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Calculate the double integral. x sin(x + y) dA, R= [0, T/6] [0, 1/3] Find the volume of the solid enclosed by the paraboloid z = 2 + x 2 + (y - 2) 2 and the planes z = 1, x = 1, x = -1, y = 0, and y = 4. Evaluate the iterated integral by converting to polar coordinates. (V4-x2 ex-y dy dx o Jo Evaluate the iterated integral. y-z (2 ) dx dy dz Vo Jo Sketch the vector field F by drawing a diagram like Figure 5 or Figure 9. F(x, y) = y i - x j/x 2 + y 2 The figure shows a vector field F and two curves C 1 and C 2 . Are the line integrals of F over C 1 and C 2 positive, negative, or zero? Explain. C2} (a) Find a function f such that F = f and (b) use part (a) to evaluate C F dr along the given curve C. F(x, y) = xy i + xy j, C: r(t) = (t 2t, t + 2t), .3,,2 0 Find (a) the curl and (b) the divergence of the vector field. F(x, y, z) = x/1 + z i + y/1 + x j + z/1 + y k The GL company makes televisions. It produces a 32-inch screen that sells for $100 profit and a 48-inch screen that sells for $150 profit. On the assembly line, the 32-inch screen requires 3 hr, and... A Lorenz curve is given by y = L(x), where 0 x 1 represents the lowest fraction of the population of a society in terms of wealth and 0 y 1 represents the fraction of the total wealth that is... (a) Are the points P 1 and P 2 sources or sinks for the vector field F shown in the figure? Give an explanation based solely on the picture. (b) Given that F(x, y) = (x, y 2 ), use the definition of... Suppose S and E satisfy the conditions of the Divergence Theorem and f is a scalar function with continuous partial derivatives. Prove that These surface and triple integrals of vector functions are... Find the distance from the origin to the line x = 1 + t, y = 2 - t, z = -1 + 2t. Use the Chain Rule to find dz/dt or dw/dt. z = x - y/x + 2y, x = e t , y = e - t- Transpose the formulae: (a) Q = aP + b to express P in terms of Q (b) Y = aY + b + I to express Y in terms of I (c) Q = 1/aP + b to express P in terms of Q If the national income, Y, is 1000 units, then consumption, C, is 800 units. Also whenever income rises by 100, consumption increases by 70. Assuming that the consumption function is linear: (a)... Express the following in terms of logbx and logby: (a) log b x 2 y (b) log b (x/y 2 ) (c) log b x 2 y 7 The number of items, N, produced each day by an assembly-line worker, t days after an initial training period, is modelled by N = 100 100e 0.4t (1) Calculate the number of items produced daily (a) 1... An antiques dealer tries to sell a vase at 45% above the $18 000 which the dealer paid at auction. (a) What is the new sale price? (b) By what percentage can the dealer now reduce the price before... Find the single percentage increase or decrease equivalent to (a) a 10% increase followed by a 25% increase (b) a 34% decrease followed by a 65% increase (c) a 25% increase followed by a 25%... Determine the APR if the nominal rate is 7% compounded continuously. A monopolists demand function is given by P + Q = 100 Write down expressions for TR and MR in terms of Q and sketch their graphs. Find the value of Q which gives a marginal revenue of zero and... A firm is the sole producer of two goods labelled 1 and 2. The demand functions are given by where Qi and Pi denote the quantity demanded and price of good i, respectively. The total cost function is... Sample annual salaries (in thousands of dollars) for entry level software engineers in Raleigh, NC, and Wichita, KS, are listed. Find the coefficient of variation for each of the two data sets. Then... The probability that an event will happen is given. Find the probability that the event will not happen. P(E) = 2/7 Event A: Randomly select a student with a birthday in April. Event B: Randomly select a student with a birthday in May. Determine whether the events are mutually exclusive. Explain your reasoning. The table shows the numbers of male and female students in the U.S. who received bachelors degrees in business in a recent year. A student is selected at random. Find the probability of each event.... A lottery has 52 numbers. In how many different ways can 6 of the numbers be selected? (Assume that order of selection is not important.) Find the probability of choosing three second-shift workers. A warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at... A student must choose from 7 classes to take at 8:00 a.m., 4 classes to take at 9:00 a.m., and 3 classes to take at 10:00 a.m. How many ways can the student arrange the schedule? Use the Fundamental... On the basis of prior counts, a quality control officer says there is a 0.05 probability that a randomly chosen part is defective. Classify the statement as an example of classical probability,... In most applications, continuous random variables represent counted data, while discrete random variables represent measured data. Determine whether the statement is true or false. If it is false,... Not putting money in a parking meter and getting a parking ticket. Determine whether the events are independent or dependent. Explain your reasoning. In a sample of 1000 U.S. adults, 200 think that most Hollywood celebrities are good role models. Two U.S. adults are selected at random without replacement. (a) Find the probability that both adults... Let x represent the number of cars in a university parking lot. Determine whether the random variable x is discrete or continuous. Explain. Let