| № |
Condition |
free/or 0.5$ |
| m67786 | Darlene purchases $20,000 worth of stock on her broker s advice and pays her broker a 1.5% broker fee. She sells her stock when it increases to $28,600 two years later, and uses a discount broker who charges $21 per trade. Compute Darlene s net proceeds after the broker fees are taken out. |
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| m67791 | Data on average credit-card debt per U.S. household are given in the table below. Model the data with a linear function, and estimate the average debt in 2007 and in 2014. Answers may vary depending on the data points used.
Year, x Credit-Card Debt
Per Household, y
1992, 0 .............................................. $ 3,803
1996, 0 ........................................ 6,912
2000, 8 ........................................ 8,308
2004, 12 ........................................ 9,577
2008, 16 ........................................ 10,691
2011, 19 ........................................ 14,750 |
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| m67793 | Data on the median age of the U.S. population in selected years are listed in the table below. Model the data with a linear function, estimate the median age in 1998, and predict the median age in 2020. Answers may vary depending on the data points used.
Year, x Total U.S. Expenditures
1970, 0 ............................ 28.0
1980, 10 ......................... 30.0
1990, 20 ......................... 32.8
2000, 30 ......................... 35.3
2008, 38 .......................... 36.8
2011, 41 .......................... 36.9* |
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| m67797 | Data on total U.S. expenditures on pets, pet products, and related services are given in the table below. Model the data with a linear function. Then, using that function, estimate total U.S. expenditures on pets in 2005 and predict total expenditures in 2015. Answers may vary depending on the data points used.
Year, x Total U.S. Expenditures
On pets (in billions)
1991, 0 ............................................... $19.6
1994, 3 ........................................... 24.9
1997, 6 ........................................... 32.5
2000, 9 .......................................... 39.7
2003, 12 .......................................... 46.8
2006, 15 .......................................... 56.9
2009, 18 .......................................... 67.1 |
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| m67812 | Dave wants to borrow $22,000 from First Finance Bank. The bank will give him a 15-year loan at an interest rate of 4.85%. How much will he pay the bank in interest over the life of the loan? Round to the nearest hundred dollars. |
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| m67813 | David is driving on the highway at the legal speed limit of 70 mi/h. He notices that there is an accident up ahead approximately 200 feet away. His reaction time is approximately 3 / 4 of a second. Is he far enough away to bring the car safely to a complete stop? Explain your answer. |
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| m67816 | Dawson Handcrafted Furniture produces chairs and sofas. Each chair requires 20 ft of wood, 1 lb of foam rubber, and 2 yd2 of fabric. Each sofa requires 100 ft of wood, 50 lb of foam rubber, and 20 yd2 of fabric. The manufacturer has in stock 1900 ft of wood, 500 lb of foam rubber, and 240 yd2 of fabric. The chairs can be sold for $120 each and the sofas for $575 each. How many of each should be produced in order to maximize income? What is the maximum income? |
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| m67817 | Deanna is 62 years old. She plans to retire in 3 years. She has $300,000 in a savings account that yields 2.25% interest com- pounded daily. She has calculated that her final working year s salary will be $94,000. She has been told by her financial advisor that she should have 65% of her final year annual income available for use each year when she retires.
a. What is the income that her financial advisor feels she must have per year once she retires?
b. Use the compounding formula to determine how much she will have in her account at the ages of 63, 64, and 65. |
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| m67818 | Deanna purchased $24,000 worth of stock and paid her broker a 1% broker fee. She sold the stock when it increased to $29,100 three years later and used a discount broker who charged $35 per trade. Compute her net proceeds after the broker fees were taken out. |
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| m67819 | Debbie buys 400 shares of stock for $23 per share, and pays a 1% commission. She sells them six years later for $23.25 per share, and pays a $30 flat fee. Are her net proceeds positive or negative? Explain. |
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| m67820 | Debbie is president of a company that produces garbage cans. The company has developed a new type of garbage can that is animal- proof, and Debbie wants to use the demand function to help set a price. She surveys ten retailers to get an approximation of how many garbage cans would be demanded at each price, and creates a table.
a. Find the equation of the linear regression line. Round the slope and y-intercept to the nearest hundredth.
b. Give the slope of the regression line and interpret the slope as a rate.
c. Find the correlation coefficient and interpret it. Round to the nearest hundredth.
d. Based on the linear regression line, how many garbage cans would be demanded at a wholesale price of $18.00? Round to the nearest hundred garbage cans.
e. Was your answer to part d an example of extrapolation or interpolation? Explain.
f. Look at your answer to part d. If the company sold that many garbage cans at $18.00, how much money would the company receive from the garbage can sales? |
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| m67822 | Decompose into partial fractions: (3x - 11) / (x2 + 2x - 3)
. |
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| m67823 | Decompose into partial fractions.
a. 5 / (x + 2)2 (x + 1)
b. (-8x + 23) / (2x2 + 5x - 12) |
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| m67824 | Decompose into partial fractions.
a. (9x3 - 24x2 + 48x) / (x - 2)4 (x + 1)
[Let the expression equal A/(x + 1) + P(x) / (x - 2)4 and find P(x)].
b. x / (x4 - a4) |
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| m67825 | Decompose into partial fractions. Check your answers using a graphing calculator.
a. (x + 7) / ((x - 3) (x + 2))
b. 2x / ((x + 1) (x - 1) |
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| m67833 | Del is buying a $250,000 home. He has been approved for a 5.75% mortgage. He was required to make a 15% down payment and will be closing on the house on July 15. How much should he expect to pay in prepaid interest at the closing? |
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| m67834 | Delia purchased a new car for $25,350. This make and model straight line depreciates to zero after 13 years.
a. Identify the coordinates of the x- and y-intercepts for the depreciation equation.
b. Determine the slope of the depreciation equation.
c. Write the straight line depreciation equation that models this situation.
d. Draw the graph of the straight line depreciation equation. |
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| m67836 | Derek is placing a seven-line classified job for an assistant. The following piecewise function gives the price of an x-line ad.
Find the difference between the cost of a 6-line ad and the cost of a 7-line ad? |
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| m67843 | Describe conditions under which you would know whether a polynomial function
is even or odd without using an algebraic procedure. Explain. |
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| m67844 | Describe each of the following correlation coefficients using the terms strong, moderate, or weak and positive or negative.
a. r = 0.21
b. r = - 0.87
c. r = 0.55
e. r = 0.99
d. r = - 0.099
f. r = - 0.49 |
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