all elethe of
respondents
were Aasked
compaments
that
belong
to
either
A
or
B
or
both.
nies on a scale of 0 to 10 in terms of how much they could trust these companies to

keep their personal information
with
that they don’t trust the
0 x [ A or
A < B 5 5 x secure,
x [zero
B ormeaning
both 6

company.

The shaded portion of the Venn diagram (Figure 2) depicts the set A < B.
Company
Apple
Google
LinkedIn
YouTube
Facebook
EXAMPLE 7 If A 5 5 a, b, c 6 and B 5 5 a, c, d 6 , then A < B 5 5 a, b, c, d 6 .
Rating
4.6
3.8
3.0
2.8
2.7

B
portfolios A
These interviews share
the varied experiences
of professionals
who use
FigUre 3
Set intersectionin
A >the
B workplace.
mathematics
Among those included are a
city manager at a photography

company and a technical
U
director at a wireless company
who uses his
A knowledgeB of
game theory to help mobile
operators develop and deliver
new technologies.
FigUre 4

A and B are disjoint

Twitter
2.4

Set intersection

and Bthe
be sets.
set of elements
common
to the
sets Athan
and 2.5,
B, written
LetLet
A Adenote
set ofThe
companies
that have

a rating
higher
let B denote the
B, is called the
of Abetween
and B. 2.5 and 4, and let C denote the set of
setAof>companies
thatintersection
have a rating
companies that have a rating
Find
A > Blower
5 5 x 0 than
x [the
B 6following sets:
x [ A3.and

a. A, B, and C
U

347

b. A x B

c. B y C

d. Ac y B

e. A y Bc

Source:
Los portion
Angeles of
Times.
The
shaded
the Venn diagram (Figure 3) depicts the set A > B.

EXAMPLE
Solution 8 Let A 5 5 a, b, c 6 , and let B 5 5 a, c, d 6 . Then A > B 5 5 a, c 6 . (Compare this result with Example 7.)

a. PAortfo
5 5 Apple,
ChristianLinkedIn,
derrick YouTube, Facebook 6
ortfoL
Lio Google,

5 1, 3, 5, 7,
EXAMPLE
9 Let A 5
9 6 , and letFacebook
B 5 5 2, 4,6 6, 8, 10 6 . Then A > B 5 [.
B 5 5 Google,
LinkedIn,
YouTube,
tit
itLLe

C 5 5 YouTube,

Facebook, Twitter 6
institution

The
9 have empty,
or null,YouTube,
intersection.
In general,
6 5theA sets A and
b. Atwo
xsets
B 5of 5Example
LinkedIn,
Facebook
Apple, Google,
B are said to be5disjoint if they have no6 elements in common—that is, if A > B 5 [
c. B y C 5 YouTube, Facebook
(see Figure
4).
c

d. A y B 5 5 Twitter 6 y 5 Google, LinkedIn, YouTube, Facebook 6 5 [
5 Apple,
Google,
LinkedIn,
Facebook
e. A y Bc105 Let
EXAMPLE
U be the
set of all

students YouTube,
in the classroom.
If M 65y 5 Apple, Twitter 6 5
5 x [5 Apple
U 0 x is6 male 6 and F 5 5 x [ U 0 x is female 6 , then F > M 5 [, so F and M are

disjoint.

EXAMPLE 14 Let U 5 5 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 6 , A 5 5 1, 2, 4, 8, 9 6 , and
Complement
5 3, 4, 5, 6,of8a6Set
B5
. Verify by direct computation that 1A < B2c 5 Ac > B c.

If U is a universal set and A is a subset of U, then the set of all elements in U
c
that are not
5 1, 2,the3,complement
6, A
Solution
A in
4, 5, 6, 8, 9of
soand
1A is
B2c 5 5A7,. 10 6 . Moreover,

Ac 5 5 3, 5, 6, 7, 10 6 and A
Bcc 5

5 55x1,0 x2,[7,U 9,
10x6o
, soA 6Ac > B c 5 5 7, 10 6 . The required
and
result follows.

U

A

The shaded portion of the Venn diagram (Figure 5) shows the set Ac.

