Math 141 WIR, Spring 2007,cBenjamin AurispaMath 141 Final Exam Review Problem SetNote: This review does not cover every concept that could be tested on a final. Please also take alook at previous Week in Reviews for more practice problems. Every instructor makes up their ownfinal, so it would be beneficial for you to also look over your old tests, quizzes, assignments, andclass notes.1. Determine whether the following matrices are regular.(a).7 .2 .5.2 .6 .3.1 .2 .4(b).8 1 .4.1 0 .3.1 0 .3(c)1 .2 .50 .6 .30 .2 .22. Suppose that in a study of Coke and Pepsi, it was f ound that currently, 75% o f people drinkCoke and 25% drink Pepsi. Every year, 72% of those who drink Coke will continue to do so,while 28% will switch to Pepsi. Further, 54% of those who drink Pepsi will continue to do so,while 46% switch to Coke.(a) What percentage of drinkers will Coke and Pepsi have after 2 years?(b) In the long run, what percentage of soda drinkers will Coke and Pepsi have?3. A guitar manufacturer determines that when the price of a guitar is $150 that the quantitydemanded is 1200. When the price is $ 225, the quantity demanded decreases by 100. Thesupplier is not willing to supply any guitars a t a price of $100, but will supply 300 guitars ata price of $175. What is the market equilibrium for this guitar manufacturer?4. Use the Gauss-Jordan Elimination Method to get the following matrix in row-reduced form."2 −4106 3−15#5. Solve the following systems of equations.(a) x − y + z = 16−2x + y + z = −53x + 2y − z = 1(b) 2x + 4y − 6z = 8−3x − 6y + 9z = 7x + 2y − 3z = 5(c) 5x + y − 2z = −133x − 6y + 3z = −18−2x + 4y − 2z = 121Math 141 WIR, Spring 2007,cBenjamin Aurispa6. Solve the following matrix equation for the variables a, b, c, and d."2 a3 b#T+"1 −2 c0 5 8#6 d−4 1−1 0= −2"−6 −51 4#7. A house costs $189 ,0 00. Benjamin makes a down payment of $12,000 and secures a loan forthe remaining balance. The loan is to be paid off over 25 years at an interest rate of 6%/yrcompounded monthly.(a) What is the required monthly payment?(b) How much total interest will be paid on this loa n?(c) Benjamin decides to refinace the loan a fter 9 years. The new loan is for 15 years at aninterest rate of 5%/yr compounded monthly. What would be his new monthly payment?8. A quiz has a total of 10 questions on it: 5 True/False and 5 Multiple Choice. The professor isvery generous and says that the student s only have to answer 7 questions of which 3 must beTrue/False and 4 must be Multiple Choice. Each multiple choice problem has 5 possible an-swers. How many ways are there to complete the test if a student answers exactly 3 True/Falseand exactly 4 Muliple Choice?9. A po tt er makes only vases and ash trays. (He’s a beginner.) Each vase requires 6 pieces ofclay and takes 8 hours to make. Each ash tray requires 4 pieces o f clay and takes 2 hours tomake. The potter makes a profit of $12 on each vase and $3 on each ash tray. He knows thatthe number of ash t rays made should be at most twice the number of vases made. The pott eronly has availabe 42 pieces of clay each week, but wants to work at least 24 hours each week.How many vases and ash trays should t he potter make each week in order t o maximize profit?Is there any leftover clay at this level of production? What would be the level of productionthat minimizes profit?10. A survey of 300 A&M students was done asking what video game systems (Atari, Nintendo,Gameboy) they had growing up. Let A be the set of students who had an Atari, N be theset of students who had a Nintendo, and G be the set of students who had a Gameboy. Thefollowing data was found.45 students only had Nintendo.156 students had a Gameboy.73 students had a ll 3 systems.11 students had a n Atari and a Gameboy but not a Nintendo.115 students had a Nintendo and a Gameboy.100 students had exactly one of these systems.101 students had a Nintendo or an Atari, but no t a Gameboy.(a) How many students had none of these g ame systems?(b) How many students had an Atari?(c) What is n((N ∩ A) ∪ (G ∩ Nc))?(d) What is the probability that a student in this group had exactly 2 of these systems?2Math 141 WIR, Spring 2007,cBenjamin Aurispa11. In a bag I have 9 Skittles and 10 M&M’s. There are 3 red Skittles, 4 yellow Skittles, and 2green Skittles. There a re 2 red M&M’s, 7 yellow M&M’s, and 1 green M&M. An experimentconsists of reaching into the bag and pulling out a piece of candy.(a) What is the probability that the chosen piece is yellow or a Skittle?(b) What is the probability that a green piece is not chosen?(c) Let E be the event that a red candy is drawn. Let F be the event that an M&M is drawn.Are E and F mutually exclusive? Are E and F independent?12. Data is given below relating the quiz averages and final exam scores of 1 0 student s in a Math141 class.Quiz Average, x 43 54 62 69 74 77 81 88 94 98Final Exam Score, y 37 55 65 67 78 80 80 85 85 99Find the least-squares line for this data and use it to predict the final exam score of a studentin this class who has a 70 quiz average.13. A bag of Hershey’s miniatures contains 10 milk chocolates, 9 Mr. Goodbar’s, 7 Krackels, and8 dark chocolates. A sample of 8 chocolates is taken from the bag. What is the probabilitythat the sample contains(a) exactly 3 milk chocolates o r exactly 4 dark chocolates?(b) at least 1 Krackel?14. In a certain g roup of students, it is known that 21% live in the dorms. Further, 67% o f thosewho live in the dorms are freshmen whereas 39% o f those who do not live in the do rms arefreshmen. What is the probabality that a student in this group who is not a freshman lives inthe dor ms?15. A simple game consists of rolling a pair of dice. The game costs $2 to play. If a double isrolled, you win $4. If the sum of the dice is 9, you win $7. If exactly o ne two is rolled, you win$1. Otherwise, you win nothing. Let X be the net winnings of a person who plays this game.Find the expected value, standard deviation, and variance of X.16. A simple economy consists of 2 sectors: food and shelter. The production of 1 unit of foodrequires the consumption of .4 units of f ood and .2 units of shelter. The production of 1 unitof shelter requires the consumption of .3 units of f ood and .2 units of shelter. Find the gr ossoutput of goods needed to satsify a consumer demand of 12,285 units of food …
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