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Name: Date: The University of Phoenix Math 212 Finite Mathematics – Online Final Exam Note: For any consideration of partial credit all work must be typed within the space provided – under each problem (YOU CAN HIT ENTER TO CREATE MORE ROOM) and the answer spaces completely filled in. I. Linear Equations and System of Linear Equations (Chapter 1 & 2) 1. Suppose that the national demand and price for a certain type of energy-efficient exhaust fan are related by p = D(q) = 495 - q, where p is the price (in dollars) and q is the demand (in thousands). a. If the demand is for 80,000 exhaust fans, then the price equals $_______________ b. At a price of $141, the demand is for ____________thousand exhaust fans. 2. Find an equation of the line containing the given pair of points (2,5) and (6,6). Y = _________________________ (Use integers or fractions for any number in the expression) 3. Kara’s Custom Tees experienced fixed costs of $400 and variable cost of $2 a shirt. Write an equation that can be used to determine the total expenses encountered by Kara’s Custom Tees and graph the equation. Y = _________________________ The GRAPH: Note let y 100’s (1 = 100) 4. The Dispatch Tool Works spend $14,000 to produce 180 parts, achieving a marginal cost of $64. Find the linear cost function. C(x) = ________________________ D(ft) T(sec) 5. The Kostas Engine Company manufactures several 2 3.15 different sizes of airplane propellers. The relationship 3 3.86 between the diameter of a propeller D and the time T for 4 4.60 100 complete revolutions is shown in the table. 5 5.30 a. What is the equation for the least squares line: 6 6.07 7 6.79 8 7.69 Y = ____________________________________ b. What is the coefficient of correlation:_________ 6. Solve the following system of equations by using the Inverse of the coefficient matrix Q. (AX = B). - 5x – y + 7z = - 7 2y + 6z = - 16 4x + 4y + 7z = - 26 (x, y, z) =____________________ 7. Find the production matrix for the following input-output and demand matrices using the open model. 0.1 0.2 4 A and D 6 . 0.55 0.4 The production matrix is: (Round the final answer to the nearest hundredth as needed. Round all intermediate values to four decimal places as needed) 8. Solve the following system by the Method of Elimination: 2x – 4y = 40 5x + 3y = -17 (x, y) = ___________________________ 9. Solve the following system by Graphing:( Attach the graph). X + y = 10 X–y=2 (x, y) = ___________________________ II. Linear Programming (Chapter 4) 10. Use the simplex method to solve the linear programming problem. Maximize: z = 7x + 3y + z Subject to: x + 4y + 10z ≤ 110 x + 2y + 11z ≤ 247 with x ≥ 0, y ≥ 0, z ≥ 0. Maximum z=_______with (x,y,z) = _________________ 11. Find the transpose of the matrix: 1 2 3 A 9 5 3 AT = 2 8 5 12. Use the Graphing method to solve the linear programming problem (Supply Graph here also) Minimize: z = 5x + y Subject to: 4x + 4y ≥ 16 4x + y ≥ 19 With x ≥ 0 and y ≥ 0 Minimize z=_______with (x,y) = _________________ 13. Convert the following to a maximization problem. Minimize: w = 2x + 3y + 5z Subject to: x+y+z≥5 X+y≥7 2x + y + 3z ≥ 6 With x ≥ 0, y ≥ 0, and z ≥0. State you Maximization Problem here: And the solution for Minimized w =_______with (x,y,z) = _________________ 14. Jayanta is raising money for the homeless, and discovers each church group requires 2 hr of letter writing and 1 hr of follow-up calls, which each labor union needs 2hr of letter writing and 3 hr of follow-up. She can raise $150 from each church group and $175 from each union. She has a maximum of 12 hours of letter writing and 16 hours of follow-up available each month. Determine the most profitable mixture of groups she should contact and the most money she can raise in a month. a. Set up the linear programming here: b. She should contact _________church group(s) and ________labor union(s), to obtain $_______________ in donations. 