Math Questions

How much should you deposit at the end of each month into an investment account that pays 7% compounded monthly to have $5 million when you retire in 38 years? How much of the $5 million comes from interest? Click the icon to view some finance formulas. In order to have $5 million in 38 years, you should deposit $ each month. (Round up to the nearest dollar.)

Select the correct answer. A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during the rotation? A. 1 B. 2 C. 4 D. 8

Find all values of c that satisfy the mean value theorem for integrals on the following interval. R(v)=v²-v; [5,8] C= (Round to two decimal places as needed. Use a comma to separate answers as needed.)

A container ship left the Dania Pier and traveled north at an average speed of 20 mph. Sometime later an aircraft carrier left traveling in the same direction but at an average speed of 30 mph. After traveling for two hours the aircraft carrier caught up with the container ship. Find the number of hours the container ship traveled before the aircraft carrier caught up. 3 hours 6 hours 4 hours 5 hours 7 hours

Suppose 50 students took an exam with results that were approximately normally distributed. If the mean was 68 and the standard deviation was 10.5, use the normal model to determine the proportion of students that scored at least a 70.

If f(x)=x²-5x and g(x) = 8 - x³, evaluate the following. a. (f+g)(4) b. (g-f)(3) c. (f.g)(-2) d. (g/f)(-4) a. (f+g)(4) = (Simplify your answer.)

Google it: According to a report of the Nielsen Company, 81% of internet searches used the Google search engine. A sample of 100 searches is studied. Use the Cumulative Normal Distribution Table or technology. Round your answer to four decimal places. (a) Approximate the probability that more than 79 of the searches used Google. The probability that more than 79 of the searches used Google was approximately 06480

A ball is launched into the air from the top of a building. Its initial velocity is 20 feet per second. The equation h - 16² +20 t + 50 can be used to model the height h of the ball in feet after t seconds. What is the height of the building the ball is being launched from? How long does it take for the ball to hit the ground?

Investors buy a studio apartment for $200,000. Of this amount, they have a down payment of $60,000. Their down payment is what percent of the purchase price? What percent of the purchase price would an $80,000 down payment be?

The number of asthma sufferers in the world was about 84 million in 1990 and 130 million in 2001. Let v represent the number of asthma sufferers (in millions) worldwide t years after 1990. (a) Write N as a linear function of t. Use exact values in your formula, not decimal approximations. N(t) = (b) Write N as an exponential function of t. Use exact values in your formula, not decimal approximations. N(t) = (c) How many asthma sufferers are predicted worldwide in the year 2014 with the linear model? (d) How many asthma sufferers are predicted worldwide in the year 2014 with the exponential model?

You're a manager in a company that produces rocket ships. Machine A and Machine B both produce cockpits and propulsion sy stems. Machine A ran for 22 hours and produced 3 cockpits and 5 propulsion systems. Machine B ran for 44 hours and produc ed 6 cockpits and 10 propulsion systems. Assume both machines produce cockpits at the same rate and both produce propuls ion systems at the same rate. Can we use a system of linear equations in two variables to solve for a unique amount of time th at it takes each machine to produce a cockpit and to produce a propulsion system? Choose 1 answer: Yes; it takes Machine A a nd Machine B 4 hours to buduce a cockpit and 2 hours to produce a propulsion system. B Yes, it takes Machine A and Machine B 2 hours to produce a cockpit and 4 hours to produce a propulsion system. No: the system has many solutions. No, the syste m has no solution.

Mr. Smith decides to feed his pet Doberman pinscher a combination of two dog foods. Each can of brand A contains 4 units of protein, 1 unit of carbohydrates, and 2 units of fat and costs 60 cents. Each can of brand B contains 1 unit of protein, 1 unit of carbohydrates, and 4 units of fat and costs 40 cents. Mr. Smith feels that each day his dog should have at least 8 units of protein, 5 units of carbohydrates, and 16 units of fat. How many cans of each dog food should he give to his dog each day to provide the minimum requirements at the least cost? Mr. Smith should give his dog can(s) of brand A and can(s) of brand B to provide the minimum requirements at the least cost.

Suppose that you borrow $2000.00 from a friend and promise to pay back $3170.00 in 3 years. What simple interest rate will you pay?

The total area under any curve representing the distribution of a variable equals 1. Explain why. . A. The total area under any curve representing the distribution of a variable does not always equals 1. The area under the standard normal curve does equal 1 but it varies by distribution. B. The area under a curve representing the distribution of a variable is equal to 1 because the area under a standard normal curve is equal to 1 and it became accepted that the area under all density curves should also equal 1. C. It is set to equal 1 to make calculations easier but it could have been set at any amount. D. Percentages for a variable are equal to areas under its density curve expressed as a percentage. An area of 1 is 100% when expressed as a percentage and 100% represents the entirety of the area.

Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit $3000 at the end of each year in an annuity that pays 7.5% compounded annually. How much will you have saved at the end of five years? Find the interest. b. Click the icon to view some finance formulas. a. After 5 years, you will have approximately $ (Do not round until the final answer. Then round to the nearest dollar as needed.)

Challenge in a company, 80% of the workers are men. If 600 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.

