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# College Algebra 7th

## Educators

AG

### Problem 1

The point that is 2 units to the left of the $y$ -axis and 4 units above the $x$ -axis has coordinates.

AG
Ankit G.

### Problem 2

If $x$ is positive and $y$ is negative, then the point $(x, y)$ is in Quadrant _____.

AG
Ankit G.

### Problem 3

The distance between the points $(a, b)$ and $(c, d)$ is _____. So the distance between (1,2) and (7,10) is _____.

AG
Ankit G.

### Problem 4

The point midway between $(a, b)$ and $(c, d)$ is _____. So the point midway between (1,2) and (7,10) is ______.

AG
Ankit G.

### Problem 5

Refer to the following figure.
Find the coordinates of the points shown.

AG
Ankit G.

### Problem 6

Refer to the following figure.
List the points that lie in Quadrants I and III.

AG
Ankit G.

### Problem 7

Plot the given points in a coordinate plane.
$$(0,5),(-1,0),(-1,-2),\left(\frac{1}{2}, \frac{2}{3}\right)$$

AG
Ankit G.

### Problem 8

Plot the given points in a coordinate plane.
$$(-5,0),(2,0),(2.6,-1.3),(-2.5,3.5)$$

AG
Ankit G.

### Problem 9

Sketch the region given by the set.
$$\{(x, y) \mid x \geq 2\}$$

AG
Ankit G.

### Problem 10

Sketch the region given by the set.
$$\{(x, y) \mid y=2\}$$

AG
Ankit G.

### Problem 11

Sketch the region given by the set.
$$\{(x, y) \mid x=-4\}$$

AG
Ankit G.

### Problem 12

Sketch the region given by the set.
$$\{(x, y) \mid y<3\}$$

AG
Ankit G.

### Problem 13

Sketch the region given by the set.
$$\{(x, y) \mid-3<x<3\}$$

AG
Ankit G.

### Problem 14

Sketch the region given by the set.
$$\{(x, y) \mid 0 \leq y \leq 2\}$$

AG
Ankit G.

### Problem 15

Sketch the region given by the set.
$$\{(x, y) \mid x y<0\}$$

AG
Ankit G.

### Problem 16

Sketch the region given by the set.
$$\{(x, y) \mid x y>0\}$$

AG
Ankit G.

### Problem 17

Sketch the region given by the set.
$$\{(x, y) \mid x \geq 1 \text { and } y<3\}$$

AG
Ankit G.

### Problem 18

Sketch the region given by the set.
$$\{(x, y) \mid x<2 \text { and } y \geq 1\}$$

AG
Ankit G.

### Problem 19

Sketch the region given by the set.
$$\{(x, y) \mid-1<x<1 \text { and }-2<y<2\}$$

AG
Ankit G.

### Problem 20

Sketch the region given by the set.
$$\{(x, y) \mid-3 \leq x \leq 3 \text { and }-1 \leq y \leq 1\}$$

AG
Ankit G.

### Problem 21

A pair of points is graphed. (a) Find the distance between them. (b) Find the midpoint of the segment that joins them.

AG
Ankit G.

### Problem 22

A pair of points is graphed. (a) Find the distance between them. (b) Find the midpoint of the segment that joins them.

AG
Ankit G.

### Problem 23

A pair of points is graphed. (a) Find the distance between them. (b) Find the midpoint of the segment that joins them.

AG
Ankit G.

### Problem 24

A pair of points is graphed. (a) Find the distance between them. (b) Find the midpoint of the segment that joins them.

AG
Ankit G.

### Problem 25

A pair of points is given. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them.
$$(0,8),(6,16)$$

AG
Ankit G.

### Problem 26

A pair of points is given. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them.
$$(-2,5),(10,0)$$

AG
Ankit G.

### Problem 27

A pair of points is given. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them.
$$(3,-2),(-4,5)$$

AG
Ankit G.

### Problem 28

A pair of points is given. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them.
$$(-1,1),(-6,-3)$$

AG
Ankit G.

### Problem 29

A pair of points is given. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them.
$$(6,-2),(-6,2)$$

AG
Ankit G.

### Problem 30

A pair of points is given. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them.
$$(0,-6),(5,0)$$

AG
Ankit G.

