Basic Math Questions and Answers

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

Within a company is a (micro)economy that is monitored by the accounting procedures. In terms of the accounts, the various departments "produce" costs, some of which are internal and some of which are direct costs. This problem shows how an open Leontief model can be used to determine departmental costs. The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $68,600 for sales and $49,000 for service. Find the total costs (in dollars) of each department. (Round your answers to the nearest whole number.) sales department $ service department $ X X

(1 point) Sylvia is running a marathon. Let D(1) represent the total distance in kilometers she has runt hours after starting. Find a formula for each of the following functions in terms of the function D. Note: Be careful with your input variables. a) M (h), the total distance in meters she has run after h hours. M(h) = b) K(m), the total distance K(m) = kilometers she has run after m minutes. c) C(s), the total distance in centimeters she has run after s seconds C(s) =

Dani had $200 in her savings account. When she turned 18, the bank began charging her a $5.00/month fee. Write a function in terms of a for the balance of her savings account if she doesn't notice the monthly fee. Complete the following. Use standard slope-intercept form. B(a)=

Green plants absorb sunlight to power photosynthesis, the chemical synthesis of food from water and carbon dioxide. The compound responsible for light absorption and the color of plants, chlorophyll, strongly absorbs light with a wavelength of 642.nm. Calculate the frequency of this light. Round your answer to 3 significant digits.

Which of the following is a composite number? Enter a, b, c, d, or e. a. 29 b. 37 c. 57 d. 41 e. 31

Decide if you are given enough information to prove that the quadrilateral is a parallelogram for each description below. One pair of opposite sides are congruent. All angles are congruent. One angle is a right angle. Diagonals are perpendicular. One pair of consecutive angles are congruent. Diagonals are perpendicular and congruent Two pairs of opposite angles are congruent. One pair of opposite sides are both parallel and cc

Let fix) be defined such that f(-1) = 1 and f'(x) = cos(-1/x2+x), where -2<x<1. Part A: Find the tangent line approximation for f(-0.9). Part B: If f(-0.9) has an actual value of 1.3, use the shape of the graph to determine if this is an overestimate or underestimate. Justify your answer.

Fill in the blanks: The goal of an optimization problem is to find the maximum or minimum value of the__ function subject to the__ The goal of an optimization problem is to find the maximum or minimum value of the function subject to the

The equation V = 17.8 +3.8x gives the value (in thousands of dollars) of an investment after a months. Interpret the Slope in this situation. The value of this investment is

Justify whether x³ + y2 = 3xy has a horizontal tangent at (2, 4). No, because 3y-3x²/2y-3x≠0 at (2,4) Yes, because 3y-3x²/2y-3x=0 at (2,4) Yes, because 3y-3x²/2y-3x=0 at (2,4) No, because 3y-3x²/2y-3x≠0 at (2,4)

Find the distance between the points using the following methods. (2,7), (9, 9) (a) the Distance Formula (b) integration

What is the polynomial function in factored form? f(x) = x³ + 2x² - 5x - 6 Enter your answer by filling in the boxes. f(x)=

Suppose a student wishes to minimize the objective function on a closed interval, but finds that it has only a single local maximum. Where should the student look for the solution to the problem? Choose the correct answer below. A. Determine the value of each endpoint for the objective function. B. Determine the value where the objective function is equal to 0. C. Determine the value where the first derivative of the objective function is equal to D. Determine the value where the second derivative of the objective function is equal to

Find the quotient and simplify your answer. If the quotient is undefined, indicate "undefined". 0 ÷23/24

Solve the following system of equations. Provide your answer below: x² - y²= 11 -3x² + 2y²= -3

Determine whether the following statements are true and give an explanation or counterexample. a. The zeroes of f' are - 3, 1, and 4, so the local extrema are located at these points. Choose the correct answer below. A. False. The zeros of f' are the inflection points of f. B. True. The zeros of f' are the local extrema of f. C. True. The zeros of f' are local extrema so long as the denominator is nonzero at those points. D. False. A zero of f' is a critical point and is a local extremum so long as it is in the domain of f(x) and f'(x) changes sign. Take, for example, the function f(x) = (x+3)³(x - 1)³(x-4)³.

The label on a 20 mL aminophylline vial indicates a strength of 500 mg/20 mL. (a) How many mL of aminophylline would contain 200 mg of this drug? (b) How many mg of aminophylline would be contained in 1 mL of this solution?