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Table of contents
  1. Preface
  2. 1 Sets
    1. Introduction
    2. 1.1 Basic Set Concepts
    3. 1.2 Subsets
    4. 1.3 Understanding Venn Diagrams
    5. 1.4 Set Operations with Two Sets
    6. 1.5 Set Operations with Three Sets
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  3. 2 Logic
    1. Introduction
    2. 2.1 Statements and Quantifiers
    3. 2.2 Compound Statements
    4. 2.3 Constructing Truth Tables
    5. 2.4 Truth Tables for the Conditional and Biconditional
    6. 2.5 Equivalent Statements
    7. 2.6 De Morgan’s Laws
    8. 2.7 Logical Arguments
    9. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  4. 3 Real Number Systems and Number Theory
    1. Introduction
    2. 3.1 Prime and Composite Numbers
    3. 3.2 The Integers
    4. 3.3 Order of Operations
    5. 3.4 Rational Numbers
    6. 3.5 Irrational Numbers
    7. 3.6 Real Numbers
    8. 3.7 Clock Arithmetic
    9. 3.8 Exponents
    10. 3.9 Scientific Notation
    11. 3.10 Arithmetic Sequences
    12. 3.11 Geometric Sequences
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  5. 4 Number Representation and Calculation
    1. Introduction
    2. 4.1 Hindu-Arabic Positional System
    3. 4.2 Early Numeration Systems
    4. 4.3 Converting with Base Systems
    5. 4.4 Addition and Subtraction in Base Systems
    6. 4.5 Multiplication and Division in Base Systems
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  6. 5 Algebra
    1. Introduction
    2. 5.1 Algebraic Expressions
    3. 5.2 Linear Equations in One Variable with Applications
    4. 5.3 Linear Inequalities in One Variable with Applications
    5. 5.4 Ratios and Proportions
    6. 5.5 Graphing Linear Equations and Inequalities
    7. 5.6 Quadratic Equations with Two Variables with Applications
    8. 5.7 Functions
    9. 5.8 Graphing Functions
    10. 5.9 Systems of Linear Equations in Two Variables
    11. 5.10 Systems of Linear Inequalities in Two Variables
    12. 5.11 Linear Programming
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  7. 6 Money Management
    1. Introduction
    2. 6.1 Understanding Percent
    3. 6.2 Discounts, Markups, and Sales Tax
    4. 6.3 Simple Interest
    5. 6.4 Compound Interest
    6. 6.5 Making a Personal Budget
    7. 6.6 Methods of Savings
    8. 6.7 Investments
    9. 6.8 The Basics of Loans
    10. 6.9 Understanding Student Loans
    11. 6.10 Credit Cards
    12. 6.11 Buying or Leasing a Car
    13. 6.12 Renting and Homeownership
    14. 6.13 Income Tax
    15. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  8. 7 Probability
    1. Introduction
    2. 7.1 The Multiplication Rule for Counting
    3. 7.2 Permutations
    4. 7.3 Combinations
    5. 7.4 Tree Diagrams, Tables, and Outcomes
    6. 7.5 Basic Concepts of Probability
    7. 7.6 Probability with Permutations and Combinations
    8. 7.7 What Are the Odds?
    9. 7.8 The Addition Rule for Probability
    10. 7.9 Conditional Probability and the Multiplication Rule
    11. 7.10 The Binomial Distribution
    12. 7.11 Expected Value
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  9. 8 Statistics
    1. Introduction
    2. 8.1 Gathering and Organizing Data
    3. 8.2 Visualizing Data
    4. 8.3 Mean, Median and Mode
    5. 8.4 Range and Standard Deviation
    6. 8.5 Percentiles
    7. 8.6 The Normal Distribution
    8. 8.7 Applications of the Normal Distribution
    9. 8.8 Scatter Plots, Correlation, and Regression Lines
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  10. 9 Metric Measurement
    1. Introduction
    2. 9.1 The Metric System
    3. 9.2 Measuring Area
    4. 9.3 Measuring Volume
    5. 9.4 Measuring Weight
    6. 9.5 Measuring Temperature
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  11. 10 Geometry
    1. Introduction
    2. 10.1 Points, Lines, and Planes
    3. 10.2 Angles
    4. 10.3 Triangles
    5. 10.4 Polygons, Perimeter, and Circumference
    6. 10.5 Tessellations
    7. 10.6 Area
    8. 10.7 Volume and Surface Area
    9. 10.8 Right Triangle Trigonometry
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  12. 11 Voting and Apportionment
    1. Introduction
    2. 11.1 Voting Methods
    3. 11.2 Fairness in Voting Methods
    4. 11.3 Standard Divisors, Standard Quotas, and the Apportionment Problem
    5. 11.4 Apportionment Methods
    6. 11.5 Fairness in Apportionment Methods
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  13. 12 Graph Theory
    1. Introduction
    2. 12.1 Graph Basics
    3. 12.2 Graph Structures
    4. 12.3 Comparing Graphs
    5. 12.4 Navigating Graphs
    6. 12.5 Euler Circuits
    7. 12.6 Euler Trails
    8. 12.7 Hamilton Cycles
    9. 12.8 Hamilton Paths
    10. 12.9 Traveling Salesperson Problem
    11. 12.10 Trees
    12. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  14. 13 Math and...
    1. Introduction
    2. 13.1 Math and Art
    3. 13.2 Math and the Environment
    4. 13.3 Math and Medicine
    5. 13.4 Math and Music
    6. 13.5 Math and Sports
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  15. A | Co-Req Appendix: Integer Powers of 10
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index

