Math Questions

You work for a marketing firm that has a large client in the automobile industry. You have been asked to estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned to gather a random sample that could be used to estimate this proportion to within a 0.04 margin of error at a 90% level of confidence. a) With no prior research, what sample size should you gather in order to obtain a 0.04 margin of error? Round your answer up to the nearest whole number. n =___households

Give an expression for f(x) with leading coefficient 3, of degree 3, and having roots x = 6, x=2 + i, and x = 2-i. • Your final answer should not contain any i's. f(x) =__ is a polynomial of degree 3 with the given roots and leading coefficient.

What are the domain and range of the sine function? Domain: All Real Numbers Range: (-1,1) Domain: All Real Numbers where x≠..... -π/2,π/2,.... Range: [-1,1] Domain: [-1,1] Range: All Real Numbers Domain: All Real Numbers Range: [-1,1]

An arch is in the form of a semi-ellipse, with its major axis as the span. If the span is 80 feet and the height is 30 feet write the standard equation. x²/900+ y²/1600=1 x²/1600+ y²/900=1 x²/6400+ y²/900=1

During a chemical reaction chemical A is turned into chemical B at a rate that is proportional to the square root of the amount of chemical A. Which equation describes the correct differential equation to model the rate of change in chemical A? dA/dt=k/ k√A dA/dt=k√A dA/dt=k/A² dA/dt = kA²

Give an expression for f(x) using only Real-valued coefficients, having degree 4, passing through the point (-8,370), with roots a = -6, a = -9, and x = -2-i. • Your final answer should not contain any i's. f(x) = is a polynomial of degree. with the given roots and passes through (-8,370).

An A-frame house overlooking the Pacific ocean has windows entirely covering one end. If the roof intersects at a 66° angle and the roof is 28 feet long from peak to ground, how much area do the windows cover? Round to the nearest hundredth.

A football was thrown into the air at a speed of 37 miles per hour at an angle of 50 from the horizontal. Express this velocity in vector form. Round your answer to four decimals.

Write these decimals as fractions in lowest terms and determine the prime factorization of the denominator in each case. (a) 0.468 (b) 0.045 (a) Write 0.468 as a fraction in lowest terms. 0.468 =

A vector with magnitude 9 points in a direction 265 degrees counterclockwise from the positive x axis. Write the vector in component form. Vector:

Solve the system by using the inverse of the coefficient matrix. -x+ 3y=9 6x-17y - 50 What is the inverse of the coefficient matrix? (Type an integer or simplified fraction for each matrix element.)

8] Ophelia Payne is walking to her office building which she knows is 150 ft high. The angle to the top of the building from her current location is 6 degrees. How much further does she need to walk?

What is the compound interest if $46,000 is invested for 5 years at 6% compounded continuously? (Round your answer to the nearest cent.) You found the total, not the interest.

For the following function, a) determine whether it is one-to-one; b) if it is one-to-one, find its inverse function. f(x)=x+9 Is the given function a one-to-one function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Yes, the function is one-to-one. The inverse function is f(x) = (Simplify your answer.) B. No, the the function is not one-to-one.

Suppose that a card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing each of the following? a) A queen b) An ace or a 9 c) A club d) A red queen a) What is the probability of drawing a queen? (Simplify your answer. Type an integer or a fraction.) b) What is the probability of drawing an ace or a 9? (Simplify your answer. Type an integer or a fraction.) c) What is the probability of drawing a club? (Simplify your answer. Type an integer or a fraction.) d) What is the probability of drawing a red queen? (Simplify your answer. Type an integer or a fraction.)

Find an equation of an ellipse satisfying the given conditions. Foci: (-4, 0) and (4, 0) Length of major axis: 12

Last year it was recorded that among the 2,896 students in the school district, 1,325 have visited the school nurse. You believe that the proportion of students who visited the school nurse this year has changed, and decide to test this using a 0.1 level of significance. Of a sample of 300 students in a school district, 153 have visited the school nurse. Match the variable to its value. 1. P 2. Po 3. n 0.458 300 0.51

The problem describes a debt to be amortized. (Round your answers to the nearest cent.) A man buys a house for $370,000. He makes a $150,000 down payment and amortizes the rest of the purchase price with semiannual payments over the next 7 years. The interest rate on the debt is 9%, compounded semiannually. (a) Find the size of each payment. (b) Find the total amount paid for the purchase. (c) Find the total interest paid over the life of the loan.

