Finite Mathematics for the Managerial, Life, and Social Sciences
12th Edition
ISBN: 9781337405782
Author: Soo T. Tan
Publisher: Cengage Learning
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Textbook Question
Chapter 7.2, Problem 9E
SOCIAL MEDIA ACCOUNTS In a survey of 1000 social media account holders, the following questions were asked: How many social medial account do you have? The results of the survey are summarized below.
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a. Determine the empirical probability distribution associated with these data.
b. What is the probability that a participant in the survey selected random answered that he or she had three or four accounts?
Source: AARP
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Chapter 7 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences
Ch. 7.1 - Explain what is meant by an experiment. Give an...Ch. 7.1 - What does it mean for two events to be mutually...Ch. 7.1 - In Exercises 1-6, let S={a,b,c,d,e,f} be a sample...Ch. 7.1 - In Exercises 1-6, let S={a,b,c,d,e,f} be a sample...Ch. 7.1 - Prob. 3ECh. 7.1 - In Exercises 1-6, let S={a,b,c,d,e,f} be a sample...Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - In Exercises 7-14, let S={1,2,3,4,5,6}, E={2,4,6},...Ch. 7.1 - Prob. 8E
Ch. 7.1 - Prob. 9ECh. 7.1 - In Exercises 7-14, let S={1,2,3,4,5,6}, E={2,4,6},...Ch. 7.1 - In Exercises 7-14, let S={1,2,3,4,5,6}, E={2,4,6},...Ch. 7.1 - In Exercises 7-14, let S={1,2,3,4,5,6}, E={2,4,6},...Ch. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - In Exercises 15-20, let S be any sample space, and...Ch. 7.1 - Prob. 17ECh. 7.1 - In Exercises 15-20, let S be any sample space, and...Ch. 7.1 - Prob. 19ECh. 7.1 - In Exercises 15-20, let S be any sample space, and...Ch. 7.1 - Consider the sample space S of Example 4, page...Ch. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Let S={1,2,3}.be a sample space associated with an...Ch. 7.1 - An experiment consists of selecting a card from a...Ch. 7.1 - An experiment consists of selecting a letter at...Ch. 7.1 - An experiment consists of tossing a coin, rolling...Ch. 7.1 - An experiment consists of spinning the hand of the...Ch. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - SELECTING JOB APPLICANTS From a list of five...Ch. 7.1 - FAMILY BIRTH ORDER An experiment consist of...Ch. 7.1 - BLOOD TYPES Human blood is classified by the...Ch. 7.1 - GAME SHOWS In a television game show, the winner...Ch. 7.1 - ATMs The manager of a local bank observes how long...Ch. 7.1 - Prob. 39ECh. 7.1 - QUALITY ASSURANCE SURVEYS The customer service...Ch. 7.1 - ASSEMBLY-TIME STUDIES A time study was conducted...Ch. 7.1 - POLITICAL POLLS An opinion poll is conducted among...Ch. 7.1 - QUALITY CONTROL As part of a quality control...Ch. 7.1 - Prob. 44ECh. 7.1 - SHUTTLE BUS USAGE A certain hotel operates a...Ch. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.2 - Define a a probability distribution and b a...Ch. 7.2 - Prob. 2CQCh. 7.2 - Prob. 3CQCh. 7.2 - Prob. 1ECh. 7.2 - In Exercises 1-8, list the simple events...Ch. 7.2 - Prob. 3ECh. 7.2 - In Exercises 1-8, list the simple events...Ch. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - In Exercises 1-8, list the simple events...Ch. 7.2 - SOCIAL MEDIA ACCOUNTS In a survey of 1000 social...Ch. 7.2 - Workplace In a survey of 26,612 Parade.com...Ch. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - GRADE DISTRIBUTIONS The grade distribution for a...Ch. 7.2 - Prob. 14ECh. 7.2 - Prob. 15ECh. 7.2 - RED LIGHT RUNNERS In a survey of 800 likely...Ch. 7.2 - Prob. 17ECh. 7.2 - Prob. 18ECh. 7.2 - Prob. 19ECh. 7.2 - CHECKING INTO A HOTEL ROOM In a survey of 3019...Ch. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - CORRECTIVE LENS USE According to Mediamark...Ch. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - Prob. 27ECh. 7.2 - If a ball is selected at random from an urn...Ch. 7.2 - Prob. 29ECh. 7.2 - A pair of fair dice is rolled. What is the...Ch. 7.2 - TRAFFIC LIGHTS What is the probability of arriving...Ch. 7.2 - ROULETTE What is the probability that a roulette...Ch. 7.2 - Prob. 33ECh. 7.2 - In Exercises 3335, determine whether the given...Ch. 7.2 - In Exercises 3335, determine whether the given...Ch. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - SELECTING JOB APPLICANTS Refer to Exercises 7.1,...Ch. 7.2 - FAMILY BIRTH ORDER Refer to Exercise 7.1, Problem...Ch. 7.2 - DISPOSITION OF CRIMINAL COURT CASES Of the 98...Ch. 7.2 - SWEEPSTAKES In a sweepstakes sponsored by Gemini...Ch. 7.2 - POLITICAL POLLS An opinion poll is conducted among...Ch. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - SPENDING METHODS In a survey of consumer spending...Ch. 7.2 - Prob. 48ECh. 7.2 - Prob. 49ECh. 7.2 - Prob. 50ECh. 7.2 - Airline Safety In an attempt to study the leading...Ch. 7.2 - Housing Appreciation In a survey conducted on fall...Ch. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.3 - Suppose that S is a sample space of an experiment,...Ch. 7.3 - Give an example, based on a real-life situation,...Ch. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - A pair of dice is rolled, and the number that...Ch. 7.3 - A pair of dice is rolled, and the number that...Ch. 7.3 - A pair of dice is rolled, and the number that...Ch. 7.3 - An experiment consists of selecting a card at...Ch. 7.3 - Prob. 8ECh. 7.3 - An experiment consists of selecting a card at...Ch. 7.3 - An experiment consists of selecting a card at...Ch. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - Raffles Five hundred raffle tickets were sold....Ch. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - In Exercises 15-22, explain why the statement is...Ch. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - In Exercises 15-22, explain why the statement is...Ch. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Let E and F be two events that are mutually...Ch. 7.3 - Prob. 24ECh. 7.3 - Let S={s1,s2,s3,s4} be the sample space associated...Ch. 7.3 - Let S={s1,s2,s3,s4,s5,s6} be the sample space...Ch. 7.3 - MAKEUP OF U.S. MOVIEGOER AUDIENCE In a survey of...Ch. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - 401k INVESTORS According to a study conducted in...Ch. 7.3 - Prob. 31ECh. 7.3 - YACHT SALES The manufacturer of the new Silver...Ch. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - Alternative Fuel Vehicles A survey was conducted...Ch. 7.3 - Forecasting Sales The probability that a shopper...Ch. 7.3 - COURSE ENROLLMENTS Among 500 freshmen pursuing a...Ch. 7.3 - CUSTOMER SURVEYS A leading manufacturer of kitchen...Ch. 7.3 - ASSEMBLY-TIME STUDIES A time study was conducted...Ch. 7.3 - USE OF LANDLINE PHONE VERSUS CELL PHONE A survey...Ch. 7.3 - TIME ON A DIET A survey on how long dieters stay...Ch. 7.3 - Prob. 45ECh. 7.3 - Prob. 46ECh. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - LOSING WEIGHT In a survey, 1012 American adults...Ch. 7.3 - Prob. 50ECh. 7.3 - RISK OF AN AIRPLANE CRASH According to a study of...Ch. 7.3 - DISTRACTED DRIVING According to a study of 100...Ch. 7.3 - PLANS TO KEEP CARS In a survey conducted to...Ch. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Fifty raffle tickets are numbered 1 through 50,...Ch. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - In Exercises 5762, determine whether the statement...Ch. 7.3 - Prob. 61ECh. 7.3 - Prob. 62ECh. 7.4 - What is the probability of an event E in a uniform...Ch. 7.4 - Prob. 2CQCh. 7.4 - An unbiased coin is tossed five times. in...Ch. 7.4 - An unbiased coin is tossed five times. In...Ch. 7.4 - Prob. 3ECh. 7.4 - An unbiased coin is tossed five times. 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Let E denote the...Ch. 7.5 - A card is drawn from a well-shuffled deck of 52...Ch. 7.5 - A card is drawn from a well-shuffled deck of 52...Ch. 7.5 - BATTERY LIFE The probability that a battery will...Ch. 7.5 - TRAFFIC LIGHTS The traffic lights at a certain...Ch. 7.5 - Prob. 25ECh. 7.5 - Five black balls and four white balls are placed...Ch. 7.5 - Prob. 27ECh. 7.5 - Refer to Exercises 7.1, Problem 36, in which you...Ch. 7.5 - SELLING A CAR Jack has decided to advertise the...Ch. 7.5 - AUDITING TAX RETURNS A tax specialist has...Ch. 7.5 - POWERBALL Powerball, introduced in October 2015,...Ch. 7.5 - Prob. 32ECh. 7.5 - EDUCATIONAL LEVEL OF VOTERS In a survey of 1000...Ch. 7.5 - Prob. 34ECh. 7.5 - Prob. 35ECh. 7.5 - EMPLOYEE EDUCATION AND INCOME The personnel...Ch. 7.5 - STUDENT FINANCIAL AID The accompanying data were...Ch. 7.5 - Two cards are drawn without replacement from a...Ch. 7.5 - FAMILY COMPOSITION In a three-child family, what...Ch. 7.5 - Prob. 40ECh. 7.5 - Prob. 41ECh. 7.5 - CAR THEFT Figures obtained from a citys police...Ch. 7.5 - SWITCHING BROADBAND SERVICE According to a survey...Ch. 7.5 - PROBABILITY OF TRANSPLANT REJECTION The...Ch. 7.5 - QUALITY CONTROL An automobile manufacturer obtains...Ch. 7.5 - HOUSING LOANS The chief loan officer of La Crosse...Ch. 7.5 - Prob. 47ECh. 7.5 - Prob. 48ECh. 7.5 - QUALITY CONTROL A box contains two defective...Ch. 7.5 - Prob. 50ECh. 7.5 - REAL ESTATE SALES Mark, a real estate agent,...Ch. 7.5 - Prob. 52ECh. 7.5 - Prob. 53ECh. 7.5 - Prob. 54ECh. 7.5 - QUALITY CONTROL It is estimated that 0.80 of a...Ch. 7.5 - Prob. 56ECh. 7.5 - PRODUCT RELIABILITY The proprietor of Cunninghams...Ch. 7.5 - Prob. 58ECh. 7.5 - Prob. 59ECh. 7.5 - Prob. 60ECh. 7.5 - Prob. 61ECh. 7.5 - Prob. 62ECh. 7.5 - Prob. 63ECh. 7.5 - Prob. 64ECh. 7.5 - Prob. 65ECh. 7.5 - Prob. 66ECh. 7.5 - Prob. 67ECh. 7.5 - Prob. 68ECh. 7.6 - What are a priori probabilities and a posteriori...Ch. 7.6 - Prob. 2CQCh. 7.6 - Prob. 3CQCh. 7.6 - Prob. 1ECh. 7.6 - In Exercises 1-3, refer to the accompanying Venn...Ch. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - In Exercises 4-6, refer to the accompanying Venn...Ch. 7.6 - Prob. 7ECh. 7.6 - Prob. 8ECh. 7.6 - Prob. 9ECh. 7.6 - The accompanying tree diagram represent a two...Ch. 7.6 - Prob. 11ECh. 7.6 - The accompanying diagram represents a two-stage...Ch. 7.6 - Prob. 13ECh. 7.6 - Prob. 14ECh. 7.6 - Prob. 15ECh. 7.6 - Prob. 16ECh. 7.6 - Prob. 17ECh. 7.6 - Prob. 18ECh. 7.6 - Prob. 19ECh. 7.6 - Prob. 20ECh. 7.6 - SEAT-BELT COMPLIANCE Data compiled by the Highway...Ch. 7.6 - CAR THEFT Figures obtained from a citys police...Ch. 7.6 - BLOOD TESTS If a certain disease is present, then...Ch. 7.6 - OPINION POLLS In a survey to determine the opinion...Ch. 7.6 - CRIME RATES Data compiled by the department of...Ch. 7.6 - Prob. 26ECh. 