Basic Math Questions and Answers

Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius. Use 3.14 for pl and round your answer to the nearest hundredth. (Hint: You may only enter numerals, decimal points, and negative signs in the answer blank)

Suppose the points from a class total 1000 points and are divided into 600 points on the Exams and 400 points on Homeworks. If you averaged 75% on the exams and 90% on the homeworks, what is your overall percentage? Try to answer this with rate and mixture equation that we have used in many contexts.

Identify whether the following equation represents an exponential function. g(x) = -22.85x - 50.75 NOT an exponential function exponential function

In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the standard deviation is 4.5 hours. How large a sample must be selected? 5 20 4 19

b = 2.35 +0.25x c = 1.75 +0.40x In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken? A) $2.60 B) $2.85 C) $2.95 D) $3.35

Look at an example of a polynomial 7x³ - 2x²+x-5, we say that the degree of this polynomial is 3, which is the highest power. For this week's discussion, briefly explain how the degree of a divider is compared to the degree of the remainder. Divide the following expression, and compare the degree of the divider: x+3 and the degree of the remainder: (7x3-2x²+x-5)/x + 3

Last year, Amanda had $20,000 to invest. She invested some of it in an account that paid 5% simple interest per year, and she invested the rest in an account that paid 9% simple interest per year. After one year, she received a total of $1720 in interest. How much did she invest in each account? Note that the ALEKS graphing calculator can be used to make computations easier. First account: $ Second account: $

P(q) = -0.01(q-250) (q - 80) The equation above gives the profit, P(q), in dollars, earned by a cupcake bakery when q cupcakes are produced. What is the best interpretation of the number 80 in this context? A 80 is a number of cupcakes for which the profit is equal to $0. B 80 is the number of cupcakes that corresponds to the maximum profit. C 80 is the number of cupcakes that corresponds to the minimum profit. D $80 is the maximum profit, in dollars.

You want to create a custom border for a picture of you and your family. The picture measures 8 inches by 10 inches. What should the width of the picture frame be if the final area, including the picture, is three times the area of the picture by itself? • Write answer as a number only. Round answer to two decimal places in needed.

Divide and check your answer. 61+7 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The quotient is with no remainder. B. The quotient is with a remainder of OC. The quotient is undefined.

Ricardo transformed the quadratic parent function f(x) to create g(x). After the transformation, he noticed that the domain and range were the same for f(x) and g(x). Which of the following could NOT represent g(x)?

4. (Like 2003 Exit) Myesha makes hand-painted pots. Her overhead costs are $650 per week, and she pays an additional $12 per pot in material costs. What will be her total expenses if she sells 50 pots this week. A $250 B $650 C $1250 D $1650

You pick a card from a deck. If you get a face card (J,Q,K), you win $5. If you get an ace, you win $30 plus an extra $60 for the ace of hearts. For any other card you win nothing. Find the expected value you will win. *

Justin opened a savings account with $900 that pays no interest. He deposits an additional $190 each week thereafter. How much money would Justin have in the account 30 weeks after opening the account?

Dakota wants cover his patio with concrete pavers. If the patio is shaped like a trapezoid whose bases are 16 feet and 18 feet and whose height is 14 feet, how many square feet of pavers will he need?

2. A student bought a pair of sunglasses in the USA and paid $35.50. In England, an identical pair of sunglasses costs £26.99. The exchange rate is £1 = $1.42. In which country were the sunglasses cheaper, and by how much?

Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point? 4 feet 3 feet 5 feet 6 feet

7) It takes a hose 5 minutes to fill a rectangular aquarium 9 inches long, 10 inches wide, and 13 inches tall. How long will it take the same hose to fill an aquarium measuring 1.5 feet by 2 feet by 2.5 feet?

