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Finite Mathematics and Applied Calculus 7th Stefan Waner Steven Costenoble-Test Bank
Sample Questions
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| 2_1_Quadratic_Functions_and_Models
1. Find the vertex of the graph of the quadratic function.
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| 2. Find the y-intercept(s) of the graph of the quadratic function.
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| 3. For the following demand equation, express the total revenue R as a function of the price p per item.
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| 4. For the following demand equation, find the largest possible revenue.
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| 5. For the following demand equation, find the largest possible revenue.
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| 6. The following chart shows the value of trade between two countries for the period 1994 – 2004 ( represents 1994).
Which of the following models best approximates the data given? (Try to answer this without actually computing values.)
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| 7. The fuel efficiency (in miles per gallon) of a sport utility vehicle (SUV) depends on its weight according to the formula
where x is the weight of an SUV in pounds. According to the model, what is the weight of the least fuel-efficient SUV?
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| 8. Suppose the amount of carbon dioxide (in pounds per 15,000 miles) released by a typical sport utility vehicle (SUV) depends on its fuel efficiency according to the formula
where x is a fuel efficiency of an SUV in miles per gallon. According to the model, what is the fuel efficiency of an SUV that has the least carbon dioxide pollution?
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| 9. The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by where q is the number of buggies it can sell in a month if the price is $x per buggy. What is the largest monthly revenue? Round your answer to the nearest dollar.
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| 10. The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand equation for Turbos is given by where q is the number of buggies it can sell in one month if the price is $x per buggy. At what price should it sell the buggies to get the largest revenue? Round the result to the nearest dollar.
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| 11. Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crowding and smaller lot sizes. In fact, if the company builds 60 houses in this particular development, it can sell them for $160,000 each, but if it builds 70 houses, it will be able to get only $150,000 each. What is the largest possible revenue the company can get? Round your answer to the nearest dollar.
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| 12. Encouraged by the popularity of your Dungeons and Dragons website, www.mudbeast.net, you have decided to charge users who log on to the site. When you charged a $1.50 access fee, your web counter showed a demand of 270 “hits” per month. After you lowered the price to $0.50, activity increased to 350 “hits” per month. Obtain the monthly revenue R as a function of the access fee x.
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| 13. The two fraternities Sigma Alpha Mu and Ep Sig plan to raise money jointly to benefit homeless people on Long Island. They will sell Starship Troopers T-shirts in the Student Center, but they are not sure how much to charge. Sigma Alpha Mu treasurer Solo recalls that they once sold 100 shirts in a week at $4 each, but Ep Sig treasurer Justino claims that, based on past experience, they can sell 400 per week if they charge $2 each. The university administration charges the fraternities $700 per week for use of the Student Center. What is the largest possible weekly profit, rounded to the nearest dollar?
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| 14. You have just opened a new nightclub, Russ’s Techno Pitstop, but you are unsure how much to charge for the cover charge (entrance fee). One week you charged $9 cover per guest and averaged 372 guests per night. The next week you charged $20 per guest and averaged 240 guests per night. Find the linear demand equation showing the number of guests q per night as a function of the cover charge p.
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| 15. You are the sales manager for Montevideo Productions, Inc., and you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,500. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 35 contracts. This is down 10 contracts from the figure last year, when your company charged only $2,000. Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo Productions, Inc., charges for development.
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| 16. For the following demand equation, find the largest possible revenue.
$ __________
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| 17. Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crowding and smaller lot sizes. In fact, if the company builds 60 houses in this particular development, it can sell them for $190,000 each, but if it builds 70 houses, it will be able to get only $170,000 each. What is the largest possible revenue the company can get?
$ __________
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| Choose the correct letter for each question.
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18. –5
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19. 2, 4
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20. none
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| 4_1_Systems_of_Two_Equations_in_Two_Unknowns
1. If the addition or subtraction of two linear equations results in the equation , then the graphs of those equations are perpendicular.
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2. If the addition or subtraction of two linear equations results in the equation , then the graphs of those equations are parallel.
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| 3. If adding two linear equations gives and subtracting them gives , then the graphs of those equations are perpendicular.
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4. If the addition or subtraction of two linear equations results in the equation , then the graphs of those equations intersect in a single point.