EXAMPLE
11 Let U 5 5 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 6 , and let A 5 5 2, 4, 6, 8, 10 6 .
$ APPLIED
EXAMPLE
15 automobile Options Let U denote the set of all cars
explorations
and
technology
Then Ac 5 5 1, 3, 5, 7, 9 6 .

in a dealer’s lot, and let

c

A
explore and discuss
These optional questions
canFigUre

be discussed
in class
5
Set complementation
or assigned
as homework.
They generally require more
thought and effort than the
usual exercises. They may
also be used to add a writing
component to the class or as
team projects.

A 5 5 x [ U 0 x is equipped with satellite radio 6
Explore and Discuss
B 5 5 x [ U 0 x is equipped with a moonroof 6
C 5 5 x [ U 0 x is equipped with keyless entry 6
Suppose A > B 2 [, A > C 2 [, and B > C 2 [. Can you conclude that

Let A, B, and C be nonempty subsets of a set U.
1.

B > C 2 [? Explain
yourofanswer
Find Aan> expression
in terms
A, B,with
andanCexample.
for each of the following sets:
2. Suppose A > B > C 2 [. Can you conclude that A > B 2 [, A > C 2 [, and

a. The
withyour
at answer.
least one of the given options
B >set
C 2of[?cars
Explain
b. The set of cars with exactly one of the given options

Unless otherwise noted, all content on this page is © Cengage Learning.

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.


..,
xv

PReFace

exploring with technology
Exploring with TECHNOLOGY
These optional discussions
u
To obtain a visual confirmation of the fact that the expression A1 1 1u B approaches
appear throughout the main
the number e 5 2.71828 . . . as u gets larger and larger, plot the graph of
body of the text and serve
x

f 1 x 2 5 A1 1 1x B in a suitable viewing window, and observe that f 1 x 2 approaches
to enhance the student’s
2.71828 . . . as x gets larger and larger. Use zoom and trace to find the value of
understanding of the concepts
470 8CHAPTER
8 Probability
Distributions
anD statistics
CHAPTER
Probability
Distributions
anD statistics
f 1 x 2 for
values of x.
and
theory
presented.
Often
470
CHAPTER 8 Probability Distributions
anDlarge
statistics
470solution
CHAPTER
8 Probability
the
of an
example inDistributions anD statistics
Excel
also be

create
pie as
charts,
as illustrated
in the following
example.
can
alsocan
be used
to used
createtopie
charts,
illustrated
in the following
example.
the text is augmented with Excel
a
Using
this be
result,
can see
as as
m illustrated
gets largerinand
larger, A example.
approaches
Excel
can also
used we
to create

pie that
charts,
the following
canPealso
used
to create
as illustrated
in the following
example.
graphical or numerical solution. PExcel
rt
1 e 2 rt 5
. Inbethis
situation,
wepie
saycharts,
that interest
is compounded
continuously.
Let’s
summarize
this
important
result.
APPLIED
EXAMPLE
3
time
use
of

college
students
Use
the
data
given
in
APPLIED EXAMPLE 3 time use of college students Use the data given in
Using technology
APPLIED
EXAMPLE
3
time
use
of
college
students
Use
the
data
given
in
Table
1 to EXAMPLE
construct
a3pietime
chart.
Table 1 APPLIED
to construct
a pie chart.

use of college students Use the data given in
Written in the traditional
Table 1 to construct a pie chart.
Continuous
Compound
Interest
Formula
Table 1 to construct a pie chart.
example-exercise format, these
optional sections show how to
A 5 Pert
(5)
TAblE T1TAblE T1
TAblE T1
use the graphing calculator and
Time
Used
on an Weekday
Average Weekday
for Full-Time
University
on an
for Full-Time
University
TAblE
T1Average
where Time Used
andStudents
College
Time

Used onStudents
an Average Weekday for Full-Time University
and College
Microsoft Excel 2010 as a tool
Time
Used on
an Average Weekday for Full-Time University
and
College
Students
P 5 Principal
Time
Use Students
(in hours)
to solve problems. (Instructions
Time Useand
Time (inTime
hours)
College
Time
Use
Time
(in
hours)
for Microsoft Excel 2007
r 5 Nominal Time
interest
Userate compounded continuously
8.5hours)
Sleeping Sleeping