### Problem 31

In these exercises we find the areas of plane figures.
Draw the rectangle with vertices $A(1,3), B(5,3), C(1,-3),$ and $D(5,-3)$ on a coordinate plane. Find the area of the rectangle.

AG
Ankit G.

### Problem 32

In these exercises we find the areas of plane figures.
Draw the parallelogram with vertices $A(1,2), B(5,2)$, $C(3,6),$ and $D(7,6)$ on a coordinate plane. Find the area of the parallelogram.

AG
Ankit G.

### Problem 33

In these exercises we find the areas of plane figures.
Plot the points $A(1,0), B(5,0), C(4,3),$ and $D(2,3)$ on a coordinate plane. Draw the segments $A B, B C, C D$, and DA. What kind of quadrilateral is $A B C D$, and what is its area?

AG
Ankit G.

### Problem 34

In these exercises we find the areas of plane figures.
Plot the points $P(5,1), Q(0,6),$ and $R(-5,1)$ on a coordinate plane. Where must the point $S$ be located so that the quadrilateral $P Q R S$ is a square? Find the area of this square.

AG
Ankit G.

### Problem 35

In these exercises we use the Distance Formula.
Which of the points $A(6,7)$ or $B(-5,8)$ is closer to the origin?

AG
Ankit G.

### Problem 36

In these exercises we use the Distance Formula.
Which of the points $C(-6,3)$ or $D(3,0)$ is closer to the point $E(-2,1) ?$

AG
Ankit G.

### Problem 37

In these exercises we use the Distance Formula.
Which of the points $P(3,1)$ or $Q(-1,3)$ is closer to the point $R(-1,-1) ?$

AG
Ankit G.

### Problem 38

In these exercises we use the Distance Formula.
(a) Show that the points (7,3) and (3,7) are the same distance from the origin.
(b) Show that the points $(a, b)$ and $(b, a)$ are the same distance from the origin.

AG
Ankit G.

### Problem 39

In these exercises we use the Distance Formula.
Show that the triangle with vertices $A(0,2), B(-3,-1),$ and $C(-4,3)$ is isosceles.

AG
Ankit G.

### Problem 40

Find the area of the triangle shown in the figure.

AG
Ankit G.

### Problem 41

In these exercises we use the converse of the Pythagorean Theorem (see page 277 ) to show that the given triangle is a right triangle.
Refer to triangle $A B C$ in the figure below.
(a) Show that triangle $A B C$ is a right triangle by using the converse of the Pythagorean Theorem.
(b) Find the area of triangle $A B C$.

AG
Ankit G.

### Problem 42

In these exercises we use the converse of the Pythagorean Theorem (see page 277 ) to show that the given triangle is a right triangle.
Show that the triangle with vertices $A(6,-7), B(11,-3)$, and $C(2,-2)$ is a right triangle by using the converse of the Pythagorean Theorem. Find the area of the triangle.

AG
Ankit G.

### Problem 43

In these exercises we use the Distance Formula.
Show that the points $A(-2,9), B(4,6), C(1,0),$ and $D(-5,3)$ are the vertices of a square.

AG
Ankit G.

### Problem 44

In these exercises we use the Distance Formula.
Show that the points $A(-1,3), B(3,11),$ and $C(5,15)$ are collinear by showing that $d(A, B)+d(B, C)=d(A, C)$.

AG
Ankit G.

### Problem 45

In these exercises we use the Distance Formula.
Find a point on the $y$ -axis that is equidistant from the points (5,-5) and (1,1).

AG
Ankit G.

### Problem 46

In these exercises we use the Distance Formula and the Midpoint Formula.
Find the lengths of the medians of the triangle with vertices $A(1,0), B(3,6),$ and $C(8,2),$ (A median is a line segment from a vertex to the midpoint of the opposite side.)

AG
Ankit G.

### Problem 47

In these exercises we use the Distance Formula and the Midpoint Formula.
Plot the points $P(-1,-4), Q(1,1),$ and $R(4,2)$ on a coordinate plane. Where should the point $S$ be located so that the figure $P Q R S$ is a parallelogram?

AG
Ankit G.

### Problem 48

In these exercises we use the Distance Formula and the Midpoint Formula.
If $M(6,8)$ is the midpoint of the line segment $A B$ and if $A$ has coordinates $(2,3),$ find the coordinates of $B$.

AG
Ankit G.