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| 5. If the addition or subtraction of two linear equations results in the equation , then the graphs of those equations are _______.
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| 6. If the addition or subtraction of two linear equations results in the equation , then the graphs of those equations are ______.
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| 7. If adding two linear equations gives and subtracting them gives , then the graphs of those equations are:
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| 8. Find the solution to the system of equations.
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| 9. Find the solution to the system of equations.
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| 10. Find the solution to the system of equations.
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| 11. Find the solution to the system of equations.
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| 12. Find all solutions of the given system and choose the graph of the system that shows the solutions.
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| 13. Find all solutions of the given system and choose the graph of the system that shows the solutions.
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| 14. Find all solutions of the given system and check your answer graphically.
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| 15. Find all solutions of the given system and choose the graph of the system that shows the solutions.
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| 16. Find all solutions of the given system, and check your answer graphically.
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| 17. Find all solutions of the given system and choose the graph of the system that shows the solutions.
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| 18. Find all the solutions to the given system, and check your answer graphically.
If the equations of the system are redundant, or if a system is inconsistent, so indicate.
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| 19. Find the intersection of the line through and and the line through and .
If the equations of the system are redundant, or if a system is inconsistent, so indicate. Round your answer to the nearest tenth.
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| 20. In March 2002 Cisco (CSCO) stock rose from $18 to $19, and America Online-Time Warner (AOL) dropped from $34 to $33. If you invested a total of $12,000 in these stocks at the beginning of March and sold them for $11,800 at the end of March, how many shares of each stock did you buy?
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| 21. In a certain month, Nortel (NT) stock started and ended the month valued at $4.70 a share, and Altria Group (MO) increased from $48 to $52 a share. If you invested a total of $5,458 in these stocks at the beginning of this month and sold them for $5,858 at the end of this month, how many shares of each stock did you buy?
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| 22. The U.S. House of Representatives has 435 members. If an appropriations bill passes the House with 51 more members voting in favor than against, how many voted for and how many voted against?
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| 23. The U.S. Senate has 100 members. For a bill to pass with a super majority, at least twice as many senators must vote for the bill as against it. If 93 senators vote, how many must vote for a bill for it to pass with a super majority?
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| 24. The best sports dorm on campus, Lombardi House, has won a total of 7 games this semester. Some of these games were soccer games, and the others were football games. According to the rules of the university, each win in a soccer gamer earns the winning house 3 points, whereas each win in a football game earns them 7 points. If the total number of points Lombardi House earned was 41, how many of each type of game did they win?
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| 25. The demand and supply functions for your college newspaper are listed in order below:
Here is the price in dollars, and represents the quantity of papers that consumers will buy, or that the paper can produce. At what equilibrium price should the newspapers be sold so that there is neither a surplus nor a shortage of papers?
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| 26. If the addition or subtraction of two linear equations gives the results:
, then the graphs of those equations will have a relationship to each other that can be described as follows.
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| 27. A system of three equations in two unknowns corresponds to three lines in the plane. Describe how these lines might be positioned if the system has no solutions?
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| 28. The U.S. Senate has 100 members. For a bill to pass with a super majority, at least twice as many senators must vote for the bill as against it. If 96 senators vote, how many must vote for a bill for it to pass with a super majority?
__________ senators must vote for the bill.
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| 29. The demand and supply functions for your college newspaper are, respectively, and , where p is the price in dollars. At what price should the newspapers be sold so that there is neither a surplus nor a shortage of papers?
__________ cents per paper
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| 30. Find all the solutions (if any) of the given system.
If the equations of the system are redundant, or if a system is inconsistent, so indicate.
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| 31. Find all the solutions (if any) of the given system.
If the equations of the system are redundant, or if a system is inconsistent, so indicate.
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| 32. Find all the solutions (if any) of the given system.
If the equations of the system are redundant, or if a system is inconsistent, so indicate.
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| 33. Find the solution of the given system.
If the equations of the system are redundant, or if a system is inconsistent, so indicate.
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| 34. Find the intersection of the line through and and the line through and .
If the equations of the system are redundant, or if a system is inconsistent, so indicate.
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