College Algebra

Michael Sullivan

Chapter 0

Review

Educators


Problem 1

The numbers in the set $\left\{x | x=\frac{a}{b}\right.$ where $a, b$ are integers and $b \neq 0\},$ are called ______ numbers

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Problem 2

The value of the expression $4+5 \cdot 6-3$ is ______.

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Problem 3

The fact that $2 x+3 x=(2+3) x$ is a consequence of the _____ Property.

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Problem 4

"The product of 5 and $x+3$ equals $6 "$ may be written as ______.

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Problem 5

True or False Rational numbers have decimals that either terminate or are nonterminating with a repeating block of digits.

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Problem 6

True or False The Zero-Product Property states that the product of any number and zero equals zero.

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Problem 7

True or False The least common multiple of 12 and 18 is 6

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Problem 8

True or False No real number is both rational and irrational.

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Problem 9

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$A \cup B$$

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Problem 10

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$A \cup C$$

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Problem 11

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$A \cap B$$

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Problem 12

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$A \cap C$$

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Problem 13

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$(A \cup B) \cap C$$

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Problem 14

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$(A \cap B) \cup C$$

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Problem 15

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$\bar{A}$$

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Problem 16

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$\bar{C}$$

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Problem 17

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$\overline{A \cap B}$$

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Problem 18

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$B \cup C$$

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Problem 19

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$\bar{A} \cup \bar{B}$$

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Problem 20

Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.
$$\bar{B} \cap \bar{C}$$

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Problem 21

List the numbers in each set that are (a) Natural mumbers, (b) Integers, (c) Rational numbers, (d) Irrational mumbers, Real number.
$$A=\left\{-6, \frac{1}{2},-1.333 \ldots(\text { the } 3 \text { 's repeat }), \pi, 2,5\right\}$$

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Problem 22

List the numbers in each set that are (a) Natural mumbers, (b) Integers, (c) Rational numbers, (d) Irrational mumbers, Real number.
$$B=\left\{-\frac{5}{3}, 2.060606 \ldots(\text { the block } 06 \text { repeats }), 1.25,0,1, \sqrt{5}\right\}$$

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Problem 23

List the numbers in each set that are (a) Natural mumbers, (b) Integers, (c) Rational numbers, (d) Irrational mumbers, Real number.
$$C=\left\{0,1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right\}$$

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Problem 24

List the numbers in each set that are (a) Natural mumbers, (b) Integers, (c) Rational numbers, (d) Irrational mumbers, Real number.
$$D=\{-1,-1.1,-1.2,-1.3\}$$

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Problem 25

List the numbers in each set that are (a) Natural mumbers, (b) Integers, (c) Rational numbers, (d) Irrational mumbers, Real number.
$$E=\left\{\sqrt{2}, \pi, \sqrt{2}+1, \pi+\frac{1}{2}\right\}$$

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Problem 26

List the numbers in each set that are (a) Natural mumbers, (b) Integers, (c) Rational numbers, (d) Irrational mumbers, Real number.
$$F=\left\{-\sqrt{2}, \pi+\sqrt{2}, \frac{1}{2}+10.3\right\}$$

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Problem 27

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$18.9526$$

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Problem 28

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$25.86134$$

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Problem 29

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$28.65319$$

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Problem 30

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$99.05249$$

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Problem 31

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$0.06291$$

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Problem 32

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$0.05388$$

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Problem 33

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$9.9985$$

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Problem 34

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$1.0006$$

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Problem 35

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$\frac{3}{7}$$

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Problem 36

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$\frac{5}{9}$$

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Problem 37

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$\frac{521}{15}$$

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Problem 38

Approximate each number ( a ) rounded and (b) truncated to three decimal places.
$$\frac{81}{5}$$

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Problem 39

Write each statement using symbols.
The sum of 3 and 2 equals 5

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Problem 40

Write each statement using symbols.
The product of 5 and 2 equals $10 .$

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Problem 41

Write each statement using symbols.
The sum of $x$ and 2 is the product of 3 and 4