8.5Time (in
are given on the companion
Sleeping
8.5
t 5 Time
in years
Leisure
3.7
Leisure
and
sportsand sports
3.7
Sleeping
8.5
website.) Illustrations showing
Leisure
and
sports
3.7
Working
andactivities
related
activities
2.9
Working Leisure
and related
2.9
A 5 Accumulated
amount
at

the
end
of
t
years
and
3.7
Working
andsports
related activities
2.9
graphing calculator screens
Educational
activities
3.3
Educational
activities
3.3
Working
andactivities
related activities
2.9
Educational
3.3
Eating
and drinking
1.0
and spreadsheets are used
Eating and
drinking

1.0
Educational
activities
3.3
Eating
and drinking
1.0
Grooming
0.7
Grooming
0.7
extensively. In keeping with
Eating
and drinking
1.0
Grooming
0.7
Traveling
1.5
TravelingGrooming
1.5
the theme of motivation
0.7
Traveling
1.5
Other
2.4
Other Traveling
2.4
through real-life examples,

1.5
Other
2.4
Other
2.4
many sourced applications are
Source:
of Labor Statistics.
Source: Bureau
of Bureau
Labor Statistics.
Source:
Bureau
of
Labor
Statistics.
included.
Source: Bureau of Labor Statistics.

64657_05_CH05_p281-340.indd 287

9/24/13 1:31 PM

A How-To Technology Index
Solution
Solution
Solution
is included at the back of the
Solution
Webybegin

by entering
the information
fromT1
Table
T1 in Columns
and
entering
the information
from Table
in Columns
A and BAon
a B on a
book for easy reference to We begin
We
begin
by
entering
the
information
from Table T1 in Columns A and B on a
spreadsheet.
Then
follow
these
steps:
spreadsheet.
Then
follow
these
steps:

We begin by entering the information from Table T1 in Columns A and B on a
Using Technology examples.
spreadsheet. Then follow these steps:
step 1 highlight
First,Then
highlight
data steps:
in
cells and
A2:A9
andas
B2:B9
asin
shown
inT4.
Figure T4.
step 1 spreadsheet.
First,
thefollow
datathe
inthese
cells
A2:A9
B2:B9
shown
Figure
step 1 First, highlight the data in cells A2:A9 and B2:B9 as shown in Figure T4.
step 1 First, highlight the data in cells A2:A9 and B2:B9 as shown in Figure T4.

8.1 Distributions of ranDom Variables

A
B
B
A
B
TimeAT5
Usewill Time
Time (in
1
Time
(in hours)
1 pie chart
B hours)
The
shown
inUse
Figure
appear.
Time Use
Time (in hours)
1
8.5
Sleeping
2
8.5
Sleeping
2
Time Use
Time (in hours)

1
8.5
Sleeping
23
3.7
Leisure
and
sports
3.7
Leisure
and
sports
3
8.5
Sleeping
2
3.7
Leisure
and
sports
3
dŝŵĞƵƐĞŽŶĂŶĂǀĞƌĂŐĞǁĞĞŬĚĂLJĨŽƌ
2.9
Working
and
related acƟviƟes
4
2.9
and
related

acƟviƟes
4
3.7
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3Working
ĨƵůůͲƚŝŵĞƵŶŝǀĞƌƐŝƚLJĂŶĚĐŽůůĞŐĞƐƚƵĚĞŶƚƐ
2.9
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and
related
acƟviƟes
4
3.3
EducaƟonal
5
3.3
acƟviƟes
5
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4EducaƟonal
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EducaƟonal
acƟviƟes
5
dƌĂǀĞůŝŶŐ

EaƟng
and
drinking
1
EaƟng
and
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6
6
3.3
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5
1
EaƟng
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67
0.7
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0.7
7
ϭϬй
1
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and
drinking
6Grooming
'ƌŽŽŵŝŶŐ
0.7
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78

