Basic Math Questions and Answers

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.

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.

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

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.)

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

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.

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.

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. $

A bicycle has a listed price of $$31.95 before tax. If the sales tax rate is 6.5 %, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.

For the rational function f(x) =1-x³/x2-x , identify any removable discontinuities. There is a removable discontinuity at x = 3. There are no removable discontinuities for this function. There is a removable discontinuity at x = 1. There are removable discontinuities at x = 0 and x = 1.

Simplify the expression 1+ 3/2y/-5/xy1 and give your answer in the form of A/B

Multiply and simplify your answer. x² - 25/x² 10x + 25.x - 5/x

If the market rate of interest is equal to the contract rate of interest, a. the selling price of the bond cannot be determined. b. the bonds will sell for less than their face amount. c. the bonds will sell for more than their face amount. d. the bonds will sell for their face amount.

A gallon of paint will cover 560 square feet of wall space. If I plan to paint a room whose walls measure 2240 square feet, how many gallons of paint will I need? To paint the room, __ gallons of paint will be needed.

Write four equivalent expressions for the given expression. -8v-5/v-2 Choose the expressions that are all equivalent. A.8v-5/v-2,-(8v-5)/v+2,-8v+5/-v+2,8v-5/v+2 B.-(8v-5)/v-2,-8v+5/v-2,-(8v-5)/-v+2,(8v-5)/-v+2 C.-8v-5/v+2,-(8v-5)/v-2,-8v-5/v+2,8v-5/v+2

(1 point) Perform the indicated operation. Note that the denominators are different. Simplify the result, if possible. 2/y-4 6/y-6

A company makes three sizes of cardboard boxes: small, medium, and large. It costs $3.50 to make a small box, $5.00 for a medium box, and $5.50 for a large box. Fixed costs are $8000. (a) Express the cost of making x small boxes, y medium boxes, and a large boxes as a function of three variables: C= f(x, y, z). f(x, y, z)= (b) Find (6000, 9000, 8000). Interpret your answer. It costs the company $ to make 6000 small boxes, 9000 medium boxes, and 8000 large boxes. (c) What is the domain of f? x≥0, -∞≤y≤∞, z≥0 -∞≤x≤∞, -∞≤y≤∞, x≤0, y ≤0, z≥0 x≥0, y ≥0, z≥0 -∞≤x≤∞, y≥0, z≥0

Which of the following are equivalent forms of the rational expression. 2x² +5x−3/ x²-x-12 (Select all that apply.) (2x - 1)(x-3)/(x-4) (x-3) 2x + 1/x-4 (x+3)(2x - 1)/(x-4) (x+3) 2(x2+5x-3)/x²-x-12 2x - 1/x-4 (2x+1)(x-3)/(x-4)(x-3)

Use the following function to answer parts a through c f(x) = 11x³+127x² +67x+11 a. List all rational zeros that are possible according to the Rational Zero Theorem. +-1, +-1/11+-11 (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) b. Use synthe division to test several possible rational zeros in order to identify one actual zero. One rational zero of the given function is __ (Simplify your answer) c. Use the zero from part (b) to find all real zeros of the polynomial function. The real zeros of the function are

Cookies are packaged in boxes that measure 18 cm by 20 cm by 6 cm. A larger box is being designed by increasing the length, width and height of the smaller box by the same amount so that the volume is at least 5280 cm³. What are the minimum dimensions of the larger box?

Classify the following events as either independent or dependent. Independent Dependent Add an answer item! Add an answer item!

A corporation issues for cash $1,000,000 of 8%, 20-year bonds, interest payable annually, at a time when the market rate of interest is 10%. The straight-line method is adopted for the amortization of a bond discount or premium. Which of the following is true? a. The amount of unamortized premium decreases from its balance at issuance date to a zero balance at maturity. b. The amount of unamortized discount decreases from its balance at issuance date to a zero balance at maturity. c. The amount of the annual interest expense gradually decreases over the life of the bonds. d. The amount of the annual interest expense is computed at 8% of the bond carrying amount at the beginning of the year.

A construction crew has just finished building a road. The crew worked for 43/8 days. If they built 21/7 kilometers of road each day, what is the total length of road they built?

Which great Mosque might have inspired Guarino Guarini for the design of the vaults of S. Lorenzo church in Turin? a. The Friday Mosque, Isfahan b. The Sehzade Mosque in Istanbul c. Taj Mahal, Agra d. Great Mosque of Córdoba

At the fair you buy an unlimited ride pass for $28 and plan to play some games costing $1.50 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. Answer f(x) =______ for x ___

A grocery store buys cereal using the cost function c(n) = { 2n when n < 100 1.9n when 100 ≤ n ≤ 500 1.8n when n > 500 where n is the number of boxes of cereal the grocery store buys and c(n) is the cost of the cereal. The grocery store then sells the cereal using the sales function s(c) = 1.3c. What is the cost of the cereal if the grocery store buys 250 boxes?