15. One gram of soybean meal provides at least 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides at least 4.5 units of vitamins and 3 calories. One gram of grain provides at least 5 units of vitamins and 10 calories. If a gram of soybean meal cost 7 cents, a gram of meat byproducts 8 cents, and a gram of grain 9 cents, what mixture of these three ingredients will provide at least 54 units of vitamins and 60 calories preserving at minimum cost? What will be the minimum cost? a. Set up the linear programming here: b. What is the mixture:_________________________________________ and what is the minimum cost $_______________ . III. Finance (Chapter 5) 16. Fritz Benjamin buys a car costing $10,900. He agrees to make payments at the end of each monthly period for 7 years. He pays 9.6% interest, compounded monthly. What is the amount of each payment? Find the total amount of interest Fritz will pay. a. Fritz’s monthly Payment is $___________________(round to the nearest cent.) b. Fritz will pay a total of $______________in interest (round to the nearest cent). 17. A family’s plan to retire in 15 years and expect to need $200,000. Determine how much they must invest today at 6.1% compounded semiannually to accomplish their goal. The Family should invest $____________________(round to the nearest $100) 18. John plans to invest $3000 at 5% interest over 6 years compounded quarterly. a. The total amount after 6 years will be $________________ b. The total amount of interest earned is $_______________ 19. Find the payment necessary to amortize a 8% loan of $2400 compounded quarterly, with 12 quarterly payments. The payment size is $_______________ 20. Find the present value of an ordinary annuity which has payments of $1800 per year for 14 years at 8% compounded annually. The present value is $__________________ IV. Probability & Statistics (Chapter 8 & 9) 21. Mixed in a drawer are 6 blue socks, 4 white socks, and 2 gray socks. You pull out one at a time without looking. a. The probability of getting 2 white socks is _______________ (type your answer as a fraction in lowest terms.) b. The probability of getting 2 socks of the same color is _____________(type your answer as a fraction in lowest terms.) 22. A health inspector must visit 3 of 15 restaurants on Monday. In how many ways can she pick a first, second, and third restaurant to visit? There are ___________ways. 23. Assume the probability that a telephone in any given telephone booth is defective is 0.2. Determine the probability that if 8 phone booths are examined, the number of defective phones is exactly 3. The probability is _____________(round answer to 4 decimal places.) 24. Pizza House offers 4 different salads, 5 different kinds of pizza, and 4 different desserts. How many different three course meals can be ordered? _____________different three course meals can be ordered. 25. Assume the probability is ½ that a child born is a girl. If a family has three children, what is the probability that they have: a. Exactly one girl:_________________ b. At most two boys:_______________ 26. Find the range, median, mean and the standard deviation of the following set of data. 163, 167, 158, 169, 157, 176, 172 Range:_________ Median:_________ Mean:_________ Standard Deviation:________ 27. The figure below contains the salaries of employees at the Raggs, Ltd. Clothing Store. Number Type Salary 1 Owner $26,900 5 Salesperson $18,100 3 Secretary $14,100 1 Custodian $13,000 What is the mean salary, median salary, mode salary and what can be said about its distribution? Mean Salary:____________ Median Salary:____________Mode Salary:_____________ The Distribution is: 28. What is the percentage of area under the normal curve between the mean and – 0.40 standard deviations from the mean? The percentage is _________% (round to the nearest percent) 29. In a certain distribution, the mean is 50 with a standard deviation of 4. Use the Empirical Rule to tell the probability that a number lies between 42 and 58. The probability a number lies in between 42 and 58 is _____________ (round to the nearest thousand.) 30. An assembly-line machine turns out washers with the following thickness (in mm). 1.26 2.05 1.79 1.86 1.38 1.55 1.33 1.85 1.54 1.55 1.36 1.27 1.33 1.36 1.88 1.46 a. The mean of the thickness is ___________mm. (round to 4 decimal places) b. The standard deviation is _____________mm (round to 4 decimal places) c. What is the probability that if I randomly chose a washer that it would be at least 1.57mm? _____________%