Basic Math Questions and Answers

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.

On a scientific or graphing calculator, approximate the following value. In 0.9090

Graph the system below and write its solution. 6x-2y=-4 y=3x+3 Note that you can also answer "No solution" or "Infinitely many" solutions.

Consider the following absolute value inequality. |9x+6| < 24 Rewrite the given inequality as two linear inequalities.

Type the correct answer in the box. Round your answer to the nearest hundredth. Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26°. Scarlett's height is 1.65 meters, so the height of the dam is meters.

Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.000165 moles per liter. Write this number in scientific notation. (b) A black rhinoceros can weigh up to 6.4 × 10³ pounds. Write this number in standard notation.

Which of the following are reasonable ways to estimate 15% of $29.95. There may be more than one reasonable method. 0.15 times 29.95 is $4.4925 30% is 3 out of 10, so that would be 9 out of 30. 15% is half of that, so $4.5 15 times 30 is $450. Adjusting the decimal place gives $45 10% of 30 is 3. 5% is half of that, so 1.5. Together, 15% is $4.5 15 times 30 is $450

Drag the blue point to a location on the coordinate plane so that the vector 7 (shown below in blue and centered at the origin) has magnitude 15 and direction 36.87° (relative to the positive x-axis). Provide your answer below:

Perform the following additions and/or subtractions: (10w² + 11w + 4) + (7w² + 8w + 3) =

Write an equation in point-slope form of the line that passes through the point (-8, -2) and has a slope of m = 5.

For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms. 12x-8y = 12 Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one.

A video club costs $25 to join. Each video that is rented costs $2.50. Let v represent the number of videos. Identify the independent and dependent variables. Then, write a rule using function notation to represent the situation.

Suppose that the price - demand equation and the cost function for the production of table saws are given, respectively, by P = 300 81,000+ 90x where x is the number of saws that can be sold at a price of $p per saw and C(x) is the total cost (in dollars) of producing x saws. Find the revenue function in terms of x. - 50 and C(x) Y

Suppose that the total cost (in dollars) of producing x food processors is given by C(x) = 1,800 + 36x -0.6 x². What is the average cos t (in dollars) of producing the 21st food processor? Round your answer to the nearest whole number.

The activity on Denise Hellings' Sears account for one billing period is shown below. Find the average daily balance and the finance charge if the billing period is March 1 through March 31, the previous balance was $155.27, and the annual simple interest rate is 21%. (Round your answers to the nearest cent.)

Consider the following points. (-3,7), (6,0) and (6, 7) Determine whether or not the given points form a right triangle. If the triangle is not a right triangle, determine if it is isosceles or scalene

Mia and Vincent are asked to choreograph a dance for the school musical.. Mia can choreograph the dance for the show in 20 hours and Vincent can choreograph the dance by himself in 16 hours. How long would it take to choregraph the dance for the musical if they worked together? Write your answer as a number only. No units. Round your answer to two decimal places, if necessary.

An IQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 2 IQ points of the true mean. Assume that o = 14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. (Round up to the nearest integer.) The required sample size is Would it be reasonable to sample this number of students? No. This number of IQ test scores is a fairly large number. No. This number of IQ test scores is a fairly small number. Yes. This number of IQ test scores is a fairly small number. Yes. This number of IQ test scores is a fairly large number.