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About 11892 results. 1294 free access solutions
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| m66306 | A college food service manager uses a table like the one below to list the number of units of ingredients, by weight, required for various menu items.
The cost per unit of each ingredient is 25 cents for flour, 34 cents for milk, 54 cents for eggs, and 83 cents for butter.
a) Write the information in the table as a 4 × 4 matrix M.
b) Write a row matrix C that represents the cost per unit of each ingredient.
c) Find the product CM.
d) State what the entries of CM represent. |
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| m66310 | A company begins an Internet advertising campaign to market a new phone. The percentage of the target market that buys a product is generally a function of the length of the advertising campaign. The estimated percentage is given by
f(t) = 100(1 - e-0.04t),
Where t is the number of days of the campaign
a) Graph the function.
b) Find f (25), the percentage of the target market that has bought the phone after a 25-day advertising campaign.
c) After how long will 90% of the target market have bought the phone? |
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| m66312 | A company introduced a new software product on a trial run in a city. They advertised the product on television and found the following data regarding the percent P of people who bought the product after x ads were run.
Number of Ads, x Percentage Who Bought, P
0 ........................................ 0.2%
10 .......................................... 0.7
20 ......................................... 2.7
30 .......................................... 9.2
40 ........................................ 27.0
50 ........................................ 57.6
60 ........................................ 83.3
70 ........................................ 94.8
80 ........................................ 98.5
90 ........................................ 99.6
a) Use a graphing calculator to fit a logistic function
P(x) = a / (1 + be-kx) to the data.
b) What percent of people bought the product when 55 ads were run 100 ads?
c) Find the horizontal asymptote for the graph. Interpret the asymptote in terms of the advertising situation. |
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| m66320 | A company that produces widgets has found its demand function to be q = -1,500p + 90,000.
a. For each dollar increase in the wholesale price, how many fewer widgets are demanded?
b. How many widgets would be demanded at a price of $20?
c. How many widgets would be demanded at a price of $21? d. What is the difference in quantity demanded caused by the $1 increase in wholesale price?
e. The company sets a price of $22.50. How many widgets will be demanded?
f. How much will all of the widgets cost the store to purchase at a price of $22.50?
g. If the store marks up the widgets that cost $22.50 at a rate of 50%, what is the retail price of each widget? |
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| m66329 | A consumer budgets $480 per month for transportation. She has determined that the cost of a round-trip train ride is $4 and the cost of each round-trip car ride (factoring in gas, oil, etc.) is $3.
a. Write a budget line equation for this situation.
b. Construct the budget line graph that models this situation.
c. What do the points on the budget line represent?
d. What do points below the budget line represent?
e. Suppose that the budgeted amount increases to $516. Construct the new budget line and the old budget line on the same axes.
f. What does the region in between the two lines represent? |
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| m66332 | A container firm is designing an open-top rectangular box, with a square base, that will hold 108 in3. Let x = the length of a side of the base.
(a) Express the surface area as a function of x.
(b) Find the domain of the function.
(c) Using the graph below, determine the dimensions that will minimize the surface area of the box. |
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| m66334 | A contractor buys a new truck for $23,000. The truck is purchased on January 1 and is expected to last 5 years, at the end of which time its trade-in, or salvage, value will be $4500. If the company figures the decline or depreciation in value to be the same each year, then the salvage value V, after t years, is given by the linear function
V(t) = $23,000 - $3700t, for 0 ≤ t ≤ 5.
(a) Graph V.
(b) Find V(0), V(1), V(2), V(3), and V(5).
(c) Find the domain and the range of this function. |
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| m66336 | A corporation is having a shareholders meeting. Not all shareholders are able to attend. In fact, most usually do not. The ownership of the corporation is represented by 2,351,000 shares of stock owned by 111,273 shareholders.
a. Must all of the shareholders own more than one share of stock?
b. If 3,411 shareholders attend the meeting, what percent of the shareholders are represented? Round to the nearest percent.
c. If the shareholders who do attend own a combined 1.8 million shares of the corporation, what percent of the shares are represented at the meeting? Round to the nearest percent. |
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| m66337 | A corporation issues 1,200,000 shares of stock at its beginning to shareholders. How many shares must a shareholder own to have a majority of the shares? |
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| m66338 | A corporation produces mini-widgets. The variable expenses are $1.24 per mini-widget, and the fixed expenses are $142,900.
a. How much does it cost to produce 1 mini-widget?
b. How much does it cost to produce 20,000 mini-widgets?
c. Express the expense function algebraically.
d. What is the slope of the expense function?
e. If the slope is interpreted as a rate, give the units that would be used. |
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| m66344 | A cross section of a nuclear cooling tower is a hyperbola with equation
x2 / 902 - y2 / 1302 = 1.