Your Turn

3.1
1.
Yes. When 54 is divided by 9, the result is 6 with no remainder. Also, 54 can be written as the product of 9 and 6.
3.2
1.
The last digit is 0, so 45,730 is divisible by 5, since the rule states that if the last digit is 0 or 5, the original number is divisible by 5.
3.3
1.
The sum of the digits is 32. Since 32 is not divisible by 9, neither is 342,887.
3.4
1.
The last digit is even, so 2 divides 43,568. The sum of the digits is 26. Since 26 is not divisible by 3, neither is 43,568. The rule for divisibility by 6 is that the number be divisible by both 2 and 3. Since 43,568 is not divisible by 3, it is not divisible by 6.
3.5
1.
Since the last digit of 87,762 is not 0, it is not divisible by 10.
3.6
1.
The number formed by the last two digits of 43,568 is 68 and 68 is divisible by 4. Since the number formed by the last two digits of 43,568 is divisible by 4, so is 43,568.
3.7
1.
Yes, 1,429 is prime.
3.8
1.
Yes, 859 is a prime number.
3.9
1.
5,067,322 is a composite number.
3.10
1.
No, 1,477 is composite.
3.11
1.
90 = 2 × 3 2 × 5
3.12
1.
85 = 5 × 17
3.13
1.
2 3 × 5 × 7
3.14
1.
The number 180 has three prime factors.
3.15
1.
The GCD is 9.
3.16
1.
The GCD of 36 and 128 is 4.
3.17
1.
40
3.18
1.
The largest square bricks that can be used are 20 cm by 20 cm.
3.19
1.
The largest team size that can be formed is 7 students.
3.20
1.
60
3.21
1.
140
3.22
1.
92,400
3.23
1.
360
3.24
1.
The sun, Venus, and Jupiter will line up again in 220,830 days.
3.25
1.
The first person to receive both giveaways would be the person who submits the 11,700th submission.
3.26
1.
integer
2.
not an integer
3.
not an integer
4.
integer
5.
integer
3.27
1.

A number line ranges from negative 10 to 10, in increments of 1. A point is marked at negative 10 and it is labeled x equals negative 10.
2.

A number line ranges from negative 7 to 7, in increments of 1. A point is marked at 4 and it is labeled x equals 4.
3.

A number line ranges from negative 7 to 7, in increments of 1. A point is marked at 0 and it is labeled x equals 0.
3.28
1.

A number line ranges from negative 42 to 30, in increments of 6. Two points are marked at negative 38 and 27.
27 > 38 and 38 < 27
3.29
1.

