TOP IN CONTEMP MATH II
TOP IN CONTEMP MATH II MATH 166
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This 6 page Class Notes was uploaded by Vivien Bradtke V on Wednesday October 21, 2015. The Class Notes belongs to MATH 166 at Texas A&M University taught by Kendra Kilmer in Fall. Since its upload, it has received 68 views. For similar materials see /class/225997/math-166-texas-a-m-university in Mathematics (M) at Texas A&M University.
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Date Created: 10/21/15
N L 4 LII 9 Math 166 Spring 2008 Week 1n Review 3 Exam 1 Review courtesy Kendra Kilmer covering Sections 2127 A1A2 6162 Please note that this review is not all inclusive Determine whether each of the following is proposition a Five is an even number b There are 150 named streets in College Station c Turn left at the second light d 2x 7 7 2 15 Let p and q denote the propositions p The number of faculty members at Texas AampM increased over the past year q The average class size at Texas AampM decreased over the past year Express the following compound propositions in words apANq b Nqu CNPYNlt1 Let p and q denote the propositions p John went to the basketball game q Crystal went to the basketball game Express each of the following statements symbolically a Crystal did not go to the basketball game but John did b Crystal went to the basketball game or John did not go to the basketball game c Neither John nor Crystal went to the basketball game Construct a truth table for each compound proposition 8 FMHNP b MNWWI LetU12345678910A13579B246810 C 1589 D 810 Findthe following aAUC b B D c cw d C AUD Using the following sets determine whether each statement is True or False U l234591215l8 A 24915B 131518C 5915 a 215EA b Boom150 c A has 16 subsets d 0 c B e ouc5915 f A andB are disjoint sets For each part draw a Venn Diagram with 3 subsets A B and C and shade the region that represents each set a Bm f cw b C AUB c AUB Cquot A survey was conducted of 100 student s dining preferences They were all asked their preference on eating at Chipotle Fitzwilly s and Pot belly s The following information was determine o 20 students like only Fitzwilly s o 30 students like exactly two of the restaurants 0 50 students like Potbelly s o 5 students like all three restaurants o o 15 students like Chipotle and Fitzwilly s o 8 students like only Fitzwilly s and Potbelly s o 60 students do not like Chipotle Fill out the Venn Diagram with this information and use it to determine how many students do not like Fitzwilly s Transportation Services is trying to decide on the width of the parking spaces in a newly created parking lot To do so they have been doing a study on the size of cars that are on campus During their study they discovered that there are a total of 12000 cars on campus that can be classi ed into three categories compact cars mediumsized cars and trucks The number of trucks is the same as the number of compact and mediumsized cars combined There are half as many compact cars as mediumsized cars and trucks combined Determine the number of each type of vehicle on campus during their study Solve the following system of linear equations by doing GaussJordan Elimination by hand 2x 7 7y 9 y 73x 5 Each of the following augmented matrices represents a system of lin ear equations Determine whether or not the augmented matrix is in rowreduced form If it IS in rowreduced form give the solution to the system of linear equations If it IS NOT in rowreduced form per form the next row operation that would need to be performed to get the augmented matrix in rowreduced form 1 o o o 4 a o 1 2 o 73 o o o 1 2 1 o 8 b o 1 77 o o 15 1 o 72 5 o 1 o 77 C 0 0 1 6 o o o o 12 Given the follwing matrices with the indicated dimensions which of the following are valid matrix operations A4gtlt37BSgtlt27C4gtlt27D3gtlt4 a 3AD b A SDT 7 B c BCT 7 5D d AB 20 13 Solve the given matrix equation for a b and c g 12 57 711 i 745 fr 1592 758 72 1 3 3 b c 9 4 What is 2ab 7 c Consider a simple economy consisting of two sectors goods and ser vices The production of 1 unit of goods requires the consumption of 01 unit of goods and 02 unit of services The production of 1 unit of services requires the consumption of 03 unit of goods and 025 unit of services Find the level of production for each sector in order to satisfy the demand for 100 million worth of goods and 400 million worth of services How much of each sector is consumed internally while satisfying this demand Math 166 Spring 2008 Week in Review 11 Final Exam Review courtesy Kendra Kilmer covering A1 amp A2 amp Chap 25678amp9 excluding Sec 54amp93 Q L U1 1 Please note that this review is not all inclusive How many 3 digit numbers can be formed from the numbers 012 57 8 9 if no digit can be repeated the rst digit must be nonzero and each number formed must be even A 10000 1year term life insurance