| № |
Condition |
free/or 0.5$ |
| m66516 | A mail-order garden equipment business shipped 120 packages one day. Customers were charged $3.50 for each standard-delivery package and $7.50 for each express-delivery package. Total shipping charges for the day were $596. How many of each kind of package were shipped? |
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| m66525 | A manufacturer determines that a product will reach the breakeven point if sold at either $80 or $150. At $80, the expense and revenue values are both $300,000. At $150, the expense and revenue values are both $100,000.
On graph paper, graph possible revenue and expense functions that depict this situation. Circle the breakeven points. |
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| m66532 | A manufacturer of tools, selling rechargeable drills to a chain of home improvement stores, charges $2 more per drill than its manufacturing cost m. The chain then sells each drill for 150% of the price that it paid the manufacturer. Find a function P(m) for the price at the home improvement stores. |
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| m66533 | A manufacturer produces exterior plywood, interior plywood, and fiberboard, which are shipped to two distributors. The table below shows the number of units of each type of product that are shipped to each warehouse.
a) Write the information in the table as a 3 × 2 matrix M.
b) Write a row matrix P that represents the profit, per unit, of each type of product.
c) Find the product PM.
d) State what the entries of PM represent. |
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| m66546 | A math instructor asked her students to keep track of how much time each spent studying a chapter on functions in her algebra-trigonometry course. She collected the information together with test scores from that chapter s test. The data are listed in the table below.
Study Time, x (in hours) Test Grade, y (in percent)
23 ............................................. 81%
15 ............................................. 85
17 ............................................. 80
9 .............................................. 75
21 ............................................. 86
13 ............................................. 80
16 ............................................. 85
11 ............................................. 93
(a) Use a graphing calculator to model the data with a linear function.
(b) Predict a student s score if he or she studies 24 hr, 6 hr, and 18 hr.
(c) What is the correlation coefficient? How confident are you about using the regression line to predict function values? |
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| m66555 | A model for advertising response is given by the function
N(a) = 1000 + 200 ln a, a ≥ 1,
Where N(a) is the number of units sold when a is the amount spent on advertising, in thousands of dollars.
a) How many units were sold after spending $1000 (a = 1) on advertising?
b) How many units were sold after spending $5000?
c) Graph the function.
d) How much would have to be spent in order to sell 2000 units? |
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| m66556 | A model rocket is launched with an initial velocity of 120 ft/sec from a height of 80 ft. The height of the rocket, in feet, t seconds after it has been launched is given by the function s(t) = -16t2 + 120t + 80. Determine the time at which the rocket reaches its maximum height and find the maximum height. |
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| m66557 | A model rocket is launched with an initial velocity of 150 ft/sec from a height of 40 ft. The function s(t) = -16t2 + 150t + 40 gives the height of the rocket, in feet, t seconds after it has been launched. Determine the time at which the rocket reaches its maximum height and find the maximum height. |
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| m66560 | A moving helper company gave Mike these two quotes. Use a system of equations to determine the hourly rates for loading/unloading and packing / unpacking?
3 hours of loading/unloading
2 hours of packing/unpacking Total cost: $480
5 hours of loading/unloading
2 hours of packing/unpacking Total cost: $680
Situation A: He hires 5 helpers to load and unload the truck and travels 80 miles on back roads for a total cost of $780.
Situation B: He hires 6 helpers to load and unload the truck and takes a highway route which adds 20 miles to the trip but gets the truck to the destination faster for a total cost of $960. |
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| m66566 | A nanometer is 0.000000001 m. Scientists have developed optical nanowires to transmit light wave s short distances. A nanowire with a diameter of 360 nanometers has been used in experiments on the transmission of light. |
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| m66576 | A Norman window is a rectangle with a semicircle on top. Sky Blue Windows is designing a Norman window that will require 24 ft of trim on the outer edges. What dimensions will allow the maximum amount of light to enter a house? |
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| m66578 | A one-cup serving of spaghetti with meatballs contains 260 Cal (calories) and 32 g of carbohydrates. A one-cup serving of chopped iceberg lettuce contains 5 Cal and 1 g of carbohydrates. (Source: Home and Garden Bulletin No. 72, U.S. Government Printing Office, Washington, D.C. 20402) how many servings of each would be required in order to obtain 400 Cal and 50 g of carbohydrates? |
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| m66584 | A parking garage charges $2 for up to (but not including) 1 hr of parking, $4 for up to 2 hr of parking, $6 for up to 3 hr of parking, and so on. Let C(t) = the cost of parking for t hours.
(a) Graph the function.
(b) Write an equation for C(t) using the greatest integer notation [t]. |
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| m66588 | A partnership owned equally by 13 partners is worth $1.3 million. The partnership loses a lawsuit worth $3 million. What is the value of any personal property each partner must forfeit to pay the settlement? Explain. |
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| m66589 | A pay phone at a railroad station charges $0.55 for the first five minutes (or part of) and $0.25 for each extra minute (or part of). Express the cost c(m) of an m-minute phone call as a piecewise function using the greatest integer function. |
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| m66590 | A pay phone at a shopping mall charges $0.68 for the first four minutes and $0.21 for each extra minute (or part of a minute).
a. Find the cost of a 10-minute call on this phone.
b. Find the cost of a 13.44-minute call on this phone. |
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| m66591 | A penny, a nickel, a dime, and a quarter are arranged in a straight line.
a) Considering just the coins, in how many ways can they be lined up?
b) Considering the coins and heads and tails, in how many ways can they be lined up? |
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| m66594 | A person who is exercising should not exceed his or her maximum heart rate, which is determined on the basis of that person s sex, age, and resting heart rate. The table below relates resting heart rate and maximum heart rate for a 20-year-old man.
Resting Heart Rate, Maximum Heart Rate,
H (in beats per minute) M (in beats per minute)
50 .................................................... 166
60 .................................................... 168
70 .................................................... 170
80 .................................................... 172
(a) Use a graphing calculator to model the data with a linear function.
(b) Estimate the maximum heart rate if the resting heart rate is 40, 65, 76, and 84.
(c) What is the correlation coefficient? How confident are you about using the regression line to estimate function values? |
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| m66603 | A phone company set the following rate schedule for an m-minute call from any of its pay phones.
a. What is the cost of a call that is under six minutes?
b. What is the cost of a 14-minute call?
c. What is the cost of a 9 1 / 2 minute call? |
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| m66605 | A piece of paper is 0.01 in. thick. It is cut and stacked repeatedly in such a way that its thickness is doubled each time for 20 times. How thick is the result? |
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