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Problem 42

Write each statement using symbols.
The sum of 3 and $y$ is the sum of 2 and $2 .$

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Problem 43

Write each statement using symbols.
The product of 3 and $y$ is the sum of 1 and 2

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Problem 44

Write each statement using symbols.
The product of 2 and $x$ is the product of 4 and 6

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Problem 45

Write each statement using symbols.
The difference $x$ less 2 equals 6

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Problem 46

Write each statement using symbols.
The difference 2 less $y$ equals 6

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Problem 47

Write each statement using symbols.
The quotient $x$ divided by 2 is 6

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Problem 48

Write each statement using symbols.
The quotient 2 divided by $x$ is 6

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Problem 49

Evaluate each expression.
$$9-4+2$$

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Problem 50

Evaluate each expression.
$$6-4+3$$

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Problem 51

Evaluate each expression.
$$-6+4 \cdot 3$$

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Problem 52

Evaluate each expression.
$$8-4 \cdot 2$$

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Problem 53

Evaluate each expression.
$$4+5-8$$

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Problem 54

Evaluate each expression.
$$8-3-4$$

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Problem 55

Evaluate each expression.
$$2-\frac{1}{2}$$

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Problem 56

Evaluate each expression.
$$2-\frac{1}{2}$$

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Problem 57

Evaluate each expression.
$$6-[3 \cdot 5+2 \cdot(3-2)]$$

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Problem 58

Evaluate each expression.
$$2 \cdot[8-3(4+2)]-3$$

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Problem 59

Evaluate each expression.
$$2 \cdot(3-5)+8 \cdot 2-1$$

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Problem 60

Evaluate each expression.
$$1-(4 \cdot 3-2+2)$$

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Problem 61

Evaluate each expression.
$$10-[6-2 \cdot 2+(8-3)] \cdot 2$$

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Problem 62

Evaluate each expression.
$$2-5 \cdot 4-[6 \cdot(3-4)]$$

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Problem 63

Evaluate each expression.
$$(5-3) \frac{1}{2}$$

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Problem 64

Evaluate each expression.
$$(5+4) \frac{1}{3}$$

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Problem 65

Evaluate each expression.
$$\frac{4+8}{5-3}$$

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Problem 66

Evaluate each expression.
$$\frac{2-4}{5-3}$$

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Problem 67

Evaluate each expression.
$$\frac{3}{5} \cdot \frac{10}{21}$$

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Problem 68

Evaluate each expression.
$$\frac{5}{9} \cdot \frac{3}{10}$$

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Problem 69

Evaluate each expression.
$$\frac{6}{25} \cdot \frac{10}{27}$$

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Problem 70

Evaluate each expression.
$$\frac{21}{25} \cdot \frac{100}{3}$$

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Problem 71

Evaluate each expression.
$$\frac{3}{4}+\frac{2}{5}$$

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Problem 72

Evaluate each expression.
$$\frac{4}{3}+\frac{1}{2}$$

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Problem 73

Evaluate each expression.
$$\frac{5}{6}+\frac{9}{5}$$

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Problem 74

Evaluate each expression.
$$\frac{8}{9}+\frac{15}{2}$$

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Problem 75

Evaluate each expression.
$$\frac{5}{18}+\frac{1}{12}$$

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Problem 76

Evaluate each expression.
$$\frac{2}{15}+\frac{8}{9}$$

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Problem 77

Evaluate each expression.
$$\frac{1}{30}-\frac{7}{18}$$

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Problem 78

Evaluate each expression.
$$\frac{3}{14}-\frac{2}{21}$$

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Problem 79

Evaluate each expression.
$$\frac{3}{20}-\frac{2}{15}$$

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Problem 80

Evaluate each expression.
$$\frac{6}{35}-\frac{3}{14}$$

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Problem 81

Evaluate each expression.
$$\frac{\frac{5}{18}}{\frac{11}{27}}$$

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Problem 82