Use the problem-solving flowchart. The sum of three times a number and three is equal to the difference of the number and nine. Find the number. Round your answer to the neatest integer, if necessary. The number is

Which shows the equation below written in the form ax2+bx+c=0? x² +7x+9=3 A. x²+4x+6=0 B. x² +7x+6=0 C. x² + 4x+12=0 D. x² +7x+12=0

Karina has two investment options for $20,000 she is saving for her future college expenses. One account pays 2.5% interest compounded monthly. The second account pays 2.2% compounded weekly. Which account will have the larger balance after 5 years? First account both account none of them Second account

If a person's temperature after x hours of strenuous exercise is T(x) = x²(7-x²) + 98.6 degrees Fahrenheit (for 0 ≤ x ≤ 2), find the rate of change of the temperature after 2 hours. °F/hr

The area under a particular normal curve between 8 and 11 is 0.7794. A normally distributed variable has the same mean and standard deviation as the parameters for this normal curve. What percentage of all possible observations of the variable lie between 8 and 11?

A variable is normally distributed with mean 10 and standard deviation 2. a. Find the percentage of all possible values of the variable that lie between 9 and 14. b. Find the percentage of all possible values of the variable that exceed 6. c. Find the percentage of all possible values of the variable that are less than 5.

Records taken from a hospital show that the times between arriving patients have a mean of 8.7 minutes with a standard deviation of 8.7 minutes. Based solely on the values of these two parameters, explain why it is unreasonable to assume that the times between arriving patients is normally distributed or even approximately so. Select the correct choice below. ***** A. It is unreasonable because the standard deviation must be greater than the mean for a variable to be normally distributed. The given standard deviation is equal to the mean. B. It is unreasonable because the time between arriving patients cannot be less than 0 minutes and all the values between 0 and the mean lie within one standard deviation. C. It is unreasonable because the standard deviation must be less than the mean for a variable to be normally distributed. The given standard deviation is equal to the mean. D. It is unreasonable because the time between arriving patients cannot be less than 0 minutes and all the values between 0 and the mean lie within two standard deviations.

A rectangle has a length of x − 6 and a width of x-7. Which equation below describes the perimeter, P, of the rectangle in terms of x? P=2x-13 P-4x-26 p=x²-13x+42 P=x-13

Find the average rate of change of the given function between the following pairs of x-values. f(x) = 4x² + 5x (a) x = 1 and x = 3 (b) x = 1 and x = 2 (c) x = 1 and x = 1.5 (d) x = 1 and x = 1.1 (e) x = 1 and x = 1.01 (f) What number do your answers seem to be approaching?

We have seen that isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use the information to the right to help find the measure of angles 1 through 5.

A company wholesales shampoo in a particular city. Their marketing research department established the following weekly supply-and-demand equations. p= x/600 + 1/2 Supply equation p= 4500/x Demand equation How many units are required for supply to equal demand? At what price per bottle will supply equal demand?

You deposit $15,000 in an account that pays 4.5% interest compounded quarterly. A. Find the future value after one year. B. Use the future value formula for simple interest to determine the effective annual yield. Click the icon to view some finance formulas. A. The future value is $

Olivia sells solar panels to homeowners. She receives a 6% commission from the first $17,000 in sales and a 22% commission for any sales over $17,000. Last month he sold $54,400 worth of solar panels. How much commission did Olivia earn from her first $17,000 in sales?

Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1600 fish. Absent constraints, the population would grow by 150% per year. If the starting population is given by po = 200, then after one breeding season the population of the pond is given by P1 = After two breeding seasons the population of the pond is given by P2=

You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot you are responsible to mow changes. The college conducts a lottery, and whichever number is drawn, represents the value. Your plot has a length which is four more than five times and the width is two less than three times .x. a.) What are the dimensions of your mowing plot? Length: Width: b.) What is the area of your plot (area= length x width)? Area: c.) If x= 12 meters, how many square meters is your plot? Area:

A bank offers a CD that pays a simple interest rate of 11.5%. How much must you put in this CD now in order to have $3,000 for a home-entertainment center in 2 years. The present value that must be invested to get $3,000 after 2 years at an interest rate of 11.5% is (Round up to the nearest cent.)

Determine the effective annual yield for each investment. Then select the better investment. Assume 360 days in a year. 14% compounded monthly; 14.25% compounded annually The effective annual yield for a 14% compounded monthly investment is %.

The city of Raleigh has 9,200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 180 said they'd vote for Brown, 157 said they'd vote for Feliz, and 13 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Round your answer to four decimal places. Preview This sample statistic suggests that we might expect Round to the nearest whole number. Preview of the 9,200 registered voters to vote for Brown.

A student is taking a true-false exam with 10 questions. Assume that the student guesses at all 10 questions. Use the accompanying tables to complete parts a through c. a. The student gets either seven or eight answers correct. The probability the student gets either seven or eight answers correct is _____ b. The student gets between four and eight answers correct, inclusive. The probability the student gets between four and eight answers correct, inclusive is _____

After you build 1 shelf, your friend wonders how long it will take you to build 9 shelves. How much time will it take to build 9 shelves, if you work at a constant rate?

