Math Questions

Use A=(5, 6, 7, 8, 9) and B={1, 3, 7, 8) to find the set A∩B. A∩B= (Use a comma to separate answers as needed.)

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R(x) → 0.] f(x) = In(x), a = 6 f(x) = In(6) + Ž n = 1 Find the associated radius of convergence R. R =

Find the distance between the points (-10, -9) and (-2,-2).

In response to rising concerns about identity theft, the number of models of paper shredders a company manufactures increased approximately steadily from 5 models in 1997 to 37 models in 2008. Find the average rate of change of the number of shredder models manufactured per year between 1997 and 2008. The average rate of change of the number of paper shredders manufactured per year between 1997 and 2008 was (Type an integer or decimal rounded to two decimal places as needed.)

Jerome is planning on tiling his bathroom floor with square tiles measuring 8 inches on each side. The bathroom measures 13 feet by 15 feet. a) What is the area of the floor, in square feet? b) Convert this area to square inches. c) How many 8 inch square tiles will Jerome need to cover the floor?

Fill in the blank so that the resulting statement is true. If you can choose one item from a group of M items and a second item from a group of N items, then the total number of two-item choices is If you can choose one item from a group of M items and a second item from a group of N items, then the total number of two-item choices is

The activity on Marny Zell's MasterCard account for one billing period is shown below. Find the average daily balance and the finance charge if the billing period is June 26 through July 25, the previous balance was $396.63, and the annual interest rate is 19.5%.

The value of a machine, V, at the end of t years is given by V = C(1-r)', where C is the original cost and r is the rate of depreciation. Find the value of a machine at the end of 4 years if the original cost was $2387 and r = 0.2. Round to the nearest cent.

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. n = 30, x = 89.6, s = 12.5, 90% confidence 83.31 <µ< 95.89 85.75 <µ< 93.45 84.93 <μ< 94.27 85.72 <µ< 93.48

A pet store keeps track of the purchases of customers over a four-hour period. The store manager classifies purchases as containing a dog product, a cat product, a fish product, or a product for a different kind of pet. The data to the right was recorded. Complete parts (a) through (d) below. (a) How many purchases were for a dog product only? purchases (Type a whole number.) (b) How many purchases were for a cat product only? 87 customers purchased a dog product, 98 customers purchased a cat product, 27 customers purchased a fish product; 24 customers purchased a dog and a cat product; 7 customers purchased a dog and a fish product, 11 customers purchased a cat and a fish product, 3 customers purchased a dog, a cat, and a fish product; 36 customers purchased a product for a pet other than a dog, a cat, or a fish. purchases (Type a whole number.) (c) How many purchases were for a dog or fish product? purchases (Type a whole number.) (d) How many purchases were there in total? purchases (Type a whole number.)

A student has a credit card that is only used for school expenses. Their fall tuition was $1295, and the cost of books was $100. Both of these are put onto their credit card. a) Suppose these are the only two expenses on their credit card. When the bill arrives, they pay the minimum payment of $30. How much will be left on their credit card bill and therefore subject to interest? b) If the annual interest rate for their credit card is 17.99%, what is the periodic (monthly) interest rate, to 2 decimal places? c) How many dollars of interest will be added to their bill for the next month, to the nearest cent?

Two variables appear to have an exponential relationship. What pattern(s) does the scatterplot suggest for the model? Select the two correct answers. It is only increasing or only decreasing. It has a point of inflection. It is only concave up or only concave down. It has one or more extrema. It is both concave up and concave down.

The hotness of chili peppers is usually measured in Scoville units. Using a log scale for Scoville units works well to compare the heat of peppers. a) A Jamaican Hot Pepper has hotness around 200,000 Scoville units. Plot this value on the log scale below. b) Another chili's hotness is shown on the number line below. What is, approximately, the hotness of the chili shown on the number line? Scoville units.

(a) Solve the equation 1500(0.733)t = 300 using the In function. Round your answer to three decimal places. (b) Solve the equation 1500 (0.733)t = 300 using the log function. Round your answer to three decimal places.

The population of foxes in a certain region over a 2-year period is estimated to be P₁(t) = 300 + 60 sin(πt/12) in month t, and the population of rabbits in the same region in month t is given by P₂(t) = 2000 + 300 cos((πt/12) Find the rate of change of the populations when t = 4. (Express a decrease in population as a negative rate of change. Round your answers to one decimal place.)