policy costs 150 If the probability that a particular person dies in the next year is 0002 nd the company s expected net gain Assume that a small town has only three industries auto energy and transportation Each of these industries acts as a supplier and a user of their products The inputoutput matrix A for this economy is given by auto energy transportation auto 02 0 4 0 1 energy 0 1 0 2 0 2 transportation 02 0 2 0 1 Find the value of the goods consumed in the internal process of production in order to satisfy an external demand for auto mobiles of 474 million external demand for energy of 948 million and an external demand for transportation of 474 mil 1011 Determine whether each of the following is a proposition a Take me to school b The school is on the righthand side of the road c 3x 5 20 Given the payoff matrix below 71 3 72 5 74 2 Find the expected payoff of the game if the row player selects row 1 1 8 of the time and the column player selects column 1 15 of the time and column 2 35 of the time An experiment consists of observing whether cars are kept in the driveway or in the garage It was found that 75 of cars are kept in the driveway and the remaining cars are kept in the garage Of those cars kept in the driveway 90 were worth less than 15000 Of those kept in the garage 80 were worth 15000 or more If a car worth less than 15000 is randomly selected what is the probability that it is in the driveway Solve the following system of linear equation using inverses 3x7y715z9 z5x79y7 2x75yz9 A girl scout convention is being held in College Station Troop 647 is bringing 7 girls Troop 916 is bringing 5 girls and Troop 525 is bringing 3 girls In how many ways can these girls sit in a row if each troop wants to sit together 0 9 A research study was done on conusmers behavior regarding their toilet paper preferences It was found that each month of the consumers using Brand A 70 will continue to use Brand A whereas 25 will switch to Brand B and 5 will switch to Brand C Of the consumers using Brand B 80 will continue to use Brand B whereas 5 will switch to Brand A and 15 will switch to Brand C Of the consumers using Brand C 95 will continue to use Brand C whereas 1 will switch to Brand A and 4 will switch to Brand B At the beginning of January it is known that 33 of the consumers are using Brand A 62 of the consumers are using Brand B and 5 of the consumers are us ing Brand C What percent of the consumers will be using Brand A at the beginning of June What percent of the consumers will be using Brand A in the long run Pivot the given matrix about the element an 1 72 5 9 0 4 78 16 0 5 3 9 Solve the following matrix equation for a b and c 5617 7 92 97042 5 7 a 9 2 7 81 96 10 5 9 100 84 Given U 123456 A 15 B 1356 andC 24 6 determine whether each statement is true or false a 13 6 B b U has 64 proper subsets c A and B are disjoint sets d A OB UC 246 e 2 E A UB What is the effective rate of interest of an account if the interest is compounded monthly and the investment will double in 20 years A group of488 Aggies are going on a road trip to the bowl game They are trying to decide how many cars vans and buses to take for the trip They has determined that each car will seat 6 people and the expenses involved for each car come out to be 100 Each van holds 14 people and costs 195 per van Each bus holds 40 people and costs 475 If they have decided that they want to take twice as many buses as vans how many vehicles of each type should they take if the budget is 6025 and they want to exactly use all of their budget and have no empty seats Amy purchases a 250000 house She makes a 5 down pay ment and then nances the remaining balance with a 30 year mortgage that charges a 625 annual interest rate compounded monthly on the unpaid balance a What is her required monthly payment b Assuming she makes exactly the required payment each month create an amortization schedule detailing the 1st 2nd 241st and 242nd payments Consider the economy of a small village consisting of two in dustries farming and weaving The farmers produce food for themselves and the weavers along with extra food for the re maining people The weavers produce cloth for themselves and 108 75 l 0 Q Q Q Q to gt the farmers along with extra cloth for the remaining people The villagers have found that to produce 1 00 of food 040 of food and 010 worth of cloth is needed locally to feed and clothe the farmers To produce 100 of cloth 030 of food and 020 of cloth is needed locally to feed and clothe the weavers The additional food and cloth produced is then available to export to the city If the city demands 7200 worth of food and 2700 worth of cloth each month how much food and cloth should be produced by the village to meet its own needs and to supply the city A survey of 550 freshmen revealed that 300 own a car 200 own a computer and 100 own neither a car nor a