Basic Math Questions and Answers

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?

A company's profit in dollars has a function of the number of widgets sold, w, is given by this function: -2w² + 120w - 30= P. How many widgets were sold if the profit was $970? 0 50 60 120 30

Solve the following logarithmic equation. Express your answer as either an exact expression or a decimal approximation rounded to four decimal places. If there is no solution, indicate "No Solution (Ø)." In(x-3) - In(x) = 5

In the last lesson, you came up with a formula for the tax a couple owed based on their wage income. A similar formula for a single person with taxable income more than $9,075 but not over $36,900 is T 0.15w-1976.25, where T is the tax owed, and w is the wage income. This formula is an example of a linear equation, and equation where every term is a constant or a single variable not raised to a power. This particular linear equation involves two variables. In this equation w would be considered the input or independent variable since it is the value typically provided to the equation, and T is the output or dependent variable since its value depends on the input, and its value is the output of the expression on the right side of the equation.

Suppose that a random sample of 9 adults has a mean score of 80 on a standardized personality test, with a standard deviation of 8. (A higher score indicates a more personable participant.) If we assume that scores on this test are normally distributed, find a 99% confidence interval for the mean score of all takers of this test. Then find the lower limit and upper limit of the 99% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers one decimal place. (If necessary, consult a list of formulas.)

A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $75 per hour. a. Write a linear model that represents the total cost of recording an album as a function of studio time (in hours). Use the variablet to represent the number is used. C= b. Is it less expensive to purchase 12 hours of recording time at the studio or a $750 music software program that you can use to record on your own com It is less expensive to purchase Explain your reasoning. The cost for 12 hours of recording time is $

Locate the critical points of the following function. Then use the Second Derivative Test to determine whether they correspond to local maxima, local minima, or neither. f(x) = 2x³-6x² +2 What is (are) the critical point(s) of f? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical point(s) is (are) x = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. There are no critical points for f.

Sam and Jen had a tax liability of $5,115 last year. They were entitled to tax credits of $119 and withholding amounted to $110 per month. Sam and Jen owed other taxes of $678. Calculate the amount of the refund or the amount of taxes due (as the case may be). $4,354 refund $4,886 refund $4,208 due $4,354 due

Complete the table of values for f(x) = 6x . Complete the table of coordinates.

Sandy and Bill put 2,870 coins into rolls of 50 coins each. How many complete rolls did they make? How many coins were left over?

- If initial velocity of a particle is 40 m/s and it is moving in a straight line under constant retardation 5 m/s². The ratio of displacement in 4 second and 4th second will be

Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 25 liters per minute. There are 700 liters in the pond to start. Let W represent the amount of water in the pond (in liters), and let T' represent the number of minutes that water has been added. Write an equation relating W to T, and then graph your equation using the axes below.

Jaquan hopes to earn $1500 in interest in 2.9 years time from $120,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds semi-annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

Janine has 12 cookies. Mark has three more than half the number of cookies that Janine has. Angelo has twice the number of cookies that Mark has. What is the ratio of the number of Angelo's cookies to the number of Janine's cookies? 3:4 3:2 1:1 4:3 2:3

A bank loaned out $31,000, part of it at the rate of 8% annual interest, and the rest at 10% annual interest. The total interest earned for both loans was $2,710.00. How much was loaned at each rate?

The revenue function is given by R(x) = x p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x) = 49(2), find the revenue if 14 units are sold. Round to two decimal places.

Estimate 25% of $98.50. Do not give the exact answer use estimation.

Find the intervals on which p is increasing and decreasing. p(z)=z² cosz - 2 cos z - 2z sin z on ( π/2, 5π/2) Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function p is increasing on the open interval(s) and decreasing on the open interval(s). (Simplify your answer. Type an exact answer, using it as needed. Type your answer in interval notation. Use a comma to separate answers needed.) B. The function p is decreasing on the open interval(s). The function p is never increasing. (Simplify your answer. Type an exact answer, using C. The function p is increasing on the open interval(s) (Simplify your answer. Type an exact answer, using D. The function p is never increasing or decreasing.

Solve the inequality: -2x+5<8 The answer as an inequality: The answer in interval notation:

The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks plus $250 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function. C(n) = 250n+6500 Answer the following questions. (a) If the total cost is $12,250, how many tons is the company transporting? (b) What is the total cost of transporting 14 tons?

Tessa has recently inherited $5600, which she wants to deposit into a CD account. She has determined that her two best bets are an account that compounds monthly at an annual rate of 4.7% (Account 1) and an account that compounds semi-annually at an annual rate of 5.1% Which account would pay Tessa more interest?