### Problem 49

In these exercises we use the Distance Formula and the Midpoint Formula.
(a) Sketch the parallelogram with vertices $A(-2,-1)$, $B(4,2), C(7,7),$ and $D(1,4)$.
(b) Find the midpoints of the diagonals of this parallelogram.
(c) From part (b) show that the diagonals bisect each other.

AG
Ankit G.

### Problem 50

In these exercises we use the Distance Formula and the Midpoint Formula.
The point $M$ in the figure is the midpoint of the line segment $A B$. Show that $M$ is equidistant from the vertices of triangle $A B C$.

AG
Ankit G.

### Problem 51

Suppose that each point in the coordinate plane is shifted 3 units to the right and 2 units upward.
(a) The point (5,3) is shifted to what new point?
(b) The point $(a, b)$ is shifted to what new point?
(c) What point is shifted to (3,4)$?$
(d) Triangle $A B C$ in the figure has been shifted to triangle $A^{\prime} B^{\prime} C^{\prime} .$ Find the coordinates of the points $A^{\prime}, B^{\prime},$ and $C^{\prime}$.

AG
Ankit G.

### Problem 52

Suppose that the $y$ -axis acts as a mirror that reflects each point to the right of it into a point to the left of it.
(a) The point (3,7) is reflected to what point?
(b) The point $(a, b)$ is reflected to what point?
(c) What point is reflected to (-4,-1)$?$
(d) Triangle $A B C$ in the figure is reflected to triangle $A^{\prime} B^{\prime} C^{\prime}$ Find the coordinates of the points $A^{\prime}, B^{\prime},$ and $C^{\prime}$.

AG
Ankit G.

### Problem 53

A city has streets that run north and south and avenues that run east and west, all equally spaced. Streets and avenues are numbered sequentially, as shown in the figure. The walking distance between points $A$ and $B$ is 7 blocks- that is, 3 blocks east and 4 blocks north. To find the straightline distance $d$, we must use the Distance Formula.
(a) Find the straight-line distance (in blocks) between $A$ and $B$.
(b) Find the walking distance and the straight-line distance between the corner of $4 \mathrm{th}$ St. and $2 \mathrm{nd}$ Ave. and the corner of 11 th $\mathrm{St}$. and 26 th Ave.
(c) What must be true about the points $P$ and $Q$ if the walking distance between $P$ and $Q$ equals the straight-line distance between $P$ and $Q ?$

AG
Ankit G.

### Problem 54

Two friends live in the city described in Exercise $53,$ one at the corner of 3 rd St. and 7 th Ave. and the other at the corner of 27 th St. and 17 th Ave. They frequently meet at a coffee shop halfway between their homes.
(a) At what intersection is the coffee shop located?
(b) How far must each of them walk to get to the coffee shop?

AG
Ankit G.

### Problem 55

The graph shows the pressure experienced by an ocean diver at two different depths. Find and interpret the midpoint of the line segment shown in the graph.

AG
Ankit G.

### Problem 56

Plot the points $M(6,8)$ and $A(2,3)$ on a coordinate plane. If $M$ is the midpoint of the line segment $A B,$ find the coordinates of $B .$ Write a brief description of the steps you took to find $B$ and your reasons for taking them.

AG
Ankit G.

### Problem 57

Plot the points $P(0,3)$, $Q(2,2),$ and $R(5,3)$ on a coordinate plane. Where should the point $S$ be located so that the figure $P Q R S$ is a parallelogram? Write a brief description of the steps you took and your reasons for taking them.

AG
Ankit G.

### Problem 58

Write each fraction in lowest terms. If the fraction is already in lowest terms, so indicate. SEE EXAMPLE 2. (OBJECTIVE 1)
$$\frac{33}{55}$$

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### Problem 59

Write each fraction in lowest terms. If the fraction is already in lowest terms, so indicate. SEE EXAMPLE 2. (OBJECTIVE 1)
$$\frac{27}{18}$$

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### Problem 60

Write each fraction in lowest terms. If the fraction is already in lowest terms, so indicate. SEE EXAMPLE 2. (OBJECTIVE 1)
$$\frac{35}{14}$$

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### Problem 61

Write each fraction in lowest terms. If the fraction is already in lowest terms, so indicate. SEE EXAMPLE 2. (OBJECTIVE 1)
$$\frac{72}{64}$$