An architect is making a model of a building she is designing. The kitchen will be 8 feet by 14 feet. The scale she is using for the model is 3 inches = 2 feet. How many 1 inch x 1 inch tiles are needed to cover the floor of the model kitchen? Tiles needed:

Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) f(x) = 3xex, a=0

The formula for changing Celsius (C) temperature to Fahrenheit (F) temperature is F = 1.8C + 32. To the nearest degree, what is the Fahrenheit temperature when the Celsius temperature is -8? A -18 degrees B -17 degrees C 17 degrees D 18 degrees

Ed must select and answer in any order four of twelve essay questions on a test. In how many ways can he do so? Enter your result in the space provided using number keys only.

Emilio buys a sofa for a total purchase price of $1,309.79. State taxes were 4.4%. What is the sales tax amount for his purchase? (Round your answer to the nearest cent.) $50.38 $55.20 $57.63 $62.37

Determine which symbol belongs in the blank to make the statement true. {-1,0,7} _{0,8,- 1,6,7}

Randy buys a lawn tractor costing $975.90. The store charges $35 for assembly and $30 for delivery. State taxes are 4% and local sales taxes are 3%. What is the total purchase price? (Round your answer to the nearest cent.) $1,082.54 $1,109.21 $1,113.76 $1,115.01

Given event T1, T2, T3, and D with p(D)=0.05, p(T1|D)=p(~T1|~D)=0.9, p(T2|D)=p(~T2|~D)=0.8, p(T3|D)=0.9 and p(~T3|~D)=1, find p(T1u T2uT3) if p(T∩T2)=0.05, p(T∩T3)=0.01, and T2 and T3 are mutually exclusive.

An aquarium tank (like at a zoo) measures 5.1 meters by 7.1 meters by 8.1 meters tall. The tank is filled to 1 foot below the top of the tank. Things you will need to do this problem (do NOT google to find other facts - use these facts): 1 ft = 0.3048 m There are 7.48 gallons in a cubic foot. The formula for the volume of this shape is length" width" height Sketch a picture of the tank and label the dimensions. It is likely easiest to do this on paper, scan and insert here either with cut/paste or the insert image button above (mountain icon).

Given: (x is number of items) Demand function: d(x) = 440-0.5x² Supply function: s(x) = 0.6x² Find the equilibrium quantity: Find the consumers surplus at the equilibrium quantity:

A produce buyer for a juice company is buying apples. He makes a choice of either New York, Oregon, Washington, or imported apples. For this contract he must also choose large or extra large. Write out the sample space and assume each outcome is equally likely. Then give the probability of the requested outcomes in parts (a) and (b) below. Write out the sample space. Choose the correct answer below. A. S=((Oregon, large), (New York,extra large), (Washington, large), (Washington, extra large), (imported, extra large)} B. S={(Oregon, large), (Oregon, extra large), (New York, large), (New York,extra large), (imported, large), (imported, extra large)} C. S={(Oregon, large), (Oregon, extra large), (New York, large), (New York, extra large), (Washington, large), (Washington, extra large), (imported, large), (imported,extra large)} D. S={(Oregon, large), (New York,large), (New York,extra large), (Washington, large), (Washington,extra large), (imported,extra large)} (a) The apples selected are extra large. (Type an integer or a simplified fraction.) (b) The apples selected are from Oregon or large. (Type an integer or a simplified fraction.)

A media rental store rented the following number of movie titles in each of these categories: 178 horror, 248 drama, 118 mystery, 326 romance, and 134 comedy. If a person selects a movie to rent, find the probability that it is a horror or comedy.

Aliza had a tax liability of $6,218 last year. She was entitled to tax credits of $748 and withholding amounted to $540 per month. Aliza owed other taxes of $606. Calculate the amount of the refund or the amount of taxes due (as the case may be). $344 refund $404 refund $1,010 refund $4,930 due

Find the distance between the points (2, 9) and (-10, 1). Hint: Use the Pythagorean theorem.

Solve by comparing the square : x2 + 8z - 2 = 0 f(x) = 5x2 - 1 Is it odd, even or neither A ball is thrown straight up, from 3 m above the ground, with a velocity of 14m/s. When does it reach it's maximun height? H (t) = 3 +14t-5t2

Dan is putting money into a savings account. He starts with $350 in the savings account, and each week he adds $30. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Dan has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 17 weeks.

Aaron's dad has a pickup truck and his mom has an SUV. Last week, his dad traveled 84 miles in the pickup truck on 4 gallons of gas. His mom traveled 72 miles in the SUV on 3 gallons of gas. How many more miles per gallon did the SUV get than the truck?

