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At a small toy manufacturer, a day’s salary for an assembly worker is $120. The supervisor wants to determine the average assembly cost per toy. An assembly worker can assemble up to 200 toys in a day. a.Write a model for the average assembly cost per toy if the worker puts together t toys in a day. 7.1-1 1

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At a small toy manufacturer, a day’s salary for an assembly worker is $120. The supervisor wants to determine the average assembly cost per toy. An assembly worker can assemble up to 200 toys in a day. b. What is the average assembly cost per toy if the worker puts together 100 toys in a day? 7.1-1 2

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At a small toy manufacturer, a day’s salary for an assembly worker is $120. The supervisor wants to determine the average assembly cost per toy. An assembly worker can assemble up to 200 toys in a day. c.What would be a reasonable domain and range for this model? Explain. 7.1-1 3

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The cost for sod (grass) is directly proportional to the number of square feet purchased. It cost $168 to purchase 400 square feet of sod. a.Write a model for the cost of this sod. 7.1-2 4

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The cost for sod (grass) is directly proportional to the number of square feet purchased. It cost $168 to purchase 400 square feet of sod. b.What is the cost for 2000 square feet of sod? 7.1-2 5

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The cost for sod (grass) is directly proportional to the number of square feet purchased. It cost $168 to purchase 400 square feet of sod. c.If Mark was charged $2310 for sod how much did he purchase? 7.1-2 6

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The illumination of a light source in foot candles is inversely proportional to the square of the distance in feet from the light source. A projector provides an illumination of 140 foot candles when placed 5 ft from the screen. a.Write a model for the illumination of this projector. 7.1-3 7

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The illumination of a light source in foot candles is inversely proportional to the square of the distance in feet from the light source. A projector provides an illumination of 140 foot candles when placed 5 ft from the screen. b.What is the illumination from this projector when it is placed 7 ft from the screen? 7.1-3 8

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a.If y varies inversely with 5x and y = 5.6 when x = 30, write an equation to represent this relationship. 7.1-4 9 b.Find y when x = 12

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The total United States debt to foreign countries can be modeled by Where D(t) is the total US debt held by foreign countries in billions of dollars t years since 2000. The United States population can be modeled by Where P(t) is the population of the United States in billions t years since 2000. Source: Models derived from data at the US Treasury Department and Google.com. a.Estimate the amount of US debt to foreign countries in 2010. 7.1-5 10

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The total United States debt to foreign countries can be modeled by Where D(t) is the total US debt held by foreign countries in billions of dollars t years since 2000. The United States population can be modeled by Where P(t) is the population of the United States in billions t years since 2000. Source: Models derived from data at the US Treasury Department and Google.com. b.Estimate the population of the US in 2010. 7.1-5 11

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The total United States debt to foreign countries can be modeled by Where D(t) is the total US debt held by foreign countries in billions of dollars t years since 2000. The United States population can be modeled by Where P(t) is the population of the United States in billions t years since 2000. Source: Models derived from data at the US Treasury Department and Google.com. c.Find a model for the average amount of foreign debt per person in the US. 7.1-5 12

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The total United States debt to foreign countries can be modeled by Where D(t) is the total US debt held by foreign countries in billions of dollars t years since 2000. The United States population can be modeled by Where P(t) is the population of the United States in billions t years since 2000. Source: Models derived from data at the US Treasury Department and Google.com. d.Estimate the average amount of foreign debt per person in the US in 2012. 7.1-5 13

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Find the domain of the following rational functions. Determine if the excluded values represent where a vertical asymptote or a hole appear in the graph. a. 7.1-6 14

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Find the domain of the following rational functions. Determine if the excluded values represent where a vertical asymptote or a hole appear in the graph. b. 7.1-6 15

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Find the domain of the following rational functions. Determine if the excluded values represent where a vertical asymptote or a hole appear in the graph. c. 7.1-6 16

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Simplify the following rational expressions. a. b. 7.2-1 17

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Simplify the following rational expressions. a. b. 7.2-2 18

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Simplify the following rational expressions. c. 7.2-2 19

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Simplify the following rational expressions. a. 7.2-3 20

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Simplify the following rational expressions. a. 7.2-4 21

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a. Divide b. Divide by by 7.2-5 22

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a. Divide b. Divide by by 7.2-6 23

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a. Use synthetic division to divide by b. Divide by 7.2-7 24

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Multiply the following rational expressions. a. b. 7.3-1 25

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Multiply the following rational expressions. a. b. 7.3-2 26

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Divide the following. a. b. 7.3-3 27

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Divide the following rational expressions. 7.3-4 28

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Find the least common denominator for each of the following sets of fractions and rewrite each fraction in terms of the LCD. a. b. 7.4-1 29

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Find the least common denominator for each of the following sets of fractions and rewrite each fraction in terms of the LCD. a. b. 7.4-2 30

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Add the following rational expressions. a. b. 7.4-3 31

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Add the following rational expressions. a. 7.4-3 32

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Add the following rational expressions. a. b. 7.4-4 33

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Subtract the following rational expressions. a. b. 7.4-5 34

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Simplify the following complex fractions. a. b. 7.4-6 35

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Solve the rational equation 7.5-1 36

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At a small toy manufacturer, a day’s salary for an assembly worker is $120. The supervisor wants to determine the average assembly cost per toy. An assembly worker can assemble up to 200 toys in a day. In section 7.1 we found the model Where is the average assembly cost in dollars per toy when t toys are put together in a day. How many toys does the worker need to put together in a day to keep the average assembly cost to $0.75 per toy? 7.5-2 37

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Solve the following rational equation. Check your answer in the original equation. 7.5-3 38

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In Section 7.1 we found a model for the average amount of foreign debt per person in the US in dollars, t years since 2000. In what year will the average amount of foreign debt per person in the US be $100,000? 7.5-4 39

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Solve the following rational equations. Check your answer in the original equation. a. 7.5-5 40

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Solve the following rational equations. Check your answer in the original equation. b. 7.5-5 41

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A new machine can produce an order of books in 6 hours. An older machine can produce the same order of books in 10 hours. How long would it take both machines working together to produce the order of books? 7.5-6 42

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