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### Problem 62

Write each fraction in lowest terms. If the fraction is already in lowest terms, so indicate. SEE EXAMPLE 2. (OBJECTIVE 1)
$$\frac{26}{21}$$

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### Problem 63

Perform each multiplication. Simplify each result when possible. SEE EXAMPLE 3. (OBJECTIVE 2).
$$\frac{1}{3} \cdot \frac{2}{5}$$

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### Problem 64

Perform each multiplication. Simplify each result when possible. SEE EXAMPLE 3. (OBJECTIVE 2).
$$\frac{3}{4} \cdot \frac{5}{7}$$

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### Problem 65

Perform each multiplication. Simplify each result when possible. SEE EXAMPLE 3. (OBJECTIVE 2).
$$\frac{4}{3} \cdot \frac{6}{5}$$

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### Problem 66

Perform each multiplication. Simplify each result when possible. SEE EXAMPLE 3. (OBJECTIVE 2).
$$\frac{7}{8} \cdot \frac{6}{15}$$

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### Problem 67

Perform each multiplication. Simplify each result when possible. SEE EXAMPLE 3. (OBJECTIVE 2).
$$12 \cdot \frac{5}{6}$$

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### Problem 68

Perform each multiplication. Simplify each result when possible. SEE EXAMPLE 3. (OBJECTIVE 2).
$$10 \cdot \frac{5}{12}$$

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### Problem 69

Perform each multiplication. Simplify each result when possible. SEE EXAMPLE 3. (OBJECTIVE 2).
$$\frac{10}{21} \cdot 14$$

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### Problem 70

Perform each multiplication. Simplify each result when possible. SEE EXAMPLE 3. (OBJECTIVE 2).
$$\frac{5}{24} \cdot 16$$

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### Problem 71

Perform each division. Simplify each result when possible. SEE EXAMPLE 5. (OBJECTIVE 2)
$$\frac{2}{5} \div \frac{3}{2}$$

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### Problem 72

Perform each division. Simplify each result when possible. SEE EXAMPLE 5. (OBJECTIVE 2)
$$\frac{4}{5} \div \frac{3}{7}$$

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### Problem 73

Perform each division. Simplify each result when possible. SEE EXAMPLE 5. (OBJECTIVE 2)
$$\frac{3}{4} \div \frac{6}{5}$$

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### Problem 74

Perform each division. Simplify each result when possible. SEE EXAMPLE 5. (OBJECTIVE 2)
$$\frac{3}{8} \div \frac{15}{28}$$

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### Problem 75

Perform each division. Simplify each result when possible. SEE EXAMPLE 5. (OBJECTIVE 2)
$$9 \div \frac{3}{8}$$

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### Problem 76

Perform each division. Simplify each result when possible. SEE EXAMPLE 5. (OBJECTIVE 2)
$$23 \div \frac{46}{5}$$

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### Problem 77

Perform each division. Simplify each result when possible. SEE EXAMPLE 5. (OBJECTIVE 2)
$$\frac{54}{20} \div 3$$

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### Problem 78

Perform each division. Simplify each result when possible. SEE EXAMPLE 5. (OBJECTIVE 2)
$$\frac{39}{27} \div 13$$

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### Problem 79

Perform each operation. Simplify each result when possible. See EXAMPLES 6-7.(OBJECTIVE 3)
$$\frac{3}{5}+\frac{3}{5}$$

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### Problem 80

Perform each operation. Simplify each result when possible. See EXAMPLES 6-7.(OBJECTIVE 3)
$$\frac{4}{7}-\frac{2}{7}$$

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### Problem 81

Perform each operation. Simplify each result when possible. See EXAMPLES 6-7.(OBJECTIVE 3)
$$\frac{5}{17}-\frac{3}{17}$$

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### Problem 82

Perform each operation. Simplify each result when possible. See EXAMPLES 6-7.(OBJECTIVE 3)
$$\frac{2}{11}+\frac{9}{11}$$

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### Problem 83

Perform each operation. Simplify each result when possible. See EXAMPLES 6-7.(OBJECTIVE 3)
$$\frac{1}{42}+\frac{1}{6}$$

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### Problem 84

Perform each operation. Simplify each result when possible. See EXAMPLES 6-7.(OBJECTIVE 3)
$$\frac{17}{25}-\frac{2}{5}$$