A 
number line ranges from negative 220 to negative 60, in increments of 10. Two points are marked at negative 213 and negative 63. 63 > 213 and 213 < 63
3.30
1.
101 is larger. 101 > 98 and 98 < 101 .
3.31
1.
38
3.32
1.
81
3.33
1.
−7. Since |−18| > |11|, the answer matches the sign of −18.
3.34
1.
−62. Since a larger positive number was subtracted from a smaller positive number, a negative result was expected.
3.35
1.
71. Subtracting a negative number is the same as adding a positive number.
3.36
1.
−17. Since |19| < |−36|, the sign of the answer matches the sign of −36, which is negative.
3.37
1.
$89
3.38
1.
2,106. Since both numbers are positive, the product is positive.
3.39
1.
−234. Since the numbers have opposite signs, the product is negative.
3.40
1.
−29. The numbers have opposite signs, so the division will result in a negative number.
3.41
1.
7. Since the signs of the numbers match, the division results in a positive number.
3.42
1.
The average daily balance was $529.
3.43
1.
313
3.44
1.
72
3.45
1.
630
3.46
1.
2,701
3.47
1.
−15
3.48
1.
1,516
3.49
1.
5
3.50
1.
403
3.51
1.
94 is not a perfect square.
2.
441 is a perfect square.
3.52
1.
not a rational number
2.
rational number
3.
rational number
4.
rational number
5.
rational number
3.53
1.
a × b = 8 × 26 = 208 and b × c = 14 × 12 = 168 . The fractions are not equivalent.
3.54
1.
3 10
3.55
1.
16 , 391 37 , 125
3.56
1.
45 73
3.57
1.
13 40
3.58
1.
37 36
3.59
1.
439 9 , 900
3.60
1.
3 17 26
3.61
1.
131 14
3.62
1.
5.108
3.63
1.
18.63
3.64
1.
1.6
3.65
1.
1 , 703 , 347 100 , 000
3.66
1.
21 110
3.67
1.
2.664
3.68
1.
38 35
2.
11 112
3.69
1.
203 192
3.70
1.
351 1 , 100 , or in decimal form, 0.319 09 ¯
3.71
1.
The process used above yields 543 260 .
3.72
1.

Studying math: 5 hours
Studying history: 2.5 hours
Studying writing: 1.25 hours
Studying physics: 1.25 hours
3.73
1.
720 calories of protein
3.74
1.
321.868 km
3.75
1.
23.656 liters
3.76
1.
4 100
2.
50 100
3.77
1.
0.14
2.
0.07
3.78
1.
300
2.
841.64
3.79
1.
120
2.
800
3.80
1.
7%
2.
85%
3.81
1.
440 calories of protein
3.82
1.
12% of registered voters in the small town voted in the primaries.
3.83
1.
We want the original price of the item, which is the total. We know the percent, 40, and the percentage of the total, $30. To find the original cost, use 100 × x n , with x = 30 and n  =  40 . Calculating with those values yields 100 × 30 40 = 75 . So, the original was $75.
3.84
1.
perfect square
2.
not a perfect square
3.
perfect square
4.
not a perfect square
3.85
1.
rational
2.
irrational
3.
irrational
4.
irrational
3.86
1.
5 22 . The rational part is 5, and the irrational part is 22 .
3.87
1.
733 . The rational part is 1, and the irrational part is 733 .
3.88
1.
11 15 . The rational part is 11, and the irrational part is 15 .
3.89
1.
18 15
3.90
1.
7.3 π
3.91
1.
The two numbers being subtracted do not have the same irrational part, so the operation cannot be performed without a calculator.
3.92
1.
12 3
2.
342 25 11
3.93
1.
37.8 6
2.
19
3.94
1.
8 15 5
2.
11 6 18
3.95
1.
25 4 + 5 13 4
3.96
1.
real
2.
not real
3.
real
3.97
1.
irrational number
2.
integer, rational number
3.
rational number
3.98
1.

A Venn diagram shows four concentric ovals. The ovals are labeled from inner to outer as follows: N, Z, Q, and R. The oval, N reads, 15 and 871. The oval, Z reads, negative 4. The oval, Q reads, 13.863. The oval, R reads, 5 times square root of 2 and negative 3 pi.

