Sample Final Exam C =

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1 Sample Final Exam Name: RELAX! Read through the entire exam to see that there are no surprises. Do the problems you like best first. Show all of your work to get partial credit where due. GOOD LUCK!! 1. (16 points) Given these matrices: A = B = C = D = Find: a) CB b) D A c) AB d) A 1 2. (10 points) Marcella wants to save money for her grandson to go to college. He is currently 4 years old. She will put away money monthly for the next 10 years. She wants him to be able to have $1,000 a month for 5 years, beginning when he is 18. Assume that she will get a 6% APR throughout this entire period. What will her monthly payment have to be? (This problem will have 3 parts: the part where she contributes to a fund, the part where the money sits and earns interest, and the part where her grandson takes out his yearly amount. All compounding will be monthly.) 1

2 3. (9 points) A jar has 6 red, 5 blue and 9 green marbles in it. Marcella reaches in and selects 7 marbles (without replacement). What are the probabilities of: a) Selecting no more than 3 green marbles? b) Selecting exactly 3 red marbles? c) Selecting exactly 4 blue marbles and 1 red marble? 4. (12 points) A farmer can buy three types of plant food, mix A, mix B, and mix C. Each cubic yard of mix A contains 20 pounds of phosphoric acid, 10 pounds of nitrogen, and 10 pounds of potash. Each cubic yard of mix B contains 10 pounds of phosphoric acid, 10 pounds of nitrogen, and 15 pounds of potash. Each cubic yard of mix C contains 20 pounds of phosphoric acid, 20 pounds of nitrogen, and 5 pounds of potash. The minimum monthly requirements are 480 pounds of phosphoric acid, 320 pounds of nitrogen, and 225 pounds of potash. If mix A costs $30 per cubic yard, mix B costs $36 per cubic yard, and mix C costs $39 per cubic yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimal cost? a) Define your variables in clear English. b) Write a system of constraints and an objective function. c) Set up the initial Simplex Tableau. d) Circle the first pivot point. DO NOT SOLVE THIS SYSTEM!! 2

3 5. (6 points) What is the coefficient of x 5 in the expansion of (4x - 3) 7? 6. (12 points) The Laddon Ice-Cream Shop has 12 flavors of ice-cream. You are going to buy a quintuple (five) scoop ice-cream cone. How many ways are there to arrange your 5 scoops of ice-cream if: a) Each scoop does not have to be a different flavor and you do not care how they are arranged. b) Each scoop has to be a different flavor and you do care how they are arranged. c) Each scoop does not have to be a different flavor and you do care how they are arranged. d) Each scoop has to be a different flavor and you do not care how they are arranged. 3

4 7. (10 points) A computer magazine surveyed its readers to determine how likely it was that people who planned to purchase new computers in the near future would buy a portable/notebook or a desktop model. The results are: Purchase in Purchase in Purchase in Totals 0 3 months 3-6 months 6-12 months Notebook/Port able Desktop Totals (You do not have to reduce your fractions.) A person is selected at random from this group. Find the probability that: a) The person planned to buy a desktop computer in the next 3-6 months. b) The person planned to buy a computer in the next 0-3 months OR that the person was planning to buy a desktop model.. c) The person planned to make a purchase in 6-12 months, given that they plan to buy a Notebook/Portable type computer. d) The person plans to buy a Notebook/Portable type computer, given that they plan to make the purchase in 6-12 months. e) The person plans to make the purchase in 3-6 months AND they plan to buy a desktop computer. 4

5 8. (10 points) At a small college the following information was gathered from 50 students: 23 students read Rolling Stone magazine 18 students read Newsweek magazine 14 students read People magazine 10 students read Rolling Stone and Newsweek magazines 9 students read Rolling Stone and People magazines 8 students read Newsweek and People magazines 5 students read all 3 magazines a) Fill in the numbers in the Venn diagram below to illustrate this problem. b) What is the probability that a student reads none of the 3 magazines? c) What is the probability that a student reads ONLY Rolling Stone? d) What is the probability that a student reads Rolling Stone given that they read Newsweek? e) What is the probability that a student reads neither Rolling Stone nor Newsweek? f) What is the probability that a student reads Rolling Stone or People or both? 5

6 9. (5 points) Marcella loans her best friend $20,000 to be amortized over 2 years at an interest rate of 6% per year compounded semiannually. How much will each of the semiannual payments be? 10. (10 points) From #9, fill out this table for the 2 years of the loan: Payment Number Outstanding principal before payment Interest due (semiannual) Payment Amount of principal repaid Outstanding principal after payment (This is the whole loan, so the last number in the right hand column should be close to 0.) 6