Math Questions

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

Compute the area of the region R bounded by the curve r = 1- cosθ. This curve was sketched in the previous homework (and you can refer to that sketch). Use the double integral method (polar integrals; section 14.3), that is, integrate function 1 over the region.

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 $

If a simple random sample is taken, and a 90% confidence interval of 1.53 <o< 2.08 is constructed from the sample statistic, s, the following is the correct interpretation: "We are 90 % confident that the interval from 1.53 to 2.08 actually does contain

Select the correct answer from the drop-down menu. Sam is flying a kite. The length of the kite string is 80 meters, and it makes an angle of 75° with the ground. The height of the kite from the ground is meters.

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.

Determine the intervals on which the following function is concave up or concave down. Identify any inflection points. f(x) = 6(x + 2)5/2 (2x-7), on [-2,00)

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?

The mean SAT score in mathematics is 519. The founders of a nationwide SAT preparation course claim that graduates of the course score higher, on average, than the national mean. Suppose that the founders of the course want to carry out a hypothesis test to see if their claim has merit. State the null hypothesis Ho and the alternative hypothesis H, that they would use.

Condense the following expressions into a single logarithm by applying the properties of logarithms. Make sure your final answer is written as a single logarithm. a. 2 log(x) - 5 log(y) + 9 log(z) = b. -2 log(z) + 5log(x) - 9 log(y) =

- 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

There are 125 passengers in the first carriage, 150 passengers in the second carriage and 175 passengers in the third carriage, and so on in an arithmetic sequence. What's the total number of passengers in the first 7 carriages? 2800 875 1750 700 1400

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.

Given the ellipse below, determine the coordinates of the two foci. Enter your answers as ordered pairs (x, y) and leave in radical form. (x-1)2/36 + (y+2)2/16 = 1

Find all solutions by factoring. 3w² - 13w=10

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.

A quadratic equation can be written in vertex form or in standard form. Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task listed below and explain why. a. Factor the equation. b. Graph the parabola. c. Identify the vertex, minimum, or maximum of the parabola. d. Solve the equation using the quadratic formula.

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.

The line y = x makes a 45° angle with the y-axis. What angle does the line y = x + 5 make with the y-axis? What angle would the line y = x + 5 make with any vertical line? Justify your answer.

(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.

Graph the solution to the following system of inequalities. 2x+5y>-20 -2x+7y<-21 Then give the coordinates of one point in the solution set.

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?

Using rectangles each of whose height is given by the value of the function at the midpoint of the rectangle's base (the midpoint rule), estimate the area under the graph of the following function, using first two and then four rectangles. f(x)= 5/x between x = 2 and x = 6 Using two rectangles, the estimate for the area under the curve is (Round to three decimal places as needed.)

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.

Graph the system below and write its solution. 3x+y=-3 y=-1/2x+2

(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 certain species of deer is to be introduced into a forest, and wildlife experts estimate the population grow to P(t) = (976)3 t4. where t represents the number of years from the time of introduction. Step 2 of 2: How long will it take for the population to reach 26352 deer, according to this model?

A company sells x ribbon winders per year at $p per ribbon winder. The demand function for ribbon winders is given by p = 250 - 0.04x. Determine the elasticity of demand when the price is $75 apiece. Round your answer to the nearest hundredth. 0.21 0.22 0.23 0.24

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.

Aurelia needs to drive 280 miles. If she drives at a rate of 65 miles per hour, to the nearest tenth of an hour, how long will the trip take?

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.

Alice and Amy decide to meet at a party. From a corner of the party hall, Amy spots Alice at the corner of the hall diagonally opposite her. If the party hall is a rectangle that measures 100 feet by 60 feet, what is the shortest distance Amy has to walk to reach Alice? Round your answer to the nearest foot. A. 40 feet B. 80 feet C. 117 feet D. 160 feet

The half-life of gold-194 is approximately 1.6 days. How much of a 15 gram sample of gold-194 would remain after 4 days? Round to three 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.