computer If a student is randomly selected from this group what is the probability that they own a car but not a computer An experiment consists of randomly selecting one card out of a standard deck of 52 cards Let E be the event that a red card is drawn and let F be the event that a club is drawn Are the events E and F mutually exclusive events Are the events E and F independent events Katie bought a house in 2000 for 300000 She nanced it with a 30 year mortgage at an annual interest rate of 725 com pounded monthly on the unpaid balance a What are her current monthly payments b After making six years of payments she decides to re nance her home in 2006 with a 30 year mortgage that has an annual interest rate of 525 compounded monthly on the unpaid balance What are her new monthly payments c How much total interest will she end up paying for this house The independent probabilities that Jenny Karen and Lindsay will attend class are 0 35 095 and 076 respectively What is the probability that exactly two of the girls will attend class For each of the following payoff matrices i Determine the max imin and minimax strategies ii Is the game strictly deter mined If so what is the saddle poin value of the game Who does the game favor 71 3 72 a i 5 74 73 4 73 5 b 2 7 71 73 2 1 A jar contains 10 pennies and 5 dimes Three coins are randomly selected from the jar Let X represent the value of the three coins ie how much money you have Find the probability distribution of X How many days will it take for a sum of 2000 to earn 50 interest if it is deposited in an account eaniing simple interest at the rate of 8 per year Classify each of the random variables as nite discrete in nite discrete or continuous a Let X represent the weight of a newboni kitten in ounces 25 Q 0 Q 1 Q 00 Q 0 L O L L N WU gt0 b Cough drops are randomly selected with replacement from a bag containing 30 cherry 20 menthol and 35 lemon Let Y represent the number of cough drops drawn until a cherry cough drop is selected c Jane serves the volleyball 100 times Let Z represent the number of times she serves an ace Two marbles are randomly selected from a bin containing 8 red and 5 green marbles If this experiment is repeated 10 times and the marbles are replaced each time what is the probability of getting 2 red marbles at least 3 times Sarah is trying to arrange 5 identical blue candle sticks 7 iden tical red candle sticks and 3 identical green candle sticks on her shelf How many distinguishable arrangements are possible Given the follwing matrices with the indicated dimensions which of the following are valid matrix operations A2gtlt4zB3gtlt17C4gtlt37D3gtlt2 a AC76DT b SDTB c 2CB d AT 7CD An experiment consists of rolling a fair sixsided die 1000 times Find the probability of rolling a 5 at most 170 times Use the ap propriate normal distribution to approximate the binomial prob ability Valerie decides to put 30 into an account every week If the account eanis 3 45year compounded weekly how much will she have in the account 15 years from now Given the following probability distribution x 7 75 20 30 PXx 0056 0 72 019 0034 Find E X VarX 039 median and mode Given 3 24631012 A 2612 B 81012 C 246 810 nd the following a A 8 b A U B C c B O A O C In College Station 85 of the population is currently an Aggie fan Each year 30 of the nonAggie fans become Aggie fans and 1 of the Aggie fans become non Aggie fans If this trend continues what percent of the population will be an Aggie fan 5 years from now If nA UB 80 nA 30 and 113 75 what is nA BC Jenny and Lisa have recently acquired some leftover inventory from a small online baby supply store Jenny has acquired 20 paci ers 18 bottles and 9 cloth diapers Lisa has acquired 15 paci ers 7 bottles and 12 cloth diapers a Organize the above information into a matrix and label it A L Equot L 0 L 1 L m 4 O 4 Q 4 L b The paci ers will sell for 2 each the bottles will sell for 4 each and the cloth diapers will sell for 12 each Write a matrix B summarizing this data c Write a matrix product involving the matrices A and B that will produce a new matrix giving the total amount of money each girl will make if they sell all of their inventory Compute the desired product and interpret the result Let X be a normal random variable with a mean of O and a stan dard deviation of 8 Find the value of b if P7b lt X lt b 0 9826 Given the payoff matrix below determine the optimal mixed strategy for the row and column player and then compute the expected payoff of the game Who does the game favor 65 2 Let p and q denote the propositions p It will be hot this summer q I will spend the summer on the beach Express the following compound propositions in words a N p A q 03 p Y q c IN N q A TrueFalse Exam consists of 15 questions In how many ways can the exam be answered so that the student answers at least 10 questions correctly An experiment