| № |
Condition |
free/or 0.5$ |
| m66606 | A ping-pong ball is dropped from a height of 16 ft and always rebounds 14 of the distance fallen.
a) How high does it rebound the 6th time?
b) Find the total sum of the rebound heights of the ball. |
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| m66607 | A pitcher s earned-run average E varies directly as the number R of earned runs allowed and inversely as the number I of innings pitched. In 2010, Bronson Arroyo of the Cincinnati Reds had an earned-run average of 3.89. He gave up 93 earned runs in 215.2 innings. How many earned runs would he have given up had he pitched 238 innings with the same average? Round to the nearest whole number. |
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| m66615 | A politician is listening to y a proposal for a new Social Security tax plan. The graph is shown. The two parts of the graph are disconnected where x = 100,000. Explain why this would be an unfair Social Security tax function. |
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| m66624 | A power line is constructed from a power station at point A to an island at point I, which is 1 mi directly out in the water from a point B on the shore. Point B is 4 mi downshore from the power station at A. It costs $5000 per mile to lay the power line under water and $3000 per mile to lay the power line under ground. The line comes to the shore at point S downshore from A. Let x = the distance from B to S.
(a) Express the cost C of laying the line as a function of x.
(b) At what distance x from point B should the line come to shore in order to minimize cost? |
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| m66627 | A private airplane leaves Midway Airport and flies due east at a speed of 180 km/h. Two hours later, a jet leaves Midway and flies due east at a speed of 900 km/h. How far from the airport will the jet overtake the private plane? |
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| m66633 | A professor is going to grade her 24 students on a curve. She will give 3 A s, 5 B s, 9 C s, 4 D s, and 3 F s. In how many ways can she do this? |
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| m66635 | A program is planned to have 5 musical numbers and 4 speeches. In how many ways can this be done if a musical numberand a speech are to alternate and a musical number is to come first? |
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| m66652 | A rancher has 360 yd of fencing with which to enclose two adjacent rectangular corrals, one for horses and one for cattle. A river forms one side of the corrals. Suppose the width of each corral is x yards.
(a) Express the total area of the two corrals as a function of x.
(b) Find the domain of the function.
(c) Using the graph of the function shown below, determine the dimensions that yield the maximum area. |
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| m66653 | A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. If a river forms one side of the corrals and 240 yd of fencing is available, what is the largest total area that can be enclosed? |
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| m66685 | A rectangle has a perimeter of 38 m and an area of 84 m2. What are the dimensions of the rectangle? |
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| m66686 | A rectangle is inscribed in a semicircle of radius 2, as shown. The variable x = half the length of the rectangle. Express the area of the rectangle as a function of x. |
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| m66687 | A rectangle that is x feet wide is inscribed in a circle of radius 8 ft.
(a) Express the area of the rectangle as a function of x.
(b) Find the domain of the function.
(c) Graph the function with a graphing calculator.
(d) What dimensions maximize the area of the rectangle? |
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| m66688 | A rectangular banner with an area of √3 m2 is being designed to advertise an exhibit at the Davis Gallery. The length of a diagonal is 2 m. Find the dimensions of the banner. |
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| m66689 | A rectangular box with volume 320 ft3 is built with a square base and top. The cost is $1.50 / ft2 for the bottom, $2.50 / ft2 for the sides, and $1 / ft2 for the top. Let x = the length of the base, in feet.
(a) Express the cost of the box as a function of x.
(b) Find the domain of the function.
(c) Graph the function with a graphing calculator.
(d) What dimensions minimize the cost of the box? |
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| m66690 | A rectangular room has length L and width W, where L and W are measured in feet.
a. Express the area in square feet algebraically.
b. If carpeting costs x dollars per square yard, express the cost of carpeting this room algebraically? |
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| m66691 | A rectangular room is 14 feet by 20 feet. The ceiling is 8 feet high.
a. Find the length and width of the smaller wall.
b. Find the area of the smaller wall.
c. Find the area of the larger wall.
d. Find the total area of the four walls in the room.
e. If a gallon of paint costs $36.50 and it covers 350 square feet on average, what is the cost of painting the room with two coats of paint? Explain your answer.
f. This room is well-insulated and is on the north side of the house.
How large an air conditioner would this room require? Round to the nearest thousand BTUs. |
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| m66692 | A rectangular room measures 13 feet by 15 feet. It is going to be carpeted with carpeting that sells for $68 per square yard.
a. What is the area of the room in square feet?
b. If the room is drawn to ¼ inch represents 1 foot scale, give the dimensions of the room in inches on the scale drawing.
c. A yard equals 3 feet. How many square feet are in a square yard?
d. How many square yards will it take to carpet the room? Round up to the next greater integer.
e. What is the total price for the carpeting?
f. In the early mid-2000s, there was a dramatic increase in the price of carpeting, since it was a petroleum-based product. As a result, selling by the yard made it look expensive. Some stores started selling carpet by the square foot. How much would a square yard of carpet selling for $8.95 per square foot cost?
g. This room is well-insulated and is on the south side of the house. It has an 8-foot-high ceiling. How large an air conditioner would this room require? Round to the nearest thousand BTUs. |
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| m66693 | A rectangular room measures 18 feet by 25 feet. It is going to be carpeted with carpeting that sells for $8.45 per square foot.
a. What is the area of the room in square feet?
b. If the room is drawn to a scale of ¼ inch represents 1 foot, give the dimensions of the room in inches on the scale drawing.
c. This room is well-insulated and on the south side of the house. It has an 8-foot-high ceiling. How large an air conditioner would this room require? Round to the nearest thousand BTUs. |
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| m66694 | A rectangular room measures x feet by y feet, where x < y. The ceiling is c feet high. The walls and the ceiling will be painted the same color.
a. Express the area of the smaller wall and the larger wall algebraically.
b. Express the total area of the room algebraically.
c. Express the area of the ceiling algebraically.
d. If a gallon of paint covers 400 square feet, express the amount of paint you will need algebraically? |
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| m66716 | A restaurant purchased a 72-in. range with six burners for $6982. The value of the range each year is 85% of the value of the preceding year. After t years, its value, in dollars, is given by the exponential function
V(t) = 6982(0.85)t.
a) Graph the function.
b) Find the value of the range after 0, 1, 2, 5, and 8 years.
c) The restaurant decides to replace the range when its value has declined to $1000. After how long will the range be replaced? |
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