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# Introductory Mathematical Analysis I MATH 1330

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This 5 page Class Notes was uploaded by Ms. Ally Koelpin on Thursday October 22, 2015. The Class Notes belongs to MATH 1330 at Texas Tech University taught by Staff in Fall. Since its upload, it has received 117 views. For similar materials see /class/226469/math-1330-texas-tech-university in Mathematics (M) at Texas Tech University.

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Date Created: 10/22/15

H E0 03 P U a Suggested Questions for Fall 2010 Final Exam A company that manufactures surfboards established the following cost and price functions C35 320 1295 pz 101 7 4m where X is in thousands of surfboards and cost and revenue are in thousands of dollars a Write an equation for the pro t function b Find the break even points c What is the maximum pro t and at what output does it occur How long will it take an investment to double in value if it is invested at a 45 compounded daily b 39 compounded semiannually A manufacturer wants to test a new lie detector before putting it on the market They select 200 people to participate in the test half are instructed to lie and the other half are instructed to tell the truth The test indicates lying in 91 of those who lied and in 5 of those who told the truth a What is the probability that a randomly chosen person lied given that the test indicated he or she lied b What is the probability that the person was telling the truth if the test indicated that he or she was lying Mike has just received a sum of 40000 from an inheritance He plans to spend 20 of it on home im provements but wants to invest the remaining amount into an account that draws interest for 10 years Option A offers simple interest at the rate of 8year Option B offers a return of 65year compounded semiannually a If Mike chooses Option A how much will he have accumulated at the end of the 10 yr period b If Mike chooses Option B how much will he have accumulated at the end of the 10 yr period c Which option should he choose The Taylors have purchased a 260000 house They make an initial down payment of 40000 and secured a mortgage with interest charged at the rate of 8year on the unpaid balance Interest computations are made at the end of each month If the loan is to be amortized over 30 years what monthly payment will the Taylors be required to make Twelve business students have applied for three available Business Excellence Scholarship awards In how many ways can the scholarships be awarded among these applicants if a No preference is given to any student b The group of applicants includes seven male students and ve female students and it is stipulated that at least one female student must be awarded a scholarship l 00 to H 0 H H H 03 H U Let m w Substance E has a half life of 20 days If 100 grams of this substance are present initially nd the amount present after t days What amount will be left after 6 days The Betzes just bought a new car They put 5000 down and got a loan for the rest The loan they received has interest of 79 a year compounded monthly If they pay 410 a month for 48 months how much was the car worth How much did they pay in interest A company car that has a seating capacity of six is to be used by six employees who have formed a car pool If only four of these employees can drive how many possible seating arrangements are there for the group License plates in a certain state consist of 4 letters followed by 4 integers greater than or equal to 0 and less than or equal to 9 How many possible license plates are there if a there are no additional restrictions b no letter or number may be repeated NH and gz z 1 Find rules for f o g and g o 1 Do not simplify Suppose that you are running a business roasting and selling coffee beans Your xed cost is 5000 and it costs you 6 for every pound of coffee you produce If you sell the coffee for 10 per pound nd the cost revenue and pro t functions for your business Lauren plans to deposit 5000 into a bank account at the beginning of next month and 200 per month into the same account at the end of that month and at the end of each subsequent month for the next 5 years If her bank pays an interest at the rate of 6 per year compounded monthly how much will Lauren have in her account at the end of 5 years Assume she makes NO withdrawals during the 5 yr period The Occupancy rate of the Wonderland Hotel located near an amusement park is given by the function 10 200 710 3 2 it 7t Tt55 t H T 81 Where t is measured in months and t 0 corresponds to the beginning of January Management has estimated that the monthly revenue in thousands of dollars is approximated by the function 02511 rrg 72 0 r 100 a Where r percent is the occupancy rate b What is the hotel s monthly revenue at the beginning of January A nonpro t organization conducted a survey of 2140 metropolitan areas teachers regarding their beliefs about educational problems The following data were obtained 900 said that lack of parental support is a problem 890 said that abused or neglected children are problems 680 said that malnutrition or students in poor health is a problem 120 said that lack of parental support and abused or neglected chilren are problems 110 said that lack of parental support and malnutrition or poor health are problems 140 said that abused or neglected children and malnutrition or poor health are problems 40 said that lack of parental support 1 1 2 2 2 a 1 00 to 0 H D abuse or neglect and malnutrition or poor health are problems What is the probability that a teacher selected at random from this group said that lack of parental support is the only problem hampering a student s schooling Hint draw a Venn diagram Newspaper Subscriptions In a survey of 300 individual investors regarding subscriptions to the New York TimesNYT Wall Street JournalWSJ and USA TodayUST the following data were obtained 122 subscribe to the NYT 150 subscribe to the WSJ 62 subscribe to the UST 38 subscribe to the NYT and WSJ 20 subscribe to the NYT