Seawater has density 1025 kg/m 3 and flows in a velocity field v = y i + x j, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward...

Let F(x, y, z) = z tan-1(y 2 ) i + z 3 ln(x 2 + 1) j + z k. Find the flux of F across the part of the paraboloid x 2 + y 2 + z = 2 that lies above the plane z = 1 and is oriented upward.

Evaluate the line integral. C xy dx + y 2 dy + yz dz, C is the line segment from (1, 0, -1), to (3, 4, 2)

Use power series to solve the differential equation y'' - xy' - 2y = 0

If you deposit $100 at the end of every month into an account that pays 3% interest per year compounded monthly, the amount of interest accumulated after n months is given by the sequence

(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and (b) find the area of triangle PQR. (b) P(0, 0, -3), Q(4, 2, 0), R(3, 3, 1)

Find a vector function that represents the curve of intersection of the cylinder x 2 + y 2 = 16 and the plane x + z = 5.

For the curve given by r(t) = (sin 3 t, cos 3 t, sin 2 t), 0 < t < y 2 , find (a) The unit tangent vector, (b) The unit normal vector, (c) The unit binormal vector, and (d) The curvature.

Suppose that over a certain region of space the electrical potential V is given by V(x, y, z) = 5x 2 - 3xy + x/z. (a) Find the rate of change of the potential at P(3, 4, 5) in the direction of the...

The contour map shows wind speed in knots during Hurricane Andrew on August 24, 1992. Use it to estimate the value of the directional derivative of the wind speed at Homestead, Florida, in the...

Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint(s). f (x, y) = x 2 y; x 2 + y 2 = 1

Select a random sample of three without replacement from the following (very small) population of firms: IBM, GM, Ford, Shell, HP, Boeing, and ITT. Use the following sequence of random digits:...

Without using a calculator, evaluate (a) 10 (2) (b) (1) (3) (c) (8) 2 (d) (5) (5) (e) 24 (2) (f) (10) (5) (g) 20/-4 (h) -27/-9 (i) (6) 5 (1) ( j) 2 x (-6) x 3 (-9)

On graph paper draw axes with values of x and y between 3 and 10, and plot the following points: P(4, 0), Q(2, 9), R(5, 8), S(1, 2) Hence find the coordinates of the point of intersection of the line...

An airline charges $300 for a flight of 2000 km and $700 for a flight of 4000 km. (a) Plot these points on graph paper with distance on the horizontal axis and cost on the vertical axis. (b) Assuming...

Amazon.com is an e-commerce firm that has shown considerable growth since its founding in 1995, and its quarterly net sales are shown in Table 14.4.4. Their 2014 annual report includes a section...

The number of people, N, employed in a chain of cafes is related to the number of cafes, n, by the equation: N = 10n + 120 (a) Illustrate this relation by plotting a graph of N against n for 0 n ...

Write down a formula for each situation: (a) A plumber has a fixed call-out charge of $80 and has an hourly rate of $60. Work out the total charge, C, for a job that takes L hours in which the cost...

The demand, Q, for a certain good depends on its own price, P, and the price of an alternative good, PA, according to Q = 30 3P + PA (a) Find Q if P = 4 and PA = 5. (b) Is the alternative good...

The total cost, TC, of producing 100 units of a good is 600 and the total cost of producing 150 units is 850. Assuming that the total cost function is linear, find an expression for TC in terms of Q,...

Table 3.12 gives the annual rate of inflation during a five-year period. If a nominal house price at the end of Year 1 was $10.8 million, find the real house price adjusted to prices prevailing at...

A bank offers a return of 7% interest compounded annually. Find the future value of a principal of $4500 after six years. What is the overall percentage rise over this period?

A department store has its own credit card facilities, for which it charges interest at a rate of 2% each month. Explain briefly why this is not the same as an annual rate of 24%. What is the annual...

An individual saves $5000 in a bank account at the beginning of each year for 10 years. No further savings or withdrawals are made from the account. Determine the total amount saved if the annual...

A builder is offered one of two methods of payment: Option 1: A single sum of $73 000 to be paid now. Option 2: Five equal payments of $15 000 to be paid quarterly with the first instalment to be...