consists of rolling a fair sixsided die and ipping a fair coin a Find the Sample Space associated with this experiment b Find the event E that an even number is rolled c Find the PE Gabe has 2500 in credit card debt on a card that charges 196 per year compounded monthly on the unpaid balance If he pays the minimum payment of 50 each month and he doesn t use it to make any more purchases how long will it take Gabe to pay off his debt An experiment consists of rolling a pair of fair sixsided dice What is the probability that the sum is at least 9 or exactly one 5 is rolled An experiment consists of randomly selecting 1 marble from a bowl containing 5 red 3 blue and 10 white marbles What is the probability that the marble selected is not white Solve the systems of linear equation using the GaussJordan elimination method a 712x742y748z 7114 2x 7y 8z 19 3x 2y 10z 9 4 4 4 m 4 o 4 1 4 m 4 0 U1 0 U1 U1 0 b 2x3y72z 10 x3yiz 73 3x4yiz7 C 3x79y6z 12 x73y2z74 2x76y4z8 IfE andF are mutually exclusive events PE 0 5 andPF 03 nd PE F0 u E0 an A crate contains 90 strawberries of which 10 are rotten If a cus tomer randomly selects 15 strawberries what is the probability that at least 3 of the strawberries are rotten A fruit stand has 30 apples 14 peaches 6 plums and 15 pears If you randomly select 8 pieces of fruit how many ways can you select exactly 4 plums or exactly 3 pears In a group of 10 people what is the probability that at least 2 of them were bon1 in the same month An experiment consists of rst performing a task in which A B or C can occur Then a second task is performed in which D or E can occur The following probabilities are known PA 0 3 PC 0 5 PDjA 0 25 PEjB 0 7 PDjC 064 Find the following a PE b PB 1E c PA U D The scores on an English exam were normally distributed with a mean of 65 and a standard deviation of 5 If 10 of the class received an A on the exam and 15 of the class received a B on the exam what was the cutoff for a B A club consists of 35 nance majors 3O accounting majors and 40 info majors This club must elect a president and vice president from the nance majors and then elect 2 representa tives from each of the two remaining majors How many ways can this be done The following is the transition matrix for a Markov process that has 3 states A B and C Note the rows and columns are represented in the matrix in the order listed above 01 0 5 03 T 0 9 02 0 65 0 03 005 a Is the above matrix stochastic b Is the above matrix regular c What does the entry 32 represent d What does the entry 13 represent A game consists of rolling a pair of fair sixsided dice If the sum of the numbers is less than 5 the player wins 5 If the sum of the numbers is greater than 9 the player wins 4 Otherwise the player loses A Find the value of A that makes this game fair U1 1 4 U1 U1 U1 U1 U1 It is known that 62 of Aggies purchased an allsports pass If 50 Aggies are randomly selected what is the probability that at most 29 of them own a sports pass Shade the following regions on a Venn Diagram a A BUC b B C c A nBuBch It is known that the length of newbonis is normal distributed with a mean of 21 inches and standard deviation of 3 inches What is the probability that a randomly selected newboni has a length between 18 and 24 inches A game consists of two players simultaneously showing one two or three ngers Carl and Rico decide to play this game If the sum of the numbers showing is less than four Carl pays Rico 3 If the sum of the numbers showing is greater than four Rico pays Carl 2 Otherwise Carl pays Rico 1 a Find the payoff matrix for this twoplayer zerosum game b Find the maximin and minimax strategies for Rico and Carl Is this game strictly determined If so what is the value of the game Who does this game favor Danny put a 5500 down payment on a car He nanced the re maining balance with a 60 month loan at a 55 annual interest rate compounded monthly on the unpaid balance If the monthly car payments are 450 what is the cash price of the car Determine the value of b for which the system of linear equa tions 4x 7 y 6 8xl7y 10 has no solution A survey was done of 700 students on their preference of fruits The following information was found 0 275 students like bananas and strawberries o 250 students like all three fruits o 400 students like grapes o 50 students like only bananas and grapes o 20 students like only grapes o 205 students do not like bananas o 60 students like only strawberries How many students like exactly one of these kinds of fruit 60 Construct a truth table for each compound proposition a p pM1 b WIDMNPM 1 Math 166 Spring 2008 Exam 3 Review Week in Review 9 courtesy Kendra Kilmer covering Sections 8186 and 5153 How much would you have to deposit in an account earning 45year simple interest if you wanted to have 1000 after 6 years 2 How much would you have in 8 years if you invest 1500 into an ac count ear39ning 