A survey of 2450 golfers showed that 281 of them are left-handed. Use this data to construct a 98% confidence interval for the proportion of golfers that are left- handed. (0.369, 0.451) (0.203, 0.293) (0.100, 0.130) (0.683, 0.712)

A random sample of 40 students has a mean annual earnings of $3120 and a population standard deviation of $677. Use this sample data to construct a 95% confidence interval for the population mean, μ, of all student earnings. ($2910, $3330) ($1987, $2346) ($4812, $5342) ($210, $110)

An object is dropped from a tower, 166 ft above the ground. The object's height above ground t sec into the fall is s=166-16t² a. What is the object's velocity, speed, and acceleration at time t? b. About how long does it take the object to hit the ground? c. What is the object's velocity at the moment of impact? The object's velocity at time t is

A class has 35 students. In how many different ways can six students form a group for an activity? (Assume the order of the students is not important.) There are different ways that the six students can form a group for an activity. (Type a whole number.)

The expression is given in standard form. Rewrite it in factored form. If it cannot be rewritten in factored form, write "cannot be done." p² + 18p-40 a (p-20)(p+2) b (p+20)(p+2) c (p+20)(p-2) d (p-20)(p-2)

A long year-end status report for work is 82 pages long. You need to print 19 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.99 each. Give your answer to the nearest cent, only for the paper you use (partial reams are OK)

Every year in Delaware there is a contest where people create cannons and catapults designed to launch pumpkins as far in the air as possible. The equation y = 15 + 110x -16x² can be used to represent the height, y, of a launched pumpkin, where x is the time in seconds that the pumpkin has been in the air. What is the maximum height that the pumpkin reaches? How many seconds have passed when the pumpkin hits the ground? (Hint: If the pumpkin hits the ground, its height is 0 feet.)

Brandon is analyzing the profits from two of his restaurant locations. The first location showed a profit of $3,000 in the first week of the year but has a showed a steady decrease in profits of 1.5% each week since then. His second location showed a profit of $1,500 in the first week of the year and has showed a steady increase in profits of 1.2% each week since then. Which system of equations can Brandon use to determine the number of weeks, x, until the profits, y, from the two locations are the same? A. y = 3,000 (1.015)^x y = 1,500 (1.012)^x B. y = 3,000(0.985)^x y = 1,500(1.012)^x C. y = -3,000 (1.015)^x y = 1,500(1.012)^x D. y = -3,000(0.985)^x Y = 1,500/(1,012)^x

Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p? A) 0.88p B) p / 0.88 C) (0.8) (1.08) p D) p / (0.8) (1.08)

Complete this expression. Assume that any variables are not equal to zero. z⁰ = Simplify the following expression completely. (5w+2)⁰ = Simplify the following. 3⁰ = Simplify the following. 0⁴ =

Factor each trinomial. Then match the polynomial (term) on the left with its factored form (definition) on the right. Column A Column B 1. x²-8x-20 a. Prime 2. x²+8x-20 b. (x-2)(x+10) 3. x² - x-20 c. (x-10)(x + 2) 4. x²-9x-20 d. (x - 5)(x+4)

The function h defined by h(t) + (49+4.9t) (10-t) models the height, in meters, of an object t seconds after it is dropped from a helicopter. From what height is the object dropped? a 500 b 490 c 480 d 460

A car company tested a sports car on a road with different inclines. The test driver tested the car by driving a distance of x miles on a flat road, (x² + 3) miles downhill, and (x-7) miles uphill. Which simplified expression is equivalent to the total distance, in miles, for which the car was tested? (2 points) a. 3x²-4 b. 3x² +10 c. x²+2x-4 d. x²+2x+10

Answer the following. (a) The total surface area of Asia is approximately 17,200,000 square miles. Write this number in scientific notation. (b) The signal from a certain satellite takes approximately 4.1 x 10^-2 seconds to reach Earth. Write this number in standard notation.

To find the distance AB across a river, a distance BC= 357 meters is laid off on one side of the river. It is found that B=115°11' and C = 11°20'. Find AB. The distance AB across the river is (Do not round until the final answer. Then round to the nearest whole number as needed.)

Consider the curve given parametrically by x=4-t², y = t³ - 3t. (a) List all of the points (x, y) where the tangent line is horizontal. (b) List all of the points (x, y) where the tangent line is vertical.