1.5
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ϯй
1.5
^ůĞĞƉŝŶŐ
8
0.7
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7Traveling
ϯϲй
1.5
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8
ĂƚŝŶŐĂŶĚ
2.4
Other
2.4
9
9
1.5
Traveling
8Other
ĚƌŝŶŬŝŶŐ
2.4
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9
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2.4
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spreadsheet

9 t4 completed
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completed
spreadsheet
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A

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Figure t4 completed spreadsheet

step 2

>ĞŝƐƵƌĞ
ĂŶĚƐƉŽƌƚƐ
Insert tab,
step 2 onClick
on the ribbon
ribbon
thenPie
select
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the Insert
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thenand
select
from
Charts

tŽƌŬŝŶŐĂŶĚ
Insert
Pie
step
2 the
Click
on
the
ribbon
tab,first
and
then
select
from
the
Charts
group.
Select
the
2D
Pie
chart
subtype
in
the
first
row
and
first
column.

A
chart
will
Select
2D
Pie
chart
subtype
in
the
row
and
first
column.
A
chart
will
ƌĞůĂƚĞĚĂĐƚŝǀŝƚŝĞƐ
step 2 Click on the Insert ribbon tab, and then select Pie from the Charts
group.
Select
the
2D
Pie
chart
subtype
in
the
first
row

and
first
column.
A
chart
will
ϭϮй
then on
appear
your worksheet.
then appear
youron
worksheet.

Select the 2D Pie chart subtype in the first row and first column. A chart will
then appear on your worksheet.
step 3 the
From
theTools
Chart
Toolsworksheet.
group
now appears
on the ribbon,
From
Chart
that
nowthat
appears
on the ribbon,

click theclick the
then
appear
ongroup
your
figure
t5 that now appears on the ribbon, click the
step
3 From
thetab,
Chart
Tools
group
Design
ribbon
tab,
and
then
select
the
chart
appearing
in the
first
row and
Design
ribbon
and
then
select

the
chart
appearing
in
the
first
row
andthe
the
pie
chart
describing
the
data
in
table
t1
step 3 From the Chart Tools group that now appears on the ribbon,
click
Design
ribbon
tab,
and then
selectNote
the that
chart
appearing
in
the displays
first

rowthe
and
first
column
of
the
Charts
Layouts
group.
Note
that
this
chart
first column
of
the
Charts
Layouts
group.
this
chart
displays
the
Design ribbon tab, and then select the chart appearing in the first row and
Unless otherwise noted, all content on this page is © Cengage Learning.
first
column
of
the
Charts

Layouts
group.
Note
that
this
chart
displays
the
percentage
day
(24spent
hours)
on
each
activity.
Next,
select
percentage
ofcolumn
a dayof(24
hours)
onspent
each
activity.
Next,
select
the
chartthe chart
first
ofa the

Charts
Layouts
group.
Note
that this
chart
displays
the
step 3

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

471


1.4 IntersectIon of straIght LInes

xvi

PReFace

49

Using the point 1 0, 12 and the slope m 5 0.5 in the point-slope form of the equation of a line, we see that the required supply equation is

p 2 1 5 0.5 1 x 2 0 2
concept Building and critical thinking
p 5 0.5x 1 1

Figure 40

1.2 Straight LineS

19

c. To find the market equilibrium, we solve simultaneously the system comprising
exercisesthe demand and supply equations obtained in parts (a) and (b)—that is, the
system

Self-Check exercises
1.2 Self-Check
Offering students immediate
p 5 0.5x
1 1 adults who smoke 1 y 2 ver1. Determine the number a such that the line passing
a. Plot 1
the5percentage
of U.S.
p 5 20.3x
feedback on key concepts, these
2p 5 0.3x 2 5
1
t2
for
the
given years.
through the points 1 a, 22 and 1 3, 62 is parallel to a line
sus
the
year

p 5 0.5x 1 1
0 5 0.8x 2 4
exercises begin each end-ofwith slope 4.
b. Draw the line L through the points 1 0, 20.82 and
Subtracting the first equation from
the second gives
1 4, 19.02.
section exercise set and contain
2. Find an equation of the line that passes through the point
c. Find an equation of the line L.
0.8x 2 4 5 0
1 3, 212 and is perpendicular to a line with slope 212.
d. Assuming that this trend continues, estimate the perboth rote and word problems
centage
of the
U.S.second
adults who
smoked
at the
x equation
5 5. Substituting this value
of x in
equation
gives
p beginning
5 3.5. of
with
3. Does the point 1 3, 232 lie on the lineand
(applications). Fully workedequilibrium quantity is2014.
5000 units, and the equilibrium price is $350