Differentiate the following functions, giving your answer in a similar form, without negative or fractional indices: (d) y = xVx (b) fx) = Jx (c) f(x) = (a) f(x) fx) =

Differentiate (a) y = 5x 2 (b) y = 3/x (c) y = 2x + 3 (d) y = x 2 + x + 1 (e) y = x 2 3x + 2 (f) y = 3x (g) y = 2x 3 6x 2 + 49x 54 (h) y = ax + b (i) y = ax 2 + bx + c ( j) y = 4x - 3/x + 7/x 2

(a) Find the elasticity of demand in terms of Q for the demand function, P = 20 0.05Q. (b) For what value of Q is demand unit elastic? (c) Find an expression for MR and verify that MR = 0 when...

If the supply equation is Q = 7 + 0.1P + 0.004P 2 find the price elasticity of supply if the current price is 80. (a) Is supply elastic, inelastic or unit elastic at this price? (b) Estimate the...

Given the demand function Q = 200 2P P A + 0.1Y 2 where P = 10, P A = 15 and Y = 100, find (a) the price elasticity of demand; (b) the cross-price elasticity of demand; (c) the income elasticity of...

Use Lagrange multipliers to find the maximum value of z = x + 2xy subject to the constraint x + 2y = 5

Find the producers surplus at Q = 9 for the following supply functions: (a) P = 12 + 2Q (b) P = 20Q + 15

A publisher decides to use one section of its plant to produce two textbooks called Microeconomics and Macroeconomics. The profit made on each copy is $12 for Microeconomics and $18 for...

National income Y varies over time t according to the following model: dY/dt = 0.6(C + I - Y) C = 0.8Y + 600 I = 800 where C is consumption and I is planned investment. Initially, Y = 2000. (a) Find...

Use Greens Theorem in the form of Equation 13 to prove Greens first identity: where D and C satisfy the hypotheses of Greens Theorem and the appropriate partial derivatives of f and g exist and are...

Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain. (a) The most popular type of investment among...

Determine whether each number describes a population parameter or a sample statistic. Explain. (a) A survey of 1003 U.S. adults ages 18 years and older found that 72% own a smartphone. (b) In a...

Determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set. Explain your reasoning. (a) The numbers of employees at fast-food restaurants in a...

Data at the ratio level cannot be put in order. Whether the statement is true or false. If it is false, rewrite it as a true statement.

What is an inherent zero? Describe three examples of data sets that have inherent zeros and three that do not.

In a survey of 1033 U.S. adults, 51% said U.S. presidents should release all medical information that might affect their ability to serve. Determine whether the study is an observational study or an...

Researchers demonstrated that adults using an intensive program to lower systolic blood pressure to less than 120 millimeters of mercury reduce the risk of death from all causes by 27%. Determine...

Every tenth person entering a mall is asked to name his or her favorite store. Identify the sampling technique used, and discuss potential sources of bias (if any). Explain.

Why is a sample used more often than a population?

What is the difference between a parameter and a statistic?

It is impossible to obtain all the census data about the U.S. population. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.

The amount of energy collected from every solar panel on a photovoltaic power plant. Determine whether the data set is a population or a sample. Explain your reasoning.

The number of wireless devices in each U.S. household. Determine whether the data set is a population or a sample. Explain your reasoning.

Use the Venn diagram to identify the population and the sample. Incomes of Home Owners in Massachusetts Incomes of home owners in Massachusetts with mortgages Incomes of home owners in Massachusetts...

A survey of 159 U.S. law firms found that the average hourly billing rate for partners was $604. Identify the population and the sample. Describe the sample data set.

A students score on the Fundamentals of Engineering exam is in the 89th percentile. Make an observation about the students exam score.

A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 153? Match the event with its probability. (a) 0.95 (b) 0.005 (c) 0.25 (d) 0 (e)...

A game show contestant must randomly select a door. One door doubles her money while the other three doors leave her with no winnings. What is the probability she selects the door that doubles her...

The probability that an event will not happen is given. Find the probability that the event will happen. P(E') = 21/61

Guessing the initial of a students middle name. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram then appropriate.

Give three observations that can be made from the graph. Monthly Active Users on 5 Social Networking Sites as of September 2016 1750 1500 1250 1000 750 500 250 Site Number of users (in millions)...

The mean is the measure of central tendency most likely to be affected by an outlier. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.

Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer. 18 15 12 9- 2 3 4 5 6 7 8 9 10 11...

Find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Weights (in pounds) of Packages on a...

You are applying for jobs at two companies. Company A offers starting salaries with = $41,000 and = $1000. Company B offers starting salaries with = $41,000 and = $5000. From which company are...

