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Condition |
free/or 0.5$ |
| m66431 | A graphing calculator has determined the following exponential regression equation: y = a*bx, a = 28,158.50, b = 0.815.
a. What is the rate of depreciation for this car?
b. How much is this car worth to the nearest dollar after 6 years?
c. How much is this car worth to the nearest hundred dollars after 39 months?
d. How much is this car worth after y years? |
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| m66432 | A graphing calculator has determined this exponential regression equation based upon car value data: y = a*bx, a = 20,952.11, and b = 0.785. What is the rate of depreciation for this car? How much is this car worth after 6 years; 78 months; w years? |
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| m66433 | A graphing calculator has determined this exponential regression equation based upon car value data: y = a*bx, a = 18,547.23 and b = 0.8625. What is the rate of depreciation 4 for this car? How much is this car worth after 6 years, 78 months, and w months? |
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| m66438 | A group of randomly-selected recent college graduates were asked how much the monthly payment is on their student loan. The responses are shown in the stem-and-leaf plot.
a. What is the total frequency?
b. How many people had monthly payments between $210 and $219?
c. What is the mode monthly payment?
d. What is the median monthly payment? |
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| m66447 | A heavy-duty flashlight mirror has a parabolic cross section with diameter 6 in. and depth 1 in.
a) Position a coordinate system with the origin at the vertex and the x-axis on the parabola s axis of symmetry and find an equation of the parabola.
b) How far from the vertex should the bulb be positioned if it is to be placed at the focus? |
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| m66448 | A homeowner wants to fence a rectangular play yard using 80 ft of fencing. The side of the house will be used as one side of the rectangle. Find the dimensions for which the area is a maximum. |
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| m66451 | A hospital dietician must plan a lunch menu that provides 485 Cal, 41.5 g of carbohydrates, and 35 mg of calcium. A 3-oz serving of broiled ground beef contains 245 Cal, 0 g of carbohydrates, and 9 mg of calcium. One baked potato contains 145 Cal, 34 g of carbohydrates, and 8 mg of calcium. A one-cup serving of strawberries contains 45 Cal, 10 g of carbohydrates, and 21 mg of calcium. (Source: Home and Garden Bulletin No. 72, U.S. Government Printing Office, Washington, D.C. 20402) How many servings of each are required to provide the desired nutritional values? |
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| m66453 | A hot-air balloon rises straight up from the ground at a rate of 120 ft / min. The balloon is tracked from a rangefinder on the ground at point P, which is 400 ft from the release point Q of the balloon. Let d = the distance from the balloon to the rangefinder and t = the time, in minutes, since the balloon was released. Express d as a function of t. |
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| m66481 | A jewelry manufacturer has determined the expense equation for necklaces to be E = 1,250q + 800,000, where q is the quantity demanded. At a particular price, the breakeven revenue is $2,600,000.
a. What is the quantity demanded at the breakeven point?
b. If the breakeven revenue changes to 3.5 million, will the quantity demanded have increased or decreased? Explain. |
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| m66483 | A kayak moves at a rate of 12 mph in still water. If the river s current flows at a rate of 4 mph, how long does it take the boat to travel 36 mi upstream? |
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| m66486 | A lake is stocked with 640 fish of a new variety. The size of the lake, the availability of food, and the number of other fish restrict the growth of that type of fish in the lake to a limiting value of 3040. The population of fish in the lake after time t, in months, is given by the function
P(t) = 3040 / (1 + 3.75e-0.32t)
a) Graph the function.
b) Find the population after 0, 1, 5, 10, 15, and 20 months. |
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| m66487 | A landscape company purchased a backhoe for $56,395. The value of the backhoe each year is 90% of the value of the preceding year. After t years, its value, in dollars, is given by the exponential function
V(t) = 56,395(0.9)t .
a) Graph the function.
b) Find the value of the backhoe after 0, 1, 3, 6, and 10 years. Round to the nearest dollar
c) The company decides to replace the backhoe when its value has declined to $30,000. After how long will the machine be replaced? |
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| m66489 | A large appliance such as a water heater is only running when it has clicked on and is actually heating water. The time your water heater is on varies according to how much you do laundry, take showers, or run the dishwasher. The national average is 3 hours per day.
a. If a water heater uses 4,200 watts, find the daily cost of running it at a cost of $0.11 per kilowatt-hour. Round to the nearest ten cents.
b. Find the annual cost of running the water heater to the nearest ten dollars.
c. A certain energy-saving water heater sells for $1,100. It will save 36% in energy costs per year compared to the water heater from parts a and b. What will be the approximate annual cost of running this water heater? Round to the nearest ten dollars. d. In how many years will the new water heater "pay for itself"? |
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| m66498 | A Leisure Time Cruises riverboat travels 46 km downstream in 2 hr. It travels 51 km upstream in 3 hr. Find the speed of the boat and the speed of the stream. |
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| m66506 | A loan used for buying a home is called a mortgage. The Fortuna to family is buying a $430,000 home. They are taking out a 30-year mortgage at a rate of 8%.
a. Compute the monthly payment.
b. Find the total of all of the monthly payments for the 30 years.
c. What is the finance charge?
d. Which is greater, the interest or the original cost of the home? |
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| m66507 | A local cable TV/Internet/phone provider charges new customers $90 for all three services, per month, for the first year under their 90 NOW promotion. Alice normally pays $59 for her monthly home phone service, $29 for Internet service, and $69 for cable television.
a. What are her percent savings if she switches to the 90 NOW plan? Round to the nearest percent.
b. Craig usually pays x dollars for phone service, half of that for Internet service, and twice that for cable TV service monthly. Represent his annual cost for these services algebraically. |
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| m66508 | A local cable TV/Internet/phone provider charges new customers $99 for all three services, per month, for the first year under their "3 for 99" promotion. Joanne normally pays $54 for her monthly home phone service, $39 for Internet service, and $49 for cable television.
a. What are her percent savings if she switches to the "3 for 99" plan? Round to the nearest percent.
b. If, after the first year, the flat fee for all three services is $129, what are her percent savings?
c. Craig usually pays p dollars for phone service, i dollars for Internet service, and c dollars for cable TV service monthly. Represent his savings under the "3 for 99" plan algebraically, as a percent. |
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| m66509 | A local hairdresser bought 450 shares of a cosmetics corporation for $33.50 per share. He sold the shares for $39.01 per share.
a. What was the percent increase in the price per share? Round to the nearest tenth of a percent.
b. What was the total purchase price for the 450 shares?
c. What was the total selling price for the 450 shares?
d. What was the percent capital gain for the 450 shares? Round to the nearest tenth of a percent. |
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| m66510 | A local newspaper charges by the character for its classified ads. Letters, numbers, spaces, and punctuation each count as one character. They charge $46 for the first 200 characters and $0.15 for each additional character.
a. If x represents the number of characters in the ad, express the cost c(x) of an ad as a piecewise function.
b. Graph the function from part a.
c. Find the coordinates of the cusp in the graph in part |
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| m66511 | A local Pennysaver charges $11 for each of the first three lines of a classified ad, and $5 for each additional line.
a. What is the price of a two-line ad?
b. What is the price of a five-line ad?
c. If x is the number of lines in the ad, express the cost c(x) of the ad as a piecewise function. |
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