2x 2 3y 2 12 5 0? Sketch the graphThus,
of thethe
line.
Source: Centers for Disease Control and Prevention.
out solutions can be found
(Figure 40).
4. SmokerS in the United StateS The following table gives
Solutions to Self-Check Exercises 1.2 can be found on
at the end of each exercise
the percentage of adults in the United States from 2006
page 24.
through 2010 who smoked in year t. Here, t 5 0 corresection. If students get stuck
spondsself-check
to the beginningexercises
of 2006.
1.4
while solving these problems,
Year, t
0
1
2
3
4
1. Find
the point of20.8
intersection
of the20.1
straight 19.8
lines with19.0
week. Both the demand and supply functions are known

they can get immediate help
Percent, y
20.5
equations 2x 1 3y 5 6 and x 2 3y 5 4.
to be linear.
before attempting to solve
a. Find the demand equation.
2. Market equilibriuM There is no demand for a certain
b. Find the supply equation.
the homework exercises.
model of a disposable camera when the unit price is $12.
c. Find the equilibrium quantity and price.
However,
when
the unit price
is $8, the quantity deApplications have been included here1.2
because
students
often
Questions
mandedConcept
is 8000/week.
The suppliers will not market any
Solutions to Self-Check Exercises 1.4 can be found on
need extra practice with setting up andcameras
solving
these
if the unit
priceproblems.
is $2 or lower. At $4/camera,

page 52.
1. however,
What is the
of a nonvertical
line? 5000
Whatcameras/
can you say
theslope
manufacturer
will market
about the slope of a vertical line?

Concept Questions
Designed to test students’
understanding of the basic
concepts discussed in the
section, these questions
encourage students to explain
learned concepts in their own
words.

2. Give (a) the point-slope form, (b) the slope-intercept
form, and
(c) the general
form of an equation of a line.
concept
Questions

4. Suppose a line L has equation Ax 1 By 1 C 5 0.
a. What is the slope of L if B 2 0?

b. What is the slope of L if B 5 0 and A 2 0?

1.4

3. Let L1 have slope m1 and let L2 have slope m2. State the
m1 and
m2 expect
if (a) Lthat
to L2 andof a
conditions
onyou
1. Explain
why
would
the intersection
1 is parallel
is perpendicular
to aLlinear
(b) L1 demand
linear
curve and
supply curve would lie
2.
in the first quadrant.
2. In the accompanying figure, C 1 x 2 is the cost function and
R 1 x 2 is the revenue function associated with a certain
exercises
product.
a. Plot the break-even point P 1 x0, y0 2 on the graph.
x0, and

the
b. Identify
the break-even
quantity,
in exercises
1–4,and
findmark
the slope
of the line shown
in each
figure.
break-even revenue, y0y, on the set of axes.
1.

3. The accompanying figure gives the demand curve and the
supply curve associated with a certain commodity.
p

1.2

y

y

2.
4

4

x

2

y = R(x)

x

–4

–2

2

x
y = C(x)

–2

x

a. –Identify
the demand
curve
and the supply curve.
2
2
4
b. Plot the point P 1 x0, p0 2 that corresponds to market
–2
equilibrium.

c. Identify and mark the equilibrium quantity, x0, and the
equilibrium price, p0, on the set of axes.

Unless otherwise noted, all content on this page is © Cengage Learning.

50

exercises
Each section contains an
ample set of exercises of a
routine computational nature
followed by an extensive set of
modern application exercises.

CHAPTER 1 Straight LineS and Linear FunctionS

1.4 exercises

64657_01_CH01_p001-072.indd 49
inUnless
exercises
the
point
intersection
otherwise 1–6,
noted, allfind
content
on this
page isof
© Cengage

Learning.

of each pair of

straight lines.