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### Problem 85

Perform each operation. Simplify each result when possible. See EXAMPLES 6-7.(OBJECTIVE 3)
$$\frac{7}{10}-\frac{1}{14}$$

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### Problem 86

Perform each operation. Simplify each result when possible. See EXAMPLES 6-7.(OBJECTIVE 3)
$$\frac{8}{25}+\frac{1}{10}$$

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### Problem 87

Perform each operation. Simplify each result when possible. SEE EXAMPLE 8.(OBJECTIVE 4)
$$4 \frac{3}{5}+\frac{3}{5}$$

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### Problem 88

Perform each operation. Simplify each result when possible. SEE EXAMPLE 8.(OBJECTIVE 4)
$$2 \frac{1}{8}+\frac{3}{8}$$

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### Problem 89

Perform each operation. Simplify each result when possible. SEE EXAMPLE 8.(OBJECTIVE 4)
$$3 \frac{1}{3}-1 \frac{2}{3}$$

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### Problem 90

Perform each operation. Simplify each result when possible. SEE EXAMPLE 8.(OBJECTIVE 4)
$$6 \frac{1}{5}-4 \frac{2}{5}$$

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### Problem 91

Perform each operation. Simplify each result when possible. SEE EXAMPLE 8.(OBJECTIVE 4)
$$3 \frac{3}{4}-2 \frac{1}{2}$$

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### Problem 92

Perform each operation. Simplify each result when possible. SEE EXAMPLE 8.(OBJECTIVE 4)
$$15 \frac{5}{6}+11 \frac{5}{8}$$

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### Problem 93

Perform each operation. Simplify each result when possible. SEE EXAMPLE 8.(OBJECTIVE 4)
$$8 \frac{2}{9}-7 \frac{2}{3}$$

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### Problem 94

Perform each operation. Simplify each result when possible. SEE EXAMPLE 8.(OBJECTIVE 4)
$$3 \frac{4}{5}-3 \frac{1}{10}$$

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### Problem 95

Change each fraction to decimal form and determine whether the decimal is a terminating or repeating
decimal. (OBJECTIVE 5)
$$\frac{3}{5}$$

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### Problem 96

Change each fraction to decimal form and determine whether the decimal is a terminating or repeating
decimal. (OBJECTIVE 5)
$$\frac{5}{9}$$

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### Problem 97

Change each fraction to decimal form and determine whether the decimal is a terminating or repeating
decimal. (OBJECTIVE 5)
$$\frac{9}{22}$$

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### Problem 98

Change each fraction to decimal form and determine whether the decimal is a terminating or repeating
decimal. (OBJECTIVE 5)
$$\frac{8}{5}$$

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### Problem 99

Perform each operation. SEE EXAMPLES 10, 11, and 12.(OBJECTIVE 5)
$$43.54+315.7$$

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### Problem 100

Perform each operation. SEE EXAMPLES 10, 11, and 12.(OBJECTIVE 5)
$$345.213-27.35$$

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### Problem 101

Perform each operation. SEE EXAMPLES 10, 11, and 12.(OBJECTIVE 5)
$$67.235-22.45$$

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### Problem 102

Perform each operation. SEE EXAMPLES 10, 11, and 12.(OBJECTIVE 5)
$$21.36+4.573$$

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### Problem 103

Perform each operation. SEE EXAMPLES 10, 11, and 12.(OBJECTIVE 5)
$$7.2 \cdot 15.6$$

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### Problem 104

Perform each operation. SEE EXAMPLES 10, 11, and 12.(OBJECTIVE 5)
$$4.21 \cdot 2.73$$

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### Problem 105

Perform each operation. SEE EXAMPLES 10, 11, and 12.(OBJECTIVE 5)
$$0 . 2 3 \longdiv { 1 . 0 4 6 5 }$$

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### Problem 106

Perform each operation. SEE EXAMPLES 10, 11, and 12.(OBJECTIVE 5)
$$4 . 7 \longdiv { 1 0 . 8 5 7 }$$

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### Problem 107

Round each of the following to two decimal places and then to three decimal places. SEE EXAMPLE 13. (OBJECTIVE 6)
$$496.2583$$

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### Problem 108

Round each of the following to two decimal places and then to three decimal places. SEE EXAMPLE 13. (OBJECTIVE 6)
$$13.0547$$