54year compounded quarterly 3 How long will it take an investment to double if it is earning 35 4 annual interest compounded mon y What is the future value of 35000 invested at 65 annual interest compounded continuously for 5 years Which would give you a better return 389lyear compounded daily or 391lyear compounded quarterly 6 If quarterly deposits of 30 are put into an account earning 35 per year compounded quarterly how much will be in the account at the end of 30 years Nick currently has 500 in his travel funds account that earns interest at 245 per year compounded monthly He plans on depositing 75 each month to save for a trip to Europe If he needs 5000 for the trip to Europe when will he be able to go Meghan deposits 10 every week into an account in which the interest is compounded wee ly In 3 years she discovers that her investment has grown to 2000 What is the effective rate of interest earned on this account 9 At the beginning of 1996 Lisa and Kevin bought a home for 125000 10 11 12 They put 5 down and then nanced the remaining price of the home with a 30 year mortgage at an 854 annual interest rate compounded monthly on the unpaid balance a What were their monthly payments b At the beginning of 2006 they decided to re nance the home with a 20 year mortgage at a 65 annual interest rate compounded monthly on the unpaid balance What are their new monthly pay ments c How much money are they saving in interest by re nancing Chris has been living it up and has accrued 6000 of credit card debt on a card that charges 184 per year compounded monthly on the unpaid balance But lucky for Chris the minimum payment due each month is only 95 a Assuming he doesn t make any more purchases how long will it take Chris to pay off his debt b If Chris decides to pay 50 extra a month how long will it take Chris to pay off his debt c How much money is he saving by paying a little extra each month Classify each random variable as nite discrete in nite discrete or con tinuous AND describelist the possible values of the random variable a An experiment consists of randomly selecting a 20 ounce bottle of coke Let X represent the actual amount of liquid in it b An experiment consists of randomly selecting jelly beans out of a jar with replacement until a green jelly bean is drawn Let Y represent the number of jelly beans drawn c An experiment consists of randomly selecting 10 students at Texas AampM Let Z represent the number of freshmen selected An experiment consists of randomly selecting two numbers without replacement from a jar that contains 5 slips of paper numbered 15 Let X represent the sum of the two numbers drawn Q a Find the probability distribution of X b Draw the histogram for the random variable X c Compute E X Lisa and Kevin decide to play a game Lisa randomly selects a sample of2 cards out of a standard deck of 52 If the two cards drawn are of the same suit Kevin pays Lisa 2 If the two cards drawn are of the same rank Lisa pays Kevin 4 Otherwise Lisa pays Kevin A Find the value ofA that makes this game fair An experiment consists of rolling a pair of fair sixsided dice Find the odds against the event that the sum of the numbers landing uppermost is 7 Students in a class of 100 were randomly assigned to groups of ve The number of freshmen in each group was observed The table below gives the results NumberofFreshmen 0 j 1 j 2 j 3 j 4 j 5 NumberofGroups 2 4 5 6 2 1 Find the mean standard deviation median and mode of the number of freshmen in a randomly selected group A random variable X has a mean of 50 and a standard deviation of 3 Use Chebychev s Inequality to determine the value of A for which P507A g X g 50A 2 09375 Studies have shown that 3 of all live births in Texas are multiple births twins triplets etc At a given hospital in which there are 50 live births a What is the probability that exactly 2 of the births are multiple births b What is the probability that at most 5 of the births are multiple births What is the probability that between 6 and 10 of the births inclu sive are multip e 39rths How many births would you expect to be multiple births in this group What is the standard deviation of the number of multiple births in this group Let X be a normal variable with p 0 and o 45 In each of the following nd a a PX 2 a 02567 b P72a g X g 211 08754 The GPAs of randomly selected freshmen at a certain university was normally distributed with a mean of 255 and a standard deviation of 030 If a freshmen is randomly selected what is the probability that their GPA is greater than 300 It is known that 76 of all students at a certain university have nancial aid If 5000 students are randomly selected what is the probability that at least 3800 but fewer than 4500 have nancial aid Use the appropri ate normal distribution to approximate the binomial probability
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