A major coffee supplier has warehouses in Seattle and San Jose. The coffee supplier receives orders from coffee retailers in Salt Lake City and Reno. The retailer in Salt Lake City needs 600 pounds of coffee, and the retailer in Reno needs 450 pounds of coffee. The Seattle warehouse has 1000 pounds available, and the warehouse in San Jose has 700 pounds available. The cost of shipping from Seattle to Salt Lake City is $2.50 per pound, from Seattle to Reno $3 per pound, from San Jose to Salt Lake City $4 per pound, and from San Jose to Reno $2 per pound. Find the number of pounds to be shipped from each warehouse to each retailer to minimize the cost. Ship pounds of coffee from Seattle to Salt Lake City. pounds of coffee from Seattle to Reno, pounds of coffee from San Jose to Reno. pounds of coffee from San Jose to Salt Lake City, and

You must decide whether to buy a new car for $23,000 or lease the same car over a three-year period. Under the terms of the lease, you can make a down payment of $2000 and have monthly payments of $150. At the end of the three years, the leased car has a residual value (the amount you pay if you choose to buy the car at the end of the lease period) of $11,000. Assume you can sell the new car at the end of the three years at the same residual value. Is it less expensive to buy or to lease?

Suppose that $5000 is deposited into an account that earns 3.5% interest compounded Semiannually. Let f(t) represent the value (in dollars) of the account at t years after depositing the $5000. Find the value of the account at t = 4 years. (Round your answers to two decimal places.) {Round your final answer to two decimal places}

A study finds that the carapace length of an adult spider is normally distributed with a mean of 19.55 mm and a standard deviation of 1.29 mm. Let x denote carapace length for the adult spider. VIIHNEN an permaye vi avvn sprecio a vapadorongan u THREE CER IV TREG The percentage of adult spiders that have carapace lengths between 17 mm and 18 mm is equal to the area under the standard normal curve between 1.98 and - 1.20. (Round to two decimal places as needed.) e. Find the z-score and direction that corresponds to the percentage of adult spiders that have carapace lengths exceeding 21 mm. The percentage of adult spiders that have carapace lengths exceeding 21 mm is equal to the area under the standard normal curve that lies to the right of (Round to two decimal places as needed)

The population of weights of a particular fruit is normally distributed, with a mean of 228 grams and a standard deviation of 12 grams. If 26 fruits are picked at random, then 7% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.

A nature center charges a $5 admission charge for children who are 12 years old or younger and $10 for those 13 years old and older. On Tuesday, the petting zoo took in $1620 from ticket sales and sold a total of 232 tickets. How many tickets of each type were sold? a. Clearly write the unknown quantities you're being asked to find and assign variables to represent each of them. Let x = Let y = b. Using the information in the problem, write a system of equations representing this scenario. You may consider making a table to organize the known and unknown quantities to help you write the system.

For the arithmetic sequence with a, = 2 and d=5, find each: (a) the first five terms The first five terms of the arithmetic sequence are (b) the 12th term The 12th term in the arithmetic sequence is (c) the sum of the first 12 terms The sum of the first 12 terms of the arithmetic sequence is

How is a normal probability plot used to detect outliers? Choose the correct answer below. A. All observations are used to construct the normal probability plot, and any observations above 0 may be outliers. B. All observations are used to construct the normal probability plot, and any observations that have a normal score greater than 2 in magnitude may be outliers. C. All observations are used to construct the normal probability plot, and any observations that fall well outside the overall pattern of the data may be outliers. D. All observations are used to construct the normal probability plot, and any observations that do not fall on a straight line may be outliers.

Based on a recent study, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with mean 7.26 and standard deviation of 0.15. Find the percentage of preterm infants who have the following arterial cord pH levels. a. pH levels between 7.00 and 7.50 b. pH levels over 7.34. a. The percentage of arterial cord pH levels that are between 7.00 and 7.50 is (Round to two decimal places as needed.)

A car traveling at speed v miles per hour on a dry road should be able to come to a full stop in the distance of D(V) = 0.055v² + 1.1v feet.+ Find the stopping distance required for a car traveling at 45 mph. (Round your answer to the nearest whole number.)

You invest $1950 in an account paying 5.9% interest compounded daily. What is the account's effective annual yield? Assume 360 days in a year.

Fill in the blanks below: a. If an ellipse has a major axis length of 8, then its semi-major axis length is_ b. If an ellipse has a minor axis length of 6, then its semi-minor axis length is c. If an ellipse has vertices at (0, 2) and (0, 2) then its major axis length is semi-major axis length is d. If an ellipse has co-vertices at (0, 1) and (0, 1) then its semi-minor axis length is Is this ellipse a horizontal ellipse or a vertical ellipse? e. If a vertical ellipse has a major axis length of 4, its vertices are at f. If a horizontal ellipse has a semi-minor axis length of 3, its co-vertices are at

You own 18 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? The probability that the CDs are in alphabetical order is

For the geometric sequence with a 32 and r= -1/4, find each (a) the first five terms (b) the 12 term (c) the sum of the first 12 terms, rounding values to two decimal places, if necessary