1. y 5 3x 1 4
y 5 22x 1 14

2.

y 5 24x 2 7
2y 5 5x 1 10

3. 2x 2 3y 5 6
5 16

4.

2x 1 4y 5 11
25x 1 3y 5 5

64657_01_CH01_p001-072.indd
3x 1196y

1
x25
4
3
2x 2 y 5 1

2

5. y 5

2
x24
3
x 1 3y 1 3 5 0

6. y 5

in exercises 7–10, find the break-even point for the firm whose
cost function C and revenue function R are given.

7. C1 x 2 5 5x 1 10,000; R 1 x 2 5 15x

8. C1 x 2 5 15x 1 12,000; R 1 x 2 5 21x
9. C1 x 2 5 0.2x 1 120; R 1 x 2 5 0.4x

10. C1 x 2 5 150x 1 20,000; R 1 x 2 5 270x

9/24/13 12:55 PM

a. Find the functions describing the daily cost of leasing
from each company.
b. Sketch the graphs of the two functions on the same set
of axes.
c. If a customer plans to drive at most 30 mi, from which
company should he rent a truck for a single day?
9/24/13

d. If a customer plans to drive at least 60 mi, from which
company should he rent a truck for a single day?

15. Decision analysis A product may be made by using Machine I or Machine II. The manufacturer estimates that
the monthly fixed costs of using Machine I are $18,000,
whereas the monthly fixed costs of using Machine II are
$15,000. The variable costs of manufacturing 1 unit of the
product using Machine I and Machine II are $15 and $20,
respectively. The product sells for $50 each.
a. Find the cost functions associated with using each
machine.
b. Sketch the graphs of the cost functions of part (a) and
the revenue functions on the same set of axes.
c. Which machine should management choose in order
to maximize their profit if the projected sales are
450 units?
550noted,
units?
650 units?
Unless
otherwise
all content
on this page is © Cengage Learning.

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

12:54 PM

PReFace

xvii

Review and study tools
Summary of principal
Formulas and terms
Each review section begins
with the Summary, which
highlights the important
equations and terms, with
page numbers given for quick
review.

ChapteR 6

summary of principal Formulas and terms

FoRmulas
1. Commutative laws

AA>B5B>A

2. Associative laws

A < 1 B < C 2 5 1A < B2 < C
A > 1 B > C 2 5 1A > B2 > C

A < 1 B > C 2 5 1A < B2 > 1 A < C 2

A > 1 B < C 2 5 1A > B2 < 1 A > C 2

3. Distributive laws

1A < B2 c 5 Ac > Bc
1A > B2 c 5 Ac < Bc

4. De Morgan’s laws

n1A < B 2 5 n1 A2 1 n1B 2 2 n1 A > B 2

5. Number of elements in the union
of two finite sets

P 1 n, r 2 5

7. Permutation of n objects, not all
distinct, taken n at a time

n!
1n 2 r2!

n!
n1! n2! cnm!

8. Combination of n distinct objects,
taken r at a time

C 1 n, r 2 5

n!
r! 1 n 2 r 2 !

6. Permutation of n distinct objects,
taken r at a time

teRms
set (342)
element of a set (342)
roster notation (342)
set-builder notation (342)
set equality (342)
subset (343)

Concept review Questions
These questions give students
a chance to check their
knowledge of the basic
definitions and concepts given
in each chapter.

ChapteR 6

empty set (343)
universal set (344)
Venn diagram (344)
set union (345)
set intersection (345)
complement of a set (345)

Concept Review Questions

Fill in the blanks.

384
CHAPTER 6 SetS
and Counting
1. A well-defined
collection
of objects is called a/an _____.
These objects are called _____ of the _____.
5. a. The set of all elements in A and/or B is called the
2. Two sets having exactly the same elements are said to be
_____ of A and B.
_____.
b. The set of all elements in both A and B is called the
_____ of A and B.
6. The set of all elements in U that are not in A is called the
_____ of A.

review exercises
Offering a solid review of the
chapter material, the Review
Exercises contain routine
computational exercises
followed by applied problems.