and UST 28 subscribe to the WSJ and UST 16 subscribe to all of these three newspapers a How many of the individual investors surveyed do not subscribe to any of these newspapers b How many subscribe to only one of these newspapers Four balls are selected at random without replacement from an urn containing three red balls and seven black balls Find the probability that exactly three balls are black Round your answer to three decimal places A study conducted by the Metro Housing Agency in a Midwestern city revealed the following information concerning the age distribution of the renters within the city Age Adult Population 76 Group who are renters 76 21 44 51 58 45 64 31 45 65 and over 18 60 a What is the probability that an adult selected at random from this population is a renter b If a renter is selected at random what is the probability that he or she is in the 21 44 age bracket c If a renter is selected at random what is the probability that he or she is 45 yr of age or older Sarah is enrolled in 401k retirement plan She has contributed 300 at the end of each month for the past 15 years Her employer has matched the contribution each month If the account earned interest at the rate 9year compounded monthly over the 15 years period determine how much does she now have in her retirement account An urn contains 7 red 4 blue and 8 black balls If two balls are selected at random without replacement from the urn what is the probability that a blue ball and black ball are selected What is the probability that in the room with 10 people at least two of them have the same birthday Find the accumulated amount A if the principal P 1000 is invested at the interest rate of 8 per year for 5 years compounded quarterly 2 OJ 2 q 2 U 2 a 2 1 28 29 30 A pair of dice is rolled and the number that appears uppermost on each die is observed nd the probability of the given event a the sum of the numbers is an odd number b a pair of 3s is thrown c the sum of the number is 7 Two cards are drawn without replacement from a well shuf ed deck of 52 playing cards a What is the probability that the rst card drawn is a diamond b What is the probability that the second card drawn is a diamond if the rst card drawn was not a diamond Mike s Sporting Goods sells elliptical trainers under two payment plans cash or installment Under the installment plan the customer pays 22 per month over 3 years with interest charged on the balance at a rate of 18 per year compounded monthly Find the cash price for an elliptical trainer if it is equivalent to the price paid by a customer using the installment plan Round to the nearest cent Computers manufactured by a certain company have a serial number consisting of a letter of the alphabet followed by a vedigit number If all the serial numbers of this type have been used how many sets have already been manufactured Assume that the number is a proper number ie does not begin with zero In a survey of 106 senior information technology and data security professionals at major US companies regarding their con dence that they had detected all signi cant security breaches in the past year the following responses were obtained Answer Very con dent Moderately con dent Not very con dent Not at all con dent Respondents 21 56 22 7 What is the probability that a respondent in the survey selected an random a Had little or no con dence that he or she detected all signi cant security breaches in the past year b Was very con dent that he or she had detected all signi cant security breaches in the past year Mark Owens an optician estimates that the probability that a customer coming into his store will purchase one or more pairs of glasses but not contact lenses is 040 and the probability that he will purchase one or more pairs of contact lenses but not glasses is 025 Hence Owens concludes that the probability that a customer coming into his store will purchase neither a pair of glasses nor a pair of contact lenses is 035 Explain why this statement is incorrect Hint Draw a Venn Diagram In a manufacturing plant three machines A B and C produce 40 35 and 25 respectively of the total production The company7s quality control department has determined that 1 of the items produced by machine A 15 of the items produced by machine B and 2 of the items produced by machine C are defective If an item is selected at random and found to be defective what is the probability that is was produced by machine 13 The accompanying data were obtained in a study conducted by the manager of SavMore Supermarket In this study the number of customers waiting in line at the express checkout at the beginning of each 3 minute interval between 9am and 12 noon on Saturday was observed 1 Customers 10111213141516171819110 lFrequencyofOccurrencel114 21711418110161314 1 31 a Find the probability distribution of the random variable X where X denotes the number of customers observed waiting in line b What is EX the expected number of customers standing in the checkout line At the beginning of 1990 the population of a certain state was 554 rural and 446 urban Based on past trends it is expected that 9 of the population currently residing in the rural areas will move into the urban areas while 18 of the population currently residing in the urban areas will move into the rural areas in the next decade What will the population distribution in that state at the beginning of 2010 Within a large metropolitan area 11 of the commuters currently use the public transportation system whereas the remaining 89 commute via automobile The city has recently revitalized and expanded its public transportation system It is expected that 6 months from now 30 ofthose who are now commuting to work via automobile will switch to public transportation and 70 will continue to commute via automobile At the same time it is expected that 20 of those now using public transportation will commute via automobile and 80 will continue to use public transportation In the long run what percent of the commuters will be using public transportation

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