Find the present value of the ordinary annuity. Payments of $40,000 made semiannually for 12 years at 4.2% compounded semiannually A. $674,532.00 B. $741,616.00 C. $751,336.00 D. $748,056.18

The half-life of radium-223 is approximately 11.43 days. How much of an 8 gram sample of radium-223 would remain after 3 days? Round to three decimal places.

At the beginning of an experiment, a scientist has 304 grams of radioactive goo. After 180 minutes, her sample has decayed to 19 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t) = How many grams of goo will remain after 14 minutes? You may enter the exact value or round to 2 decimal places.

If the alternator-to-engine drive ratio is 2.35 to 1, what rpm will the alternator have when the engine is idling at 500 rpm? Hint: Use a direct proportion. The alternator will have rpm when the engine is idling at 500 rpm. (Type a whole number or a decimal.)

Perform the indicated operation. Note that the denominators are the same. Simplify the result, if possible. (x² 1 / x² - 4x - 5) - (34 -2x / x² - 4x - 5 ) -

A man buys a car for $39,000. If the interest rate on the loan is 12%, compounded monthly, and if he wants to make monthly payments of $600 for 60 months, how much must he put down? (Round your answer to the nearest cent.) $

Sandi weighs 145 lb, but she has started a new diet plan that promises she will lose 3 lb per month every month until she reaches her goal weight. Write a linear equation that describes how much Sandi weighs, V, each month, and then use your equation to find out how many months it will take her to get to 115 lb. Use X to denote the number of months since Sandi started her new diet. The linear equation that describes how much Sandi weighs each month is =

Country A has an exponential growth rate of 3.6% per year. The population is currently 4,957,000, and the land area of Country A is 27,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land? This will happen in year(s). (Round to the nearest integer.)

In the first part of the video, Freddie was posed the problem of having 400 baseball cards and selling 150 cards, and asked how many cards he had left. He used a standard algorithm to set up the problem and solve. Freddie explained his work in the following steps. (i) zero minus zero is zero (ii) zero minus five is five (iii) four minus one is three Which step is incorrect in Freddie's work? (iii) (ii) (i) None, the solution is correct

Find the prime factorization of 96 using a factor tree. Enter the prime factors you find from smallest to largest separated by the multiplication symbol, e.g. 2x2x3 x 5.

The distribution of NBA scores follows approximately a normal distribution with a mean of 102 and a variance of 81. What is the probability that a team from a randomly chosen game will score between 93 and 111 points in a given game? 0.317 0.500 0.683 0.954

An ordered pair (x, ß) for which the system of linear equations (1 + a)x+By+ z = 2 ax + (1+B)y+z=3 ax+By+ 2z = 2 has a unique solution, is (a) (2, 4) (b) (-4, 2) (c) (1, -3) (d) (-3, 1)

Based on the following data, what is the quick ratio, rounded to one decimal point? Accounts payable $ 30,000 Accounts receivable 60,000 Accrued liabilities 5,000 Cash 40,000 Fixed assets 670,000 Intangible assets 50,000 Inventory 69,000 Long-term investments 80,000 Long-term liabilities 100,000 Prepaid expenses 1,000 Temporary investments 30,000 a. 3.7 b. 2.9 c. 4.3 d. 5.1

Bonds Payable has a balance of $1,000,000 and Discount on Bonds Payable has a balance of $12,500. If the issuing corporation redeems the bonds at 99, what is the amount of gain or loss on redemption? a. $2,500 gain b. $22,500 gain c. $22,500 loss d. $2,500 loss

Find the center of mass of the given system of point masses lying on the x-axis. m₁ = 0.2, m₂ = 0.3, m3 = 0.4, m4 = 0.1 X₁ = 1, X₂ = 2, X3 = 3, x4 = 4 x̄ =

Which of the following is a prime number? Enter a, b, c, d, or e. a. 211 b. 187 C. 219 d. 183 e. 177