ChapteR 6

set complementation (346)

multiplication principle (362)
generalized multiplication principle (363)
permutation (368)
n-factorial (370)
combination (374)

3. If every element of a set A is also an element of a set B,
then A is a/an _____ of B.
4. a. The empty set [ is the set containing _____ elements.
7. Applying
De Morgan’s
can write_____ elements.
b. The universal
set is Laws,
the setwe
containing
1 A x B x C 2 c 5 _____.

8. An arrangement of a set of distinct objects in a definite
order is called a/an _____; an arrangement in which the
order is not important is a/an _____.

Review exercises

64657_06_CH06_p341-386.indd 383

9/24/13 12:56 PM

in exercises 1–4, list the elements of each set in roster notation.

1. 5x 0 3x 2 2 5 7 and x is an integer6

For exercises 17–20, let

2. 5x 0 x is a letter of the word TALLAHASSEE6

U 5 5 all participants in a consumer-behavior survey
conducted by a national polling group 6

4. 5x 0 1 x 2 32 1 x 1 42 5 0 and x is a negative integer6

B 5 5 consumers who used cloth rather than disposable
diapers 6

3. The set whose elements are the even numbers between 3
and 11

Let A 5 5a, c, e, r 6. in exercises 5–8, determine whether the set
is equal to A.

5. 5r, e, c, a6

7. 5x 0 x is a letter of the word racer6

in exercises 9–12, shade the portion of the accompanying figure that represents the given set.
U

C

Unless otherwise noted, all content on this page is © Cengage Learning.

D 5 5 consumers who voluntarily recycled their garbage 6

17. A > C

18. A < D

19. B y D

20. C c x D c

c

8. 5x 0 x is a letter of the word cares6

B

C 5 5 consumers who boycotted a company’s products
because of its record on the environment 6
describe each set in words.

6. 5x 0 x is a letter of the word career6

A

A 5 5 consumers who avoided buying a product
because it is not recyclable 6

n
5

n A 2 5 120, n1B2 5 80, and n1A y B2 5 50. in
exercises 21–26, find the number of elements in each set.

21. n1A < B 2
c

23. n1 B 2

25. n1 A y B 2
c

22. n1 Ac 2

24. n1 Ac > B 2

26. n1 Ac y Bc 2

in exercises 27–30, evaluate each quantity.

27. C1 20, 182

28. P19, 72

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.


xviii

PReFace

386

Before Moving On . . .
Found at the end of each
chapter review, these exercises
give students a chance to
determine whether they
have mastered the basic
computational skills developed
in the chapter.

CHAPTER 6 SetS and Counting

Chapter 6 Before Moving on . . .
1. Let U 5 5a, b, c, d, e, f, t6, A 5 5a, d, f, t6, B 5 5d, f, t6,
and C 5 5b, c, e, f 6. Find:
a. A > 1B < C 2
b. 1A > C 2 < 1 B < C2
c. Ac
2. Let A, B, and C be subsets of a universal set U, and
suppose that n 1 U2 5 120, n 1 A 2 5 20, n 1 A y B 2 5 10,
n 1 A y C2 5 11, n 1 B y C 2 5 9, and
n1 A y B y C2 5 4. Find n3A y 1 B x C2 c 4.

3. In how many ways can four compact discs be selected
from six different compact discs?
4. From a standard 52-card deck, how many 5-card poker
hands can be dealt consisting of 3 deuces and 2 face cards?
5. There are six seniors and five juniors in the Chess Club at

Madison High School. In how many ways can a team
consisting of three seniors and two juniors be selected
from the members of the Chess Club?

action-Oriented Study tabs
Convenient color-coded study tabs make it easy for students to flag pages that they want to return to
later, whether for additional review, exam preparation, online exploration, or identifying a topic to be
discussed with the instructor.