The equation of a conic section is given in a familiar form. Identify the type of graph that the equation has, without actually graphing. x-3y²-5y = 0 Choose the correct classification below. Hyperbola Parabola Ellipse Circle

Fill in the blanks in the statement below. The__represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. It is denote___

How many code symbols can be formed using 3 out of 7 letters of A, B, C, D, E, F, G if the letters: a) are not repeated? b) can be repeated? c) are not repeated but must begin with D? d) are not repeated but must begin with DE? For each part, give the answer using permutation notation, factorial notation, or other operations. Then evaluate. E. 1.6P2 G. 75 F. 6! H. 7³ There are 30 possible code symbols. (Simplify your answer.) d) What is the answer using the proper notation? A. 77 C. 5! E. 1.6P2 G. 75 B. 6! D. 7! F. 7³ H.1.1.5P1 There are 5 possible code symbols. (Simplify your answer.)

In trapezoid BYTE, BE || YT and median LM is drawn. (a) LM = 35. If the length of BE exceeds the length of YT by 13, find the lengths of the bases. (b) If YT=x+9, LM = x + 15, and BE = 2x-5, find the lengths of YT, LM, and BE.

7. A warren of bunnies is growing at 14% per month. a. Find the approximate doubling time. b. If the warren is currently at a population of 400 bunnies, use the approximate doubling time to find the size of the warren in 2 years. c. Find the exact doubling time. Round to 2 decimal places. d. If the warren is currently at a population of 400 bunnies, use the exact doubling time to find the size of the warren in 2 years. e. What is the relative error caused by using the approximate doubling time instead of the exact doubling time? Round to 2 decimal places.

The recommended number of hours of sleep per night is 8 hours, but everybody "knows" that the average college student sleeps less than 7 hours. The number of hours slept last night by 10 randomly selected college students is listed below. Complete the following hypothesis test: H: μ = 7, H₂: μ< 7, a = 0.05. 6.9 6.6 6.8 6.5 7.5 6.5 7.9 5.2 5.4 6.6 (a) Find t. (Give your answer correct to two decimal places.) (1) Find the p-value. (Give your answer correct to four decimal places.)

At the fair you buy an unlimited ride pass for $22 and plan to play some games costing $2.50 per game. Write a function in x that represents the total amount you spend on rides and games at the fair. Be sure to indicate any domain restrictions.

Find the probability. There are twelve shirts in your closet, six blue and six green. Two of the blue shirts and two of the green shirts fit well. The others are too big. You randomly select a shirt to wear. It is blue or is too big. 6/11≈ 0.545 10/11≈ 0.909 7/8=0.875 5/6≈ 0.833 8/11≈ 0.727

A laptop computer is purchased for $3200. Each year, its value is 80% of its value the year before. After how many years will the laptop computer be worth $1000 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer. _years

A painting sold for $277 in 1978 and was sold again in 1990 for $485. Assume that the growth in the value V of the collector's item was exponential. a) Find the value k of the exponential growth rate. Assume V₂ = 277. k=_ (Round to the nearest thousandth.) b) Find the exponential growth function in terms of t, where t is the number of years since 1978. V(t)=_ c) Estimate the value of the painting in 2015. $_ (Round to the nearest dollar.) d) What is the doubling time for the value of the painting to the nearest tenth of a year? _years (Round to the nearest tenth.) e) Find the amount of time after which the value of the painting will be $2173. _years (Round to the nearest tenth.)

The owner of a local chain of grocery stores is always trying to minimize the time it takes her customers to check out. In the past, she has conducted many studies of the checkout times, and they have displayed a normal distribution with a mean time of 12.8 minutes. and a standard deviation of 2.6 minutes. She has implemented a new schedule for cashiers in hopes of reducing the mean checkout time. A random sample of 33 customers visiting her store this week resulted in a mean of 11.8 minutes. Does she have sufficient evidence to claim the mean checkout time this week was less than 12.8 minutes? Use α = 0.02. (a) Find z. (Round your answer to two decimal places.) (ii) Find the p-value. (Round your answer to four decimal places.)

Following the birth of a child, a parent wants to make an initial investment Po that will grow to $50,000 for the child's education at age 17. Interest is compounded continuously at 6%. What should the initial investment be? Such an amount is called the present value of $50,000 due 17 years from now. The present value is about $. (Do not round until the final answer. Then round to two decimal places as needed.)

Residents of a gated community use a five-digit code to open the gate. What is the probability that a robber will enter the code correctly on a first random try? Assume the code allows repeated digits. 0.00001 0.0001 0.001 0.01

Someone brought a box of twenty-four doughnuts to soccer practice. They all look the same but the fillings differ. Ten are cherry, eight are custard, and six are chocolate. If one player eats three doughnuts selected randomly, what is the probability that all three were chocolate? 5/506 1/2,024 1/20 1/506

If the claim of researchers is that the mean score is more than 92, what would be the correct alternate hypothesis for it? Mean score is less than 92. Mean score is more than 92. Mean score is equal to 92. Mean score is different from 92.

Mr. and Mrs. Evans hope to send their daughter to college in thirteen years. How much money should they invest now at an interest rate of 8% per year, compounded continuously, in order to be able to contribute $8000 to her education? Do not round any intermediate computations, and round your answer to the nearest cent.

