cKathryn Bollinger and her Fall 2000 Math 141 Students, December 4, 2011 1Review Problems for Final ExamNote: This review covers topics from Sections 5.2 & 5.3, as well as a variety of topics presented throughout thesemester. This review does not cover every concept that could be tested on a final exam. Please also take a lookat the previous Week-in-Reviews for more practice problems.1. If Louis d eposits $50 at th e end of each month into a savings account earning interest at a rate of 7.25%per year compounded monthly, how much will he have at the end of 30 years (assuming that he makes nowithdrawals during that period)? How much interest will he earn?2. You wish to retire with $1,000,000 in a retirement account, which you will make equal monthly deposits toduring the 45 years that you work. If the account will pay interest at a rate of 5% per year compoundedmonthly, how much should you deposit each month in order to have your million? What is the effectiveannual yield of this account?3. You are looking to buy a new car and have only $1000 for a down payment. The car you wish to buy hasa cash price of $22,500. If the best financing option you find charges interest at a rate of 3.5% per yearcompounded monthly, how big would your monthly payments be in order to pay off the car in 60 months,assuming you use the money you already have for a down payment? In 48 months? In 36 months?4. Ten years ago Quincy made a down payment on a house of 20% of th e purchase price and secured a bankloan of $72,500 to finance the remaining amount. The mortgage was for a term of 30 years, with an interestrate of 7.25% per year compounded monthly on the unpaid balance to be amortized through equal monthlypayments.(a) What is the outstanding principal on Quincy’s house now?(b) How much equity does Quincy have in the house now?(c) How much total interest will Quincy pay over the life of the loan?(d) At this time, interest rates have dropped to 5% per year compou nded monthly on a 15-year mortgageand Quincy is thinking about refin an cing. If he r efinances, what will his new monthly payments be?(e) How much money, if any, will Quincy save by refinancing (assumming no additional refinancing costs)?5. Sally buys a new $1000 television by paying $100 and financing the remaining $900. The terms of her financeagreement state that the unpaid balance will be charged interest at a rate of 15% per year, compoundedmonthly, and the money is to be repaid over a 2 year period through equal installments made at the end ofeach month.(a) What will Sally’s monthly payments be?(b) How much of the first payment goes towards paying down the loan?(c) Fill in the first 6 lines of the amortization schedule.End of Pmts TO TO OutstandingPeriod Remaining Payment Interest Principal Principal EQUITY012345(d) How much equity will Sally have in her computer after 1 year?cKathryn Bollinger and her Fall 2000 Math 141 Students, December 4, 2011 26. A company making radios finds that the total cost of producing 100 radios is $9,000 and that the total costof producing 150 radios is $13,000. Each radio sells for $110. Let x be the number of radios made and s old.Find the(a) cost function.(b) revenue function.(c) profit function.(d) break-even point and explain its meaning.7. Use the Method of Corners to solve the following:OBJ: Max P = 2x + 5ySUBJ TO: x + y ≤ 103x + y ≥ 12−2x + 3y ≥ 3x ≥ 0, y ≥ 08. Given U = {0, 1, 2, . . . , 10}, A = {1, 3, 5, 7, 9}, B = {2, 3, 4, 5, 6}, and C = {4, 8, 10}, find the following sets.(a) A ∪ BC(b) (CC∩ A)C(c) B ∩ (AC∪ C)9. How many distinct ways can the letters in the word HULLABALOO be arranged?10. Suppose the weights of cats are normally distributed with an average weight of 8 poun ds and a standarddeviation of 1.75 pound s. What is the probability that a randomly selected cat weighs between 6 and 15pounds?11. Solve the following for a, b, c, and d.4"−3 07 2#−1"2 −45 2#+ 3"1 (c − 2)b 4#T="(d + 4) −25 a#12. There is a fruit market that has 120 oranges, 500 cherries, and 200 apples. Of these, there are 4 rottenoranges, 100 rotten cherries, and 10 rotten apples. What’s the pr ob ab ility that a customer will select 2rotten oranges of 2 oranges he/she picked, 1 rotten apple of 1 apple he/she picked, and 30 rotten cherries of40 cherries he/she picked?13. It is known that 28% of a p articular population enjoys eating seafood. From this population, 300 people areselected at random.(a) What is the probability that exactly 80 people enjoy eating seafood?(b) What is the probability that at least 75 people, but no more than 125 people, enjoy eating seafood?cKathryn Bollinger and her Fall 2000 Math 141 Students, December 4, 2011 314. You pay $5.00 to play the following game. You have 2 chances to draw a ball from a bag. If you draw awhite ball, you win nothing and if you draw a purple ball you win six dollars. In the bag there are 30 ballstotal - 20 are white and 10 are purple. After th e first ball is drawn it is replaced before the next ball isdrawn.(a) Find the expected net winnings of this game.(b) Is this game fair? Why or why not?15. You are given the follow ing data: (0,0), (1,2), (3,5), (4,6), and (6,9), where x-values r epresent the numberof items sold (in hundreds) and y-values represent the amount of profit made (in thousands of dollars).(a) Find the least-squares line for the data.(b) Is the line you found a good fit for the data? Why or why not?(c) Use your line to predict the amount of profit made when 550 items are sold.(d) Use your line to predict the amount of items which must be sold to generate a profit of $32,500.16. A child wants to build a block city. Each house requires 50 square blocks, 100 rectangular blocks, and 4windows. Each store requir es 50 square blocks, 125 rectangular blocks, and 8 win dows. Each school requires100 squ are blocks, 75 rectangular blocks, and 20 wind ows. If there are 5250 s q uare blocks, 7375 rectangularblocks, and 880 windows, how many houses, stores, and schools can the child build if all of the materials areto be used?17. Shade the portion of a Venn diagram that represents the set (AC∪ B)C∩ CC.18. Kathryn has a collection of 18 different Tweety Birds - 8 plush toys, 6 plastic figurines, and 4 porcelainfigurines. She wants to arrange all of these on one shelf.(a) How m any total arrangements exist?(b) How many total arrangements are possible if all Tweety Birds made out of the same m aterial aregrouped together?19.
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