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### Problem 109

Round each of the following to two decimal places and then to three decimal places. SEE EXAMPLE 13. (OBJECTIVE 6)
$$6,025.3982$$

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### Problem 110

Round each of the following to two decimal places and then to three decimal places. SEE EXAMPLE 13. (OBJECTIVE 6)
$$1.6048$$

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### Problem 111

Perform each operation.
$$\frac{5}{12} \cdot \frac{18}{5}$$

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### Problem 112

Perform each operation.
$$\frac{5}{4} \cdot \frac{12}{10}$$

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### Problem 113

Perform each operation.
$$\frac{17}{34} \cdot \frac{3}{6}$$

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### Problem 114

Perform each operation.
$$\frac{21}{14} \cdot \frac{3}{6}$$

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### Problem 115

Perform each operation.
$$\frac{2}{13} \div \frac{8}{13}$$

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### Problem 116

Perform each operation.
$$\frac{4}{7} \div \frac{20}{21}$$

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### Problem 117

Perform each operation.
$$\frac{21}{35} \div \frac{3}{14}$$

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### Problem 118

Perform each operation.
$$\frac{23}{25} \div \frac{46}{5}$$

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### Problem 119

Perform each operation.
$$\frac{3}{5}+\frac{2}{3}$$

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### Problem 120

Perform each operation.
$$\frac{4}{3}+\frac{7}{2}$$

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### Problem 121

Perform each operation.
$$\frac{9}{4}-\frac{5}{6}$$

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### Problem 122

Perform each operation.
$$\frac{2}{15}+\frac{7}{9}$$

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### Problem 123

Perform each operation.
$$3-\frac{3}{4}$$

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### Problem 124

Perform each operation.
$$5+\frac{21}{5}$$

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### Problem 125

Perform each operation.
$$\frac{17}{3}+4$$

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### Problem 126

Perform each operation.
$$\frac{13}{9}-1$$

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### Problem 127

Use a calculator to perform each operation and round each answer to two decimal places.
$$474.81+23.4532$$

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### Problem 128

Use a calculator to perform each operation and round each answer to two decimal places.
$$843.45213-712.765$$

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### Problem 129

Use a calculator to perform each operation and round each answer to two decimal places.
$$25.25 \cdot 132.179$$

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### Problem 130

Use a calculator to perform each operation and round each answer to two decimal places.
$$234.874 \cdot 242.46473$$

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### Problem 131

Use a calculator to perform each operation and round each answer to two decimal places.
$$0 . 4 5 6 )\overline { 4 . 5 6 9 4 3 2 3 }$$

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### Problem 132

Use a calculator to perform each operation and round each answer to two decimal places.
$$4 3 . 2 2 5 )\overline { 3 2 . 4 6 5 7 4 8 }$$

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### Problem 133

Use a calculator to perform each operation and round each answer to two decimal places.
$$55.77443-0.568245$$

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### Problem 134

Use a calculator to perform each operation and round each answer to two decimal places.
$$0.62317+1.3316$$

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### Problem 135

SEE EXAMPLES 4, 9, AND 14. (OBJECTIVE 7)
A farmer has plowed $12 \frac{1}{3}$ acres of a $43 \frac{1}{2}$ -acre field. How much more needs to be plowed?

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### Problem 136

SEE EXAMPLES 4, 9, AND 14. (OBJECTIVE 7)
The four sides of a garden measure $7 \frac{2}{3}$ feet, $15 \frac{1}{4}$ feet, $19 \frac{1}{2}$ feet, and $10 \frac{3}{4}$ feet. Find the length of the fence needed to enclose the garden.

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### Problem 137

SEE EXAMPLES 4, 9, AND 14. (OBJECTIVE 7)
A designer needs $4 \frac{1}{3}$ yards of material for each dress he makes. How much material will he need to make 15 dresses?

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### Problem 138

SEE EXAMPLES 4, 9, AND 14. (OBJECTIVE 7)
Each lap around a stadium track is $\frac{1}{4}$ mile. How many laps would a runner have to complete to run 26 miles?

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### Problem 139

SEE EXAMPLES 4, 9, AND 14. (OBJECTIVE 7)
After hurricane damage estimated at 187.75 dollar million, a county sought relief from three agencies. Local agencies gave 46.8 million dollar and state agencies gave 72.5 million dollar. How much must the federal government contribute to make up the difference?