7.6 - Prob. 27ECh. 7.6 - Prob. 28ECh. 7.6 - Prob. 29ECh. 7.6 - PERSONNEL SELECTION Applicants for temporary...Ch. 7.6 - TERRORISM In a survey of 1504 adults nationwide...Ch. 7.6 - DETECTING SHOPLIFTERS The management of Marks...Ch. 7.6 - Prob. 33ECh. 7.6 - OPINION POLLS A survey involving 400 likely...Ch. 7.6 - Prob. 35ECh. 7.6 - SELECTION OF SUPREME COURT JUDGES In a past...Ch. 7.6 - AGE DISTRIBUTION OF RENTERS A study conducted by...Ch. 7.6 - PRODUCT RELIABILITY The estimated probability that...Ch. 7.6 - An experiment consists of randomly selecting one...Ch. 7.6 - GUN OWNERS IN THE SENATE As of January 3, 2013,...Ch. 7.6 - RELIABILITY OF MEDICAL TESTS A medical test has...Ch. 7.6 - RELIABILITY OF MEDICAL TESTS Refer to Exercise 41....Ch. 7.6 - QUALITY CONTROL Jansen Electronics has four...Ch. 7.6 - Prob. 44ECh. 7.6 - QUALITY CONTROL. A halogen desk lamp produced by...Ch. 7.6 - Prob. 46ECh. 7.6 - AUTO-ACCIDENT RATES An insurance company has...Ch. 7.6 - Prob. 48ECh. 7.6 - Prob. 49ECh. 7.6 - VOTER TURNOUT BY INCOME Voter turnout drops...Ch. 7.6 - Prob. 51ECh. 7.6 - Prob. 52ECh. 7.6 - Prob. 53ECh. 7.6 - Prob. 54ECh. 7.CRQ - Fill in the blanks. An activity with observable...Ch. 7.CRQ - Prob. 2CRQCh. 7.CRQ - Prob. 3CRQCh. 7.CRQ - Prob. 4CRQCh. 7.CRQ - Prob. 5CRQCh. 7.CRQ - Prob. 6CRQCh. 7.CRE - Let E and F be two mutually exclusive events, and...Ch. 7.CRE - Prob. 2CRECh. 7.CRE - Prob. 3CRECh. 7.CRE - Prob. 4CRECh. 7.CRE - An urn contains six red balls, five black balls,...Ch. 7.CRE - Prob. 6CRECh. 7.CRE - Prob. 7CRECh. 7.CRE - Prob. 8CRECh. 7.CRE - Prob. 9CRECh. 7.CRE - Prob. 10CRECh. 7.CRE - Prob. 11CRECh. 7.CRE - Prob. 12CRECh. 7.CRE - The accompanying tree diagram represents an...Ch. 7.CRE - An experiment consists of tossing a fair coin...Ch. 7.CRE - QUALITYCONTROL In a group of 20 ballpoint pens on...Ch. 7.CRE - Prob. 16CRECh. 7.CRE - Prob. 17CRECh. 7.CRE - Prob. 18CRECh. 7.CRE - Prob. 19CRECh. 7.CRE - Prob. 20CRECh. 7.CRE - Prob. 21CRECh. 7.CRE - Prob. 22CRECh. 7.CRE - Prob. 23CRECh. 7.CRE - Prob. 24CRECh. 7.CRE - SAFETY OF AMERICAN-MADE PRODUCTS The accompanying...Ch. 7.CRE - Prob. 26CRECh. 7.CRE - Prob. 27CRECh. 7.CRE - Prob. 28CRECh. 7.CRE - Prob. 29CRECh. 7.CRE - Prob. 30CRECh. 7.CRE - Prob. 31CRECh. 7.CRE - Prob. 32CRECh. 7.CRE - Prob. 33CRECh. 7.CRE - FAMILY COMPOSITION Consider the composition of a...Ch. 7.CRE - Prob. 35CRECh. 7.CRE - Tax Preparation A survey in which people were...Ch. 7.CRE - Prob. 37CRECh. 7.CRE - Prob. 38CRECh. 7.CRE - Prob. 39CRECh. 7.CRE - Prob. 40CRECh. 7.CRE - Prob. 41CRECh. 7.CRE - Prob. 42CRECh. 7.CRE - QUALITY CONTROL Copykwik has four photocopy...Ch. 7.CRE - Prob. 44CRECh. 7.CRE - Prob. 45CRECh. 7.CRE - BEVERAGE PREFERENCES In study of scientific...Ch. 7.CRE - Prob. 47CRECh. 7.CRE - Prob. 48CRECh. 7.CRE - Prob. 49CRECh. 7.CRE - Prob. 50CRECh. 7.BMO - Let S={s1,s2,s3,s4,s5,s6} be the sample space...Ch. 7.BMO - Prob. 2BMOCh. 7.BMO - Prob. 3BMOCh. 7.BMO - Prob. 4BMOCh. 7.BMO - Prob. 5BMO
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- Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 34.4 27.1 30.8 28.0 32.2 27.6 32.8 25.2 31.4 33.5 24.7 28.4 Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives ABABABABAABB. Test the sequence for randomness about the median with a 5% level of significance. Verify that the number of runs is 10. What is the upper critical value c2? arrow_forwardSand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 34.4 27.1 30.8 28.0 32.2 27.6 32.8 25.2 31.4 33.5 24.7 28.4 Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives ABABABABAABB. Test the sequence for randomness about the median with a 5% level of significance. Verify that the number of runs is 10. What is the upper critical value c2?arrow_forward29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.arrow_forward
- Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 27.3 34.6 30.6 27.8 33.4 31.5 27.3 31.2 32.0 24.7 24.4 28.2 Test this sequence for randomness about the median. Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives BAABAABAABBB. Verify that the number of runs is 7, the lower critical number is 3, and the upper critical number is 11. Use a 5% level of significance. State the conclusion of the test and interpret your results.arrow_forward29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.arrow_forward4. Assume that a risk-free money market account is added to the market described in Q3. The continuously compounded rate of return on the money market account is log (1.1). (i) For each given μ, use Lagrange multipliers to determine the proportions (as a function of μ) of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. (ii) Determine the market portfolio in this market and calculate its Sharp ratio.arrow_forward
- 3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05, Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75. (i) Given that an investor is targeting a total expected return of μ = 0.2. What portfolio weights should they choose to meet this goal with minimum portfolio variance? Correct all your calculations up to 4 decimal points. (ii) Determine the global minimum-variance portfolio and the expected return and variance of return of this portfolio (4 d.p.). (iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient frontier. (iv) Without further calculation, explain how the minimum variance of the investor's portfolio return will change if the two risky assets were independent.arrow_forward2. A landlord is about to write a rental contract for a tenant which lasts T months. The landlord first decides the length T > 0 (need not be an integer) of the contract, the tenant then signs it and pays an initial handling fee of £100 before moving in. The landlord collects the total amount of rent erT at the end of the contract at a continuously compounded rate r> 0, but the contract stipulates that the tenant may leave before T, in which case the landlord only collects the total rent up until the tenant's departure time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r. (i) Calculate the expected total payment EW the landlord will receive in terms of T. (ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides that the rental rate r should depend on the contract length T by r(T) = λ √T 1 For each given λ, what T (as a function of X) should the landlord choose so as to maximise their expected utility? Justify your answer. Hint. It might be…arrow_forwardPlease solving problem2 Problem1 We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.arrow_forward
- Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forwardThis question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. A B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3t) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot(3πt) sin(3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411- 4 -2 sin (3лt) (d)…arrow_forward5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward
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