Evaluate each expression.
$$\frac{\frac{5}{21}}{\frac{2}{35}}$$

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Problem 83

Evaluate each expression.
$$\frac{1}{2} \cdot \frac{3}{5}+\frac{7}{10}$$

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Problem 84

Evaluate each expression.
$$\frac{2}{3}+\frac{4}{5} \cdot \frac{1}{6}$$

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Problem 85

Evaluate each expression.
$$2 \cdot \frac{3}{4}+\frac{3}{8}$$

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Problem 86

Evaluate each expression.
$$3 \cdot \frac{5}{6}-\frac{1}{2}$$

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Problem 87

Use the Distributive Property to remove the parentheses.
$$6(x+4)$$

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Problem 88

Use the Distributive Property to remove the parentheses.
$$4(2 x-1)$$

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Problem 89

Use the Distributive Property to remove the parentheses.
$$x(x-4)$$

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Problem 90

Use the Distributive Property to remove the parentheses.
$$4 x(x+3)$$

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Problem 91

Use the Distributive Property to remove the parentheses.
$$2\left(\frac{3}{4} x-\frac{1}{2}\right)$$

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Problem 92

Use the Distributive Property to remove the parentheses.
$$3\left(\frac{2}{3} x+\frac{1}{6}\right)$$

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Problem 93

Use the Distributive Property to remove the parentheses.
$$(x+2)(x+4)$$

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Problem 94

Use the Distributive Property to remove the parentheses.
$$(x-2)(x+1)$$

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Problem 95

Use the Distributive Property to remove the parentheses.
$$(x-2)(x+1)$$

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Problem 96

Use the Distributive Property to remove the parentheses.
$$(x-4)(x+1)$$

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Problem 97

Use the Distributive Property to remove the parentheses.
$$(x-8)(x-2)$$

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Problem 98

Use the Distributive Property to remove the parentheses.
$$(x-4)(x-2)$$

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Problem 99

Explain to a friend how the Distributive Property is used to justify the fact that $2 x+3 x=5 x$

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Problem 100

Explain to a friend why $2+3 \cdot 4=14,$ whereas $(2+3) \cdot 4=20$

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Problem 101

Explain why $2(3 \cdot 4)$ is not equal to $(2 \cdot 3) \cdot(2 \cdot 4)$

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Problem 102

Explain why $\frac{4+3}{2+5}$ is not equal to $\frac{4}{2}+\frac{3}{5}$

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Problem 103

Is subtraction commutative? Support your conclusion with an example.

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Problem 104

Is subtraction associative? Support your conclusion with an example.

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Problem 105

Is division commutative? Support your conclusion with an example.

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Problem 106

Is division associative? Support your conclusion with an example.

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Problem 107

If $2=x,$ why does $x=2 ?$

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Problem 108

If $x=5,$ why does $x^{2}+x=30 ?$

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Problem 109

Are there any real numbers that are both rational and irrational? Are there any real numbers that are neither? Explain your reasoning.

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Problem 110

Explain why the sum of a rational number and an irrational number must be irrational.

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Problem 111

A rational number is defined as the quotient of two integers. When written as a decimal, the decimal will either repeat or terminate. By looking at the denominator of the rational number, there is a way to tell in advance whether its decimal representation will repeat or terminate. Make a list of rational numbers and their decimals. See if you can discover the pattern. Confirm your conclusion by consulting books on number theory at the library. Write a brief essay on your findings.

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Problem 112

The current time is 12 noon CST. What time (CST) will it be $12,997$ hours from now?

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Problem 113

Both $\frac{a}{0}(a \neq 0)$ and $\frac{0}{0}$ are undefined, but for different reasons. Write a paragraph or two explaining the different reasons.

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