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### Problem 140

SEE EXAMPLES 4, 9, AND 14. (OBJECTIVE 7)
$26.5 \%$ of the 12,419,000 citizens of Illinois are nonwhite. How many are nonwhite?

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### Problem 141

The following circle graph shows the various sources of retirement income for a typical retired person. Use this information in Exercises $141-142.$
If a retiree has 36,000 dollar of income, how much is expected to come from pensions and Social Security?

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### Problem 142

The following circle graph shows the various sources of retirement income for a typical retired person. Use this information in Exercises $141-142.$
If a retiree has 52,000 dollar of income, how much is expected to come from earned income?

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### Problem 143

In the manufacture of active-matrix color LCD computer displays, many units must be rejected as defective. If $23 \%$ of a production run of 17,500 units is defective, how many units are acceptable?

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### Problem 144

Almost all of the water must be removed when food is preserved by freeze-drying. Find the weight of the water removed from 750 pounds of a food that is $36 \%$ water.

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### Problem 145

This year, sales at Positronics Corporation totaled 18.7 million dollar. If the projection of $12 \%$ annual growth is true, what will be next year's sales?

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### Problem 146

In tryouts for the Olympics, a speed skater had times of $44.47,43.24,42.77,$ and 42.05 seconds. Find the average time. Give the result to the nearest hundredth. (Hint: Add the numbers and divide by 4.)

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### Problem 147

Samuel drove his car 16,275.3 miles last year, averaging 25.5 miles per gallon of gasoline. If the average cost of gasoline was 3.45 dollar per gallon, find the fuel cost to drive the car.

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### Problem 148

A woman earns 48,712.32 dollar in taxable income. She must pay $15 \%$ tax on the first 23,000 dollar and $28 \%$ on the rest. In addition, she must pay a Social Security tax of $15.4 \%$ on the total amount. How much tax will she need to pay?

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### Problem 149

A rectangular parking lot is 253.5 feet long and 178.5 feet wide. A 55 -gallon drum of asphalt sealer covers 4,000 square feet and costs 97.50 dollar. Find the cost to seal the parking lot. (Sealer can be purchased only in full drums.)

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### Problem 150

Each TV a retailer buys costs 3.25 dollar per day for warehouse storage. What does it cost to store 37 TVs for three weeks?

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### Problem 151

A manufacturer of computer memory boards has a profit of 37.50 dollar on each standard-capacity memory board, and 57.35 dollar on each high-capacity board. The sales department has orders for 2,530 standard boards and 1,670 high-capacity boards. Which order will produce the greater profit?

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### Problem 152

A Holstein cow will produce 7,600 pounds of milk each year, with a $3 \frac{1}{2} \%$ butterfat content. Each year, a Guernsey cow will produce about 6,500 pounds of milk that is $5 \%$ butterfat. Which cow produces more butterfat?

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### Problem 153

Each year, a typical dairy cow will eat 12,000 pounds of food that is $57 \%$ silage. To feed 30 cows, how much silage will a farmer use in a year?

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### Problem 154

Two carpenters bid on a home remodeling project. The first bids 9,350 dollar for the entire job. The second will work for 27.50 dollar per hour, plus 4,500 dollar for materials. He estimates that the job will take 150 hours. Which carpenter has the lower bid?

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### Problem 155

A high-efficiency home heating system can be installed for 4,170 dollar, with an average monthly heating bill of 57.50 dollar. A regular furnace can be installed for 1,730 dollar, but monthly heating bills average 107.75 dollar. After three years, which system has cost more altogether?

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### Problem 156

Refer to Exercise $155 .$ Decide which furnace system will have cost more after five years.

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### Problem 157

Describe how you would find the common denominator of two fractions.

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### Problem 158

Explain how to convert an improper fraction into a mixed number.

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### Problem 159

Explain how to convert a mixed number into an improper fraction.

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### Problem 160

Explain how you would decide which of two decimal fractions is the larger.

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### Problem 161

In what situations would it be better to leave an answer in the form of an improper fraction?

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### Problem 162

When would it be better to change an improper-fraction answer into a mixed number?

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### Problem 163

Can the product of two proper fractions be larger than either of the fractions?

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### Problem 164

How does the product of one proper and one improper fraction compare with the two factors?

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