Venn diagram showing ‒4, 13.863, 15, 871, 5 2 , and 3 π
3.99
1.
dstributive property
2.
additive inverse property
3.100
1.
9 × 8 = 99 . Using that, the problem can be changed to 99 × 8 . Change to 99 = ( 100 1 ) . Using the distributive property, 99 × 8 = ( 100 1 ) × 8 = 100 × 8 1 × 8 = 800 8 = 792 .
3.101
1.
93 = 9 (mod 12)
2.
387 = 3 (mod 12)
3.102
1.
4:00
3.103
1.
9:00
3.104
1.
4
3.105
1.
5:00
3.106
1.
Thursday
3.107
1.
12 21
2.
Since the bases are not the same (one is 3, the other 4), this cannot be simplified using the product rule for exponents.
3.108
1.
b 9
3.109
1.
b 2
3.110
1.
2 14 × 19 14
3.111
1.
a 6 × b 6
3.112
1.
14 9 5 9
2.
a 5 18 5
3.113
1.
11 48
2.
a 42
3.114
1.
7 5 12 3
2.
5 3 c 7
3.115
1.
6 × 13 8
2.
c 5 × 2 9
3.116
1.
7 72 10 40 × 6 24
2.
16 a 18 b 12
3.117
1.
Is not written in scientific notation; 42.67 is not at least 1 and less than 10.
2.
Is written in scientific notation
3.
Is not written in scientific notation; The absolute value of –80.91 is not at least 1 and less than 10.
3.118
1.
3.38 × 10 4
2.
4.5 × 10 3
3.
1 × 10 0
3.119
1.
0.0046113 × 10 12
3.120
1.
14 , 911.0 × 10 6
3.121
1.
1,020,000
2.
0.0000409
3.122
1.
9.601 × 10 13
2.
1.53 × 10 6
3.123
1.
1.198 × 10 4
2.
2.07 × 10 39
3.124
1.
1.14256 × 10 43
3.125
1.
9.0777 × 10 28
3.126
1.
6.87 × 10 7
2.
6.2881 × 10 3
3.127
1.
2.4 × 10 5
2.
3.75 × 10 0
3.128
1.
The transistor is 1.38 × 10 8 m larger than the diameter of an atom.
3.129
1.
Neptune is 8.930 × 10 1 , or 89.3, times further from the sun that Mercury.
3.130
1.
7.5 × 10 9 cubic meters
3.131
1.
A person exhales, on average, 8.4 × 10 2 , or 840 pounds of carbon dioxide per year.
3.132
1.
This is an arithmetic sequence. Every term is the previous term minus 2.2.
2.
This is not an arithmetic sequence. The difference between terms 1 and 2 is 2, but between terms 3 and 4 the difference is 4. The differences are not the same.
3.
This is an (infinite) arithmetic sequence. Every term is the previous term plus 6. The ellipsis indicates the pattern continues.
3.133
1.
a 1 = 4.5 , d = 3.6 , a 36 = 310.5
3.134
1.
d = 5 , a 1 = 24 , and a 151 = 726
3.135
1.
12,675.5
3.136
1.
Christina will save $265 in week 52.
3.137
1.
There are 2,520 seats in the theater.
3.138
1.
It is a geometric sequence; common ratio is 5.
2.
It is not a common ratio; term 2 is the first term multiplied by −2, but the sixth term is the fifth term multiplied by 3.
3.
It is a geometric sequence; common ratio is 1 10 .
3.139
1.
3 2
2.
2,048
3.140
1.
84,652,645
2.
40.444444
3.141
1.
The amount in the account was $11,671.03 (rounded to two decimal places).
3.142
1.
There are 1.6493 × 10 13 organisms after 20 hours.
3.143
1.
0. 99996948242188

Check Your Understanding

1.
31 and 701 are prime. 56, 213 and 48 are composite.
2.
2 × 5 × 457
3.
2
4.
630
5.
The maximum number of bags that can be filled in this way is 10.
6.
−4, 430
7.
A number line ranges from negative 7 to 7, in increments of 1. Three points are marked at negative 2, 4, and 7. The points are labeled x equals negative 2, x equals 4, and x equals 7, respectively.
8.
−13, −7, −2, 4, 10
9.
7
10.
13
11.
36
12.
parentheses
13.
exponents
14.
−22
15.
parentheses
16.
49
17.
41 , 4 3 , 2.75 , 0.2 13 ¯ are rational; 13 is not.
18.
3 5
19.
19 24
20.
34 100
21.
3 11 12
22.
7 33
23.
3 2
24.
Using the process from the chapter, 307 336 , and there are other answers.
25.
3 11 12
26.
$110.25
27.
228
28.
7 new employees will be hired.
29.
10 5
30.
7 7
31.
48 5
32.
4 7 7
33.
77 , −19 , 38.902
34.
N Z N Q N R Z Q Z R Q R
35.
distributive property
36.
2
37.
1
38.
5
39.
Friday
40.
a 8
41.
5 4 or 1 5 4
42.
6 9 b 9
43.
c 3 7 3
44.
3 6 a 12 4 6 b 30
45.
4.56 × 10 3
46.
567 , 000 , 000
47.
5.48 × 10 3
48.
9.55 × 10 6
49.
3.552 × 10 8
50.
5.75 × 10 3
51.
A pile of dollar bills that reaches the moon would contain 3.521 × 10 12 bills.
52.
No. The difference from term 1 to term 2 is different than the difference from term 4 to term 5.
53.
8
54.
613
55.
d = 3 , a 1 = 14
56.
35050
57.
There will be 426 people in their survey group after 100 days.
58.
Yes, each term is the previous term multiplied by 2.
59.
The common ratio is −10.
60.
2,919.293 (rounded off to three decimal places)
61.
5.714 (rounded to three decimal places)
62.
$30,188.57 (rounded off to two decimal places)
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