x represent the snowfall (in inches) in Nome, Alaska, last winter. Determine whether the random variable x is discrete or continuous. Explain. The histogram represents a binomial distribution with 5 trials. Match the histogram with the appropriate probability of success p. Explain your reasoning. (a) p = 0.25 (b) p = 0.50 (c) p = 0.75 P(x)... Thirty-two percent of U.S. employees who are late for work blame oversleeping. You randomly select six U.S. employees who are late for work and ask them whether they blame oversleeping. The random... Sixty-eight percent of undergraduate students admit to cheating on tests or in written work. You randomly select six undergraduate students. Find the probability that the number of undergraduate... You randomly select one card from a standard deck of 52 playing cards. Event A is selecting a diamond. Determine the number of outcomes in the event. Then decide whether the event is a simple event... Probability experiment consists of rolling a 12-sided die, numbered 1 to 12. Find the probability of the event. Event A: rolling a 2 Probability experiment consists of rolling a 12-sided die, numbered 1 to 12. Find the probability of the event. Event F: rolling a number divisible by 5 Event C: randomly choosing a resident who is not 14 years old or younger. Find the probability of the event One out of every 119 tax returns that a tax auditor examines requires an audit. Find the probability that (a) The first return requiring an audit is the 25th return the tax auditor examines, (b) The... Determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard... Find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area. 1.3 Find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability. P(z < -2.58 or z > 2.58) The random variable x is normally distributed with mean = 174 and standard deviation = 20. Find the indicated probability. P(172 < x < 192) A population has a mean and a standard deviation . Find the mean and standard deviation of the sampling distribution of sample means with sample size n. = 150, = 25, n = 50 The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.4 million cells per microliter and a... As the sample size increases, the mean of the distribution of sample means increases. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. What are the two types of hypotheses used in a hypothesis test? How are they related? The data set represents the scores of 12 randomly selected students on the SAT Physics Subject Test. Assume the population test scores are normally distributed and the population standard deviation... Construct a 99% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed. Use the figure, which shows the results... A statistical hypothesis is a statement about a sample. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The statement represents a claim. Write its complement and state which is H 0 and which is H a . 645 The statement represents a claim. Write its complement and state which is H 0 and which is H a . 5 A tablet manufacturer claims that the mean life of the battery for a certain model of tablet is more than 8 hours. Write the claim as a mathematical statement. State the null and alternative... A used textbook selling website claims that at least 60% of its new customers will return to buy their next textbook. Describe type I and type II errors for a hypothesis test of the indicated claim. An urban planner claims that the noontime mean traffic flow rate on a busy downtown college campus street is 35 cars per minute. Describe type I and type II errors for a hypothesis test of the... A null hypothesis is rejected with a level of significance of 0.05. Is it also rejected at a level of significance of 0.10? Explain. Find the critical value(s) and rejection region(s) for the type of z-test with level of significance a. Include a graph with your answer. Left-tailed test, = 0.03 Test the claim about the population mean at the level of significance a. Assume the population is normally distributed. Claim: = 40; = 0.05; = 1.97 Sample statistics: x = 39.2, n = 25 A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is 6.3 seconds. A random sample of 33 sedans has a mean acceleration time from 0 to 60 miles per hour... State whether each standardized test statistic t allows you to reject the null hypothesis. Explain. (a) t = 1.4 (b) t = 1.42 (c) t = -1.402 3 4 o = 1.402 2 3 -4 -3 -2 -1 1. A credit reporting agency claims that the mean credit card debt by state is greater than $5500 per person. You want to test this claim. You find that a random sample of 30 states has a mean credit... Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance . Right-tailed test, n = 10, = 0.10 An education researcher claims that 57% of college students work year-round. In a random sample of 300 college students, 171 say they work year-round. At = 0.10, is there enough evidence to support... Sample 1: The maximum bench press weights for 53 football players Sample 2: The maximum bench press weights for the same 53 football players after completing a weight lifting program Classify the two... Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases? What if the variables have a negative linear correlation? Test the claim about the difference between two population means 1 and 2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed.... A demographics researcher claims that the mean household income in a recent year is greater in Cuyahoga County, Ohio, than it is in Wayne County, Michigan. In Cuyahoga County, a sample of 19... A demographics researcher claims that the mean household income in a recent year is the same in Ada County, Idaho, and Cameron Parish, Louisiana. In Ada County, a sample of 18 residents has a mean... The one-way commuting times from home to work for all employees working at a large company have a bell-shaped curve with a mean of 34 minutes and a standard deviation of 8 minutes. Using the... In a survey of 1000 drivers from the Midwest, 855 wear a seat belt. In a survey of 1000 drivers from the South, 909 wear a seat belt. At = 0.10, can you support the claim that the proportion of... The ages (in years) of 11 children and the numbers of words in their vocabulary (a) Display the data in a scatter plot, (b) Calculate the sample correlation coefficient r, (c) Describe the type of... The table in Exercise 25 shows the maximum weights (in kilograms) for which one repetition of a half squat can be performed and the jump heights (in centimeters) for 12 international soccer players.... A research center claims that more than 80% of U.S. adults think that mothers should have paid maternity leave. In a random sample of 50 U.S. adults, 82% think that mothers should have paid maternity... The following table lists the average one-way commuting times (in minutes) from home to work for 30 metropolitan areas around the world with more than 1 million residents (urbandemographics.... The statement represents a claim. Write its complement and state which is H 0 and which is H a . P 0.64 An amusement park company owns three hotels on an adjoining site. A guest relations manager wants to study the time it takes for shuttle buses to travel from each of the hotels to the amusement park... According to a Gallup poll conducted August 710, 2014, 48% of American workers said that they were completely satisfied with their jobs. Assume that this result is true for the current population of... In a Harris Poll conducted October 1520, 2014, American adults were asked to think ahead 2 to 5 years and assess if they feel solar energy will contribute to meeting our energy needs. Of the... A gardener has six rows available in his vegetable garden to place tomatoes, eggplant, peppers, cucumbers, beans, and lettuce. Each vegetable will be allowed one and only one row. How many ways are... How many different ways can a senior project manager and an associate project manager be selected for an analytics project if there are eight data scientists available? In a one-tail hypothesis test where you reject H 0 only in the upper tail, what is the p-value if Z STAT = +2.00? In Problem 9.36, what is your statistical decision if you test the null hypothesis at the 0.05 level of significance? In Problem 9.36 In a one-tail hypothesis test where you reject H 0 only in the... How do the average credit scores of people living in different American cities differ? The data in Credit Scores is an ordered array of the average credit scores of 2,570 American cities. a.... The financial services call center in Problem 2.20 also monitors call duration, the amount of time spent speaking to customers on the phone. The file CallDuration contains the following data for... Referring to the results of Problems 10.67 and 10.68 concerning the weight and granule loss of Boston and Vermont shingles, write a report that summarizes your conclusions. Are you an impulse shopper? A survey of 500 grocery shoppers indicated that 29% of males and 40% of females make an impulse purchase every time they shop. Assume that the survey consisted of 250... Thirty companies comprise the DJIA. Just how big are these companies? One common method for measuring the size of a company is to use its market capitalization, which is computed by multiplying the... You wish to explain to your boss what effect taking the base-10 logarithm of the salary values in the companys database will have on the data. As a simple example, you compare a salary of $10,000... Do Millennials or Gen-Xers feel more tense or stressed out at work? A survey of employed adults conducted online by Harris Interactive on behalf of the American Psychological Association revealed the... As in Exercise 15, youre phoning local businesses. You call three firms. What is the probability that all three are owned by women? In Exercise 15 The 2000 Census showed that 26% of all firms in the... Tobys Trucking Company determined that the distance traveled per truck per year is normally distributed, with a mean of 50 thousand miles and a standard deviation of 12 thousand miles. a. What... The amount of water in a two-liter bottle is approximately normally distributed with a mean of 2.05 liters with a standard deviation of 0.025 liter. a. What is the probability that an individual... The weight of an energy bar is approximately normally distributed with a mean of 42.05 grams with a standard deviation of 0.025 gram. a. What is the probability that an individual energy bar contains... One of the major measures of the quality of service provided by any organization is the speed with which the organization responds to customer complaints. A large family-held department store selling... In a survey of 1,003 adults concerning complaints about restaurants, 732 complained about dirty or ill-equipped bathrooms and 381 complained about loud or distracting diners at other tables. Source:...
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