Basic Math Questions and Answers

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?

Jenny buys a dining table costing $795.95. The store charges $55 for delivery. State taxes are 5.5% and local sales taxes are 1.5%. What is the total purchase price? (Round your answer to the nearest cent.) $905.67 $906.67 $909.67 $910.52

(a) The diameter of Uranus at its equator is approximately 5.11 x 10 kilometers. Write this number in standard notation. (b) An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.0000835 meters. Write this number in scientific notation.

(a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 7.68 x 10 -4 meters. Write this number in standard notation. (b) The diameter of Mars at its equator is approximately 6790 kilometers. Write this number in scientific notation.

Sharon works as a sales associate and earns all of her salary in commission. a) Last month, she had sales that totaled $24,000. However, when she received her paycheck, she saw that she had received $33,000 in commission. Why must this be an error? b) Human Resources caught the error. Sharon was supposed to receive $3300 in commission. What is Sharon's commission rate? c) The next month Sharon received $2200 in commission. What was the amount of her sales that month?

Bubba is saving up money for a down payment on a condominium. He currently has $2535, but knows he can get a loan at a lower interest rate if he can put down $3303. If he invests the $2535 in an account that earns 4.2 % annually, compounded quarterly, how long will it take Bubba to accumulate the $33037 Round your answer to two decimal places. If necessary.

(a) The signal from a certain satellite takes approximately 0.0078 seconds to reach Earth. Write this number in scientific notation. (b) The total surface area of South America is approximately 6.89 x 106 square miles. Write this number in standard notation.

Solve the inequality: 2x +5 <8 The answer as an inequality: The answer in interval notation: The answer on a number line: 5

A company finds the demand x, in thousands, for their kites to be x = 400 - p² at a price of p dollars. Find the elasticity of demand when the price is $4. Write your answer to two decimal places and start with 0 if your answer is between 1 and 0 or 1 and 0.

Graph the system below and write its solution. 6x-2y=-6 y=3x+3

Chester hopes to earn $1500 in interest in 3.3 years time from $15,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds quarterly, 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.

Billy said that the depreciation value S(in dollars) of his upgraded Rav4 after t years can be modeled by S(t) = 28000 (0.8)t. What is the rate of depreciation after 1 year? Write your answer to two decimal places. Billy said that the depreciation value S(in dollars) of his upgraded Rav4 after t years can be modeled by S(t) = 28000 (0.8)t. What is the rate of depreciation after 5 years? Write your answer to two decimal places.

5y3 = -2(5-x) Step 2 of 2: Find the equation of the line which passes through the point (-10,- 11) and is parallel to the given line. Express your answer in slope-intercept form. Simplify your answer.

Thunderstorm Speeds A meteorologist who sampled 13 thunderstorms found that the average speed at which they traveled across a certain state was 17 miles per hour. The standard deviation of the sample was 1.6 miles per hour. Use a graphing calculator and round the answers to at least one decimal place. Find the 97% confidence interval of the mean. Assume the variable is normally distributed.