Jeremy has a total of $25 in dimes and nickels. He has 4 more dimes than nickels. Which system of equations can be used to determine the number of dimes, d, and the number of nickels, n, that Jeremy has?

Water is passed through a pipe containing porous material to filter out pollutants. Each inch of pipe removes 50% of the pollutant entering. (a) True or false: The first inch of the pipe removes 50 % of the pollutants and the second inch removes the remaining 50 %. (b) What length of pipe is needed to remove all but 8% of the pollutants? Round your answer to three decimal places. inches of pipe removes all but 8% of the pollutants.

Robin is single. Her taxable income is $71,511. Find the tax liability using the Tax Table, Exhibit 18-3 from your text. $8,200.32 $10,280.42 $11,671.92 $15,732.42

Isosceles trapezoid ABCD with AB || CD has m (<A) = m (<B) = 60°, small base CD = 12 cm and non-parallel side BC = 24 cm. Find the large base AB and the lengths of the diagonals AC and BD.

Bernie and LuLu are selling fruit for a local fundraiser. Customers can buy boxes of apples or boxes of oranges. Bernie sold 7 boxes of apples and 7 boxes of oranges for a total of $147. LuLu sold 7 boxes of apples and 10 boxes of oranges for a total of $183. Determine the cost of one box of apples and one box of oranges.

Cesar is making a model of the Eiffel Tower. The height of the tower is 984 feet, and Cesar wants to make a 1.5-foot model. What scale should Cesar use? Find the scale in inches to feet. Round your answer to the nearest tenth of a foot.

Solve the equation 0.05e^-0.344t = 0.15 using natural logs. NOTE: Enter the exact answer. t =

Tiles containing the letters for the word "ENCYCLOPEDIA" are placed in a bag. If you reach into the bag and select one tile at random, what are the odds against drawing the letter E?

Yolanda owns some property that has an assessed value of $59,928. Find the tax due if the tax rate is 8.33% of the assessed value. (Round your answer to the nearest cent.) $4,794.24 $4,974.02 $4,992.00 $5,393.52

A marble is drawn from a box containing 3 yellow, 5 white, and 13 blue marbles. Find the odds in favor of drawing the following (a) A yellow marble (b) A blue marble (c) A white marble (a) In reduced form, the odds in favor of drawing a yellow marble are (Simplify your answers.) (b) In reduced form, the odds in favor of drawing a blue marble are (Simplify your answers.) (c) In reduced form, the odds in favor of drawing a white marble are (Simplify your answers.)

A cross section of a nuclear cooling tower is a hyperbola with equation x² /90² - y² /130² - = 1. The tower is 450 ft tall, and the distance from the top of the tower to the center of the hyperbola is half the distance from the base of the tower to the center of the hyperbola. Find the diameter of the top and the base of the tower.

Let U= {a,b,c,d,e,f,6,7,8,9,10,11), X = {a,b,c,7,8,9), and Y = {b,d,f,6,8,10}. List the members of the set X'nY', using set braces. X'nY' = {} (Use a comma to separate answers as needed.)

Amy and Derek are married and filing jointly. Their taxable income is $36,847. Use the Tax Table, Exhibit 18-3 from your text to find the tax liability. $4,040.64 $4,149.64 $4,231.14 $4,421.64

A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 7.6 hours. 0.0008 0.0025 0.0036 0.0103

Your grade point average (GPA) is a form of a weighted average. That is, 4 units of A counts more than 4 units of B. The most common weight for grades is A, 4 points; B, 3 points; C, 2 points; D, 1 point; and F, 0 points. To find a GPA, 1. Multiply the points for each grade by the number of units for the course. 2. Find the sum of these products. 3. Divide this sum by the total number of units taken. Find the GPA for 4 units of F in astronomy, 3 units of D in geometry, 2 units of A in sociology, and 3 units of B in biology. Round your answer to the nearest tenth.

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that R(x) → 0.] f(x) = e-4x

Suppose that the profit obtained from the sale of x fish -fry dinners is given by P(x) = -0.025x² + 8x - 40. What is the marginal profit, in dollars from the sale of the 101st fish-fry dinner? Write your answer to two decimal places and donot use the dollar sign symbol.

A simple random sample is taken from a population and yields the following data for a variable of the population. 9 34 38 37 19 24 11 19 21 32 Find a point estimate for the population standard deviation (that is, the standard deviation of the variable). A point estimate for the population standard deviation is