The tower is 450 ft tall, and the distance from the top of the tower to the center of the hyperbola is half the distance from the base of the tower to the center of the hyperbola. Find the diameter of the top and the base of the tower.
The eccentricity of a hyperbola is defined as e = c > a. For a hyperbola, c > a > 0, so e > 1 when e is close to 1, a hyperbola appears to be very narrow as the eccentricity increases, the hyperbola becomes "wider." |
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| m66349 | A DC10 airplane travels 3000 km with a tailwind in 3 hr. It travels 3000 km with a headwind in 4 hr. Find the speed of the plane and the speed of the wind. |
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| m66350 | A deferred payment plan is also similar to an installment plan, except there are very low monthly payments until the end of the agreement. At that point, the entire purchase must be paid in full. If it is not paid, there will be high finance charges. Often, there is no interest-stores use no-interest deferred payment plans to attract customers. Many times there is also no down payment.
a. Chris purchases a living room furniture set for $4,345 from Halloran Gallery. She has a one-year, no interest, no money down, deferred payment plan. She does have to make a $15 monthly payment for the first 11 months. What is the sum of these monthly payments?
b. How much must Chris pay in the last month of this plan?
c. What is the difference between the layaway plan in Exercise 12 and the deferred payment plan? |
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| m66351 | a. Determine the correlation coefficient and linear regression equation that expresses the square footage as a function of the monthly rent. Round the numbers in the equation to the nearest hundredth.
b. Use your regression equation to determine the square footage you might expect if renting a $1,710 apartment? |
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| m66352 | (a) Determine whether the relation 51{(-4, 7), (3, 0), (1, 5), (0, 7) is a function. Answer yes or no.
(b) Find the domain of the relation.
(c) Find the range of the relation. |
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| m66353 | a) Determine whether there is a maximum of minimum value and find that value.
b) Determine whether there is a maximum or minimum value and find that value.
c) Find the range?
1. h(x) = - 2x2 + 3x - 8
2. g(x) = x2 - 10x + 2 |
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| m66354 | A device used in golf to estimate the distance d, in yards, to a hole measures the size s, in inches, that the 7-ft pin appears to be in a viewfinder. Express the distance d as a function of s. |
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| m66355 | A diabetic patient wishes to prepare a meal consisting of roasted chicken breast, mashed potatoes, and peas. A 3-oz serving of roasted skinless chicken breast contains 140 Cal, 27 g of protein, and 64 mg of sodium. A one-cup serving of mashed potatoes contains 160 Cal, 4 g of protein, and 636 mg of sodium, and a one-cup serving of peas contains 125 Cal, 8 g of protein, and 139 mg of sodium. (Source: Home and Garden Bulletin No. 72, U.S. Government Printing Office, Washington, D.C. 20402) How many servings of each should be used if the meal is to contain 415 Cal, 50.5 g of protein, and 553 mg of sodium? |
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| m66357 | A dietician must plan a breakfast menu that provides 460 Cal, 9 g of fat, and 55 mg of calcium. One plain bagel contains 200 Cal, 2 g of fat, and 29 mg of calcium. A one-tablespoon serving of cream cheese contains 100 Cal, 10 g of fat, and 24 mg of calcium. One banana contains 105 Cal, 1 g of fat, and 7 g 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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| m66385 | a) Find the vertex.
b) Find the axis of symmetry.
c) Determine whether there is a maximum or minimum value and find that value.
1. g(x) = x2 - 6
2. f (x) = -x2 + 6x - 8
3. G(x) = -2x2 - 4x - 7 |
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