instructor Resources
enhanCed WeBaSSiGn®

Printed Access Card: 978-1-285-85758-9
Online Access Code: 978-1-285-85761-9
Exclusively from Cengage Learning, Enhanced WebAssign combines the exceptional
mathematics content that you know and love with the most powerful online homework
solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and interactive, fully customizable e-books (YouBook),
helping students to develop a deeper conceptual understanding of their subject matter.
Quick Prep and Just In Time exercises provide opportunities for students to review
prerequisite skills and content, both at the start of the course and at the beginning of
each section. Flexible assignment options give instructors the ability to release assignments conditionally on the basis of students’ prerequisite assignment scores. Visit us
at www.cengage.com/ewa to learn more.
COMpLete SOLUtiOnS ManUaL by Soo t. tan

Written by the author, the Complete Solutions Manual contains solutions for all exercises in the text, including Exploring with Technology and Explore and Discuss exercises. The Complete Solutions Manual is available on the Instructor Companion Site.
CenGaGe LearninG teStinG pOWered BY COGnerO

Cengage Learning Testing Powered by Cognero is a flexible, online system that allows
you to author, edit, and manage test bank content from multiple Cengage Learning
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your classroom, or wherever you want. Access to Cognero is available on the Instructor Companion Site.

64657_06_CH06_p341-386.indd 386

SOLUtiOn BUiLder (www.cengage.com/solutionbuilder)

This online instructor database offers complete worked-out solutions to all exercises
in the text, including Exploring with Technology and Explore and Discuss questions.
Solution Builder allows you to create customized, secure solutions printouts (in PDF
format) matched exactly to the problems you assign in class.
inStrUCtOr COMpaniOn Site

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lecture and class tools is available online at www.cengage.com/login. Access and
download PowerPoint presentations, images, solutions manual, videos, and more.
Unless otherwise noted, all content on this page is © Cengage Learning.

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

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PReFace

xix

student Resources
StUdent SOLUtiOnS ManUaL by Soo t. tan (ISBN-13: 978-1-285-84572-2)

Giving you more in-depth explanations, this insightful resource includes fully workedout solutions for selected exercises in the textbook, as well as problem-solving strategies, additional algebra steps, and review for selected problems.
enhanCed WeBaSSiGn®

Printed Access Card: 978-1-285-85758-9
Online Access Code: 978-1-285-85761-9
Enhanced WebAssign (assigned by the instructor) provides you with instant feedback
on homework assignments. This online homework system is easy to use and includes
helpful links to textbook sections, video examples, and problem-specific tutorials.
CenGaGeBrain.COM

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acknowledgments
I wish to express my personal appreciation to each of the following reviewers, whose
many suggestions have helped make a much improved book.
Zach Abernathy
Winthrop University

Laurie McManus
St. Louis Community College at Meramec

Mark Antkowicz
Colorado Technical University

Markus Pomper
Indiana University East

Andrea Brown
Ivy Tech Community College

John Roepke
Doane College

Ashot Djrbashian
Glendale Community College

Peter Shenkin
John Jay College of Criminal Justice, CUNY

Amy Franklin
Jacksonville State University

Beimnet Teclezghi
New Jersey City University

Jean Johnson
Jacksonville State University

Brenda F. Tiefenbruck
University of St. Thomas

Peter Knopf
Pace University

Kenneth V. Turner, Jr.
Anderson University

Thurai Kugan
John Jay College of Criminal Justice, CUNY

Francis J. Vasko
Kutztown University

Melanie Ledwig
Victoria College

Mary Wright
Southern Illinois University Carbondale

Myra Maxwell
University of Indianapolis

Jill Zarestky
Texas A&M University

I also thank reviewers of previous editions whose comments and suggestions have
helped to get the book this far.

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.


xx

preface 

I also wish to thank Tao Guo for the excellent job he did as the accuracy checker

for this text. I also thank the editorial and production staffs of Cengage Learning—
Richard Stratton, Rita Lombard, Laura Wheel, Jennifer Cordoba, Andrew Coppola,
Cheryll Linthicum, and Vernon Boes—for all of their help and support during the
development and production of this edition. I also thank Martha Emry and Barbara
Willette, who both did an excellent job ensuring the accuracy and readability of this
edition. Simply stated, the team I have been working with is outstanding, and I truly
appreciate all of their hard work and efforts.
S. T. Tan

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.