There are thirty-six students in your chemistry class, including yourself. You will be in a randomly selected lab group of four people, counting yourself. What is the probability that your three friends Ann, Bob, and Carlos are in your lab group?

Amy and Chuck each buy a house in the same neighborhood for $250,000. Amy's monthly mortgage payment is $400 more per month than Chuck's. Which one of the following statements could explain this difference? Amy chose a shorter term for her mortgage, so her monthly payments are higher. Chuck has a lower credit score, so his interest payments are also lower. Amy made a larger down payment, so her monthly payments are also larger. Chuck made a larger down payment, so his monthly payments are larger.

Find the compound interest and future value. Round your answers to the nearest cent. Do not round intermediate steps. Principal Rate Compounded Time $530 4.35% Quarterly 5 years The future value is $ and the compound interest is $

Write the exponential function y= 500e-0.07t in the form y =abt (a) Once you have rewritten the formula, give b accurate to at least four decimal places. b= _______ help (numbers) If t is measured in years, indicate whether the exponential function is growing or decaying and find the annual growth/decay rate. The rate you determine should be positive in either the case of growth or the case of decay (by choosing decay, the negative rate is implied). (b) The annual ? rate is % per year (round to the nearest 0.01%).

For the polynomial below, 1 is a zero. f(x) = x³ - 7x² + 8x - 2 Express f(x) as a product of linear factors.

If a building contractor hires 6 day laborers and 1 concrete finisher, his payroll for the day is $1110. If he hires 1 day laborer and 4 concrete finishers, his daily cost is $875. Find the daily wage for each type of worker. Solve the problem using matrices. The daily wage for the laborer is $. The daily wage for the concrete finisher is

In the Ohio lottery Classic Lotto game 6 numbers are drawn at random from 49 possible numbers. What is the probability of your lottery ticket matching all six numbers? Hint: Order is not important.

In 2012, there were about 313 million people in the United States, and just under 9 million of them had assets of $1 million or more. At the same time, there were 8,336,697 people in New York City, and 727,100 of them had assets of $1 million or more. Compute the density of millionaires in the general population for New York City and the whole United States. Based on those numbers, select any of the choices below which are true. New York has a density of millionaires more than twice that of the country as a whole. The density of millionaires is about the same for New York City as for the United States. Millionaires seem to prefer New York City to much of the rest of the United States. There is something in the water of New York City that encourages millionaires.

David has available 400 yards of fencing and wishes to enclose a rectangular area. Express the area A of the rectangle a a function of the width w of the rectangle. For what value of w is the area largest? What is the maximum area? Sketch the graph of A(w).

Estacia wants to learn more about excluded values. a. Explain to Estacia why x cannot be 4 in the expression x+2/x-4 b. Find the excluded values of x in each of the expressions of problem 3-99. c. Create an expression that has the excluded values of x = -6 and x≠1/3 . Be prepared to share your expression to the class.

In ΔHIJ, ∠H ≈ ∠J, JH = 10 and IJ = 14. Find the length of HI. ?

The cost of reserving a particular domain name is $22 up front plus $4.89 per month. Find the cost of reserving that domain name for the following: (a). 2 months The cost of reserving a particular domain name for 2 months is

What happens to the value of a fraction when the numerator (the top) approaches (gets very close to) zero? What happens to the value of a fraction when the denominator (the bottom) approaches (gets very close to) zero? What happens to the value of a fraction when the numerator (the top) gets much much larger than the denominator? What happens to the value of a fraction when the denominator (the bottom) gets much much larger than the numerator? Use at least 4 sentences total in answering thele 4 questions.

Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 64 cm²? cm²/s

)) An angle measures 4° less than the measure of its supplementary angle. What is the measure of each angle? ______° and _______°

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. 4x² + y² =160 36x² - y² = 0 .... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is {} (Type an ordered pair. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Express complex numbers in terms of i. Use a comma to separate answers as needed.) B. There are infinitely many solutions. C. The solution is the empty set.

Let f(x)=2x²-3x - 2/3x² + 10x - 25 This function has: 1) A y-intercept at the point 2) x-intercepts at the point(s) 3) Vertical asymptotes at x = 4) Horizontal asymptote at y =

In a study of 600 meals served at 75 campus cafeterias, 190 had less than 10 grams of fat but not less than 350 calories; 194 had less than 350 calories b not less than 10 grams of fat; 117 had over 350 calories and over 10 grams of fat. (a) What percentage of meals had less than 10 grams of fat? Round your answer to the nearest tenth of a percent. of the meals studied, __% of them had less than 10 grams of fat. X Ś