Construct a cumulative frequency distribution and an ogive for the data set using six classes. Then describe the location of the greatest increase in frequency. Retirement Ages Data set: Retirement...

Event A: Randomly select a member of the U.S. Congress. Event B: Randomly select a male U.S. Senator. Determine whether the events are mutually exclusive. Explain your reasoning.

Use the ogive to approximate (a) the number in the sample. (b) the location of the greatest increase in frequency. Black Bears 80 Weight (in pounds) Cumulative frequency 72.5 115.5 158.5 201.5 244.5...

The table shows the results of a survey that asked 506 Maine adults whether they favored or opposed a tax to fund education. A person is selected at random from the sample. Find the probability of...

The state of Virginias license plates have three letters and four digits. Assuming that any letter or digit can be used, how many different license plates are possible? Use the Fundamental Counting...

The probability of rolling 2 six-sided dice and getting a sum of 9 is 1/9. Classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain...

Determine whether the events are mutually exclusive. Explain your reasoning. Event A: Randomly select a student born on the 30th of a month Event B: Randomly select a student with a birthday in...

(a) Find the mean, variance, and standard deviation of the probability distribution, and (b) Interpret the results. The number of games played in each World Series from 1903 through 2016 6. 8 Games...

Sixty-two percent of U.S. adults get news on social media sites. You randomly select five U.S. adults. Find the probability that the number of U.S. adults who get news on social media sites is (a)...

A restaurant offers a $15 dinner special that lets you choose from 6 appetizers, 12 entres, and 8 desserts. How many different meals are available when you select an appetizer, an entre, and a...

Thirty-six percent of Americans think there is still a need for the practice of changing their clocks for Daylight Savings Time. You randomly select seven Americans. Find the probability that the...

Assuming that no questions are left unanswered, in how many ways can a six-question true or false quiz be answered? Use the Fundamental Counting Principle.

Use the bar graph at below, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random is...

Find each probability. (a) P(x > 20) (b) P(0 < x < 5) (c) P(x < 9 or x > 27) The random variable x is normally distributed with mean = 18 and standard deviation = 7.6.

Random samples of size 8 are drawn from the population and the mean of each sample is determined. Is the sampling distribution of sample means normally distributed? Explain. The per capita disposable...

For the same sample statistics, which level of confidence would produce the widest confidence interval? Explain your reasoning. (a) 90% (b) 95% (c) 98% (d) 99%

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...

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...

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...

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. . -0.7 0 1.2

The random variable x is normally distributed with mean = 174 and standard deviation = 20. Find the indicated probability. P(x > 155)

Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile. 0.2090

In a survey of U.S. women, the heights in the 20- to 29-year age group were normally distributed, with a mean of 64.2 inches and a standard deviation of 2.9 inches. Find the probability that a...

The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 20 minutes and a standard deviation of 5 minutes. Find the probability that a randomly selected...

Find the positive z-score for which 12% of the distributions area lies between -z and z. Find the indicated z-score.

The per capita energy consumption level (in kilowatt-hours) in Venezuela for a recent year can be approximated by a normal distribution, as shown in the figure. (a) What consumption level represents...

The test scores for the analytical writing section of the Graduate Record Examination (GRE) can be approximated by a normal distribution, as shown in the figure. (a) What is the maximum score that...

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. = 45, = 15, n = 100

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. = 1275, = 6, n = 1000

As the sample size increases, the standard deviation 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.

The diameters (in inches) of four machine parts are 1.000, 1.004, 1.001, and 1.003. Use a sample size of 2. A population and sample size are given. (a) Find the mean and standard deviation of the...

A water footprint is a measure of the appropriation of fresh water. The per capita water footprint in the United States for a recent year is approximately normally distributed, with a mean of 1.64...

From 1871 through 2016, the mean return of the Standard & Poors 500 was 10.72%. A random sample of 38 years is selected from this population. What is the probability that the mean return for the...

In a sample of 1000 fines issued by the city of Toronto for parking infractions, the mean fine was $47.12 and the standard deviation was $48.24. A random sample of size 55 is selected from this...

Find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area. 0.46

Find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area. -2.35 -0.8 0

Find the indicated area under the standard normal curve. If convenient, use technology to find the area. To the right of z = 3.22

Find the critical value z c necessary to construct a confidence interval at the level of confidence c. c = 0.85

Find the critical value z c necessary to construct a confidence interval at the level of confidence c. c = 0.75