Twelve students entered an essay contest in which the winner gets $500, second place gets $200, and third place gets $100. How many ways are there to rank the students first, second, and third? Each student only entered one essay and no student received two prizes. 1,320 220 33 132

The junior class has $300 to invest in a candy sale. They can sell no more than 9 cases of suckers and they must sell at least 18 cases of M & M's. Suckers cost $4 a case and M&M's cost $12 a case. If the profit on a case of suckers is $10 and the profit on a case of M & M's is $20, how many each should they buy to maximize their profit?

Twenty students are working at a car wash to raise money for the homeless shelter in their town. Two students are chosen to go pick up pizzas for lunch. How many different ways can two students be chosen to make the pizza run? 190 380 40 300

Kindergarten children have heights that are approximately normally distributed about a mean of 39 inches and a standard deviation of 2 inches. If a random sample of 18 is taken, what is the probability that the sample of kindergarten children has a mean height of less than 39.25 inches? (Round your answer to four decimal places.) Enter a number.

On an assignment, there are two true or false questions. You have no idea what the correct answer is to either one so you guess. a. What is the probability that you get both of them right by guessing? Explain your answer. b. What is the probability that you get exactly one of them right by guessing? Explain your answer. Write your answers as fractions. a. The probability that you get both of them right is b. The probability that you get exactly one of them is right

A grocer wants to mix two kinds of candy. One kind sells for $0.95 per pound, and the other sells for $1.35 per pound. He wants to mix a total of 28 pounds and sell it for $1.15 per pound. How many pounds of each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)

Milan is saving up money for a down payment on a condominium. She currently has $2525, but knows she can get a loan at a lower interest rate if she can put down $3258. If she invests the $2525 in an account that earns 5.3 % annually, compounded quarterly, how long will it take Milan to accumulate the $32587 Round your answer to two decimal places, if necessary.

Value of home and life span are two variables that have been shown to have positive correlation but no cause-and-effect relationship. Describe at least one possible reason for the correlation. Select all that apply. A. People who have more valuable homes tend to live more stressful lives, and stress generally decreases life spans. B. Greater wealth allows people to afford more valuable homes and to spend more money on health care, and greater health care spending generally enables people to live longer. C. Homes in large cities tend to be more valuable than homes in rural areas, large cities tend to have more pollution than rural areas, and greater exposure to pollution decreases life spans. D. Exercise tends to increase life spans, people who live within walking distance of amenities tend to walk more than those who do not, and homes that are within walking distance of amenities tend to be more valuable than homes that are not.

On-Time Delivery Company acquired an adjacent lot to construct a new warehouse, paying $34,000 in cash and giving a short-term note for $281,000. Legal fees paid were $1,590, delinquent taxes assumed were $13,800, and fees paid to remove an old building from the land were $21,400. Materials salvaged from the demolition of the building were sold for $4,700. A contractor was paid $957,600 to construct a new warehouse. Determine the cost of the land to be reported on the balance sheet. $

For each of the following equations, identify which conic section the equation represents (circle, ellipse, hyperbola or parabola), state the orientation (vertical or horizontal), and the coordinates of the center (for circles, ellipses, and hyperbolas) or the vertex (for parabolas).

(a) What is the probability that a randomly selected pregnancy lasts less than 258 days? The probability that a randomly selected pregnancy lasts less than 258 days is approximately 0.3085. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) pregnancies to last more than 258 days. If 100 pregnant individuals were selected independently from this population, we would expect B. If 100 pregnant individuals were selected independently from this population, we would expect 31 pregnancies to last less than 258 days. pregnancies to last exactly 258 days. C. If 100 pregnant individuals were selected independently from this population, we would expect

a. Find the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice.(Round to two decimal places as needed.) A. There are two critical values; the lower critical value is and the upper critical value is B. There is one critical value; the critical value is

Determine the value of k such that the planes 2x-3y+kz=4 and ky-z+3=0 are perpendicular and the value of k such that the planes are parallel. k = 2, no such value k = 0, no such value no such value, k = 0 no such value, k = 2

Find S, through S, and then use the pattern to make a conjecture about S, Prove the conjectured formula for S, by mathematical induction. Sn:1/22+1/66+1/132+1/220+...+1/11n(n+1) Find S, through S5- (Type an integer or a simplified fraction.) S₁ =

Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs of the equations. z =√x² + y² z = 0 x² + y²= 4

Solve the following equation for all radian solutions and if 0 < t <2π. Give all answers as exact values in radians. Do not use a calculator. list. If there is no solution, enter NO SOLUTION.) 3 cos t = 9 cost t-3√3 (a) all radian solutions (Let k be any integer.) t=rad (b) 0≤t <2n t= rad