Basic Math Questions and Answers

Multiply the following rational expression and state the restrictions on the variable: 4n²+32n 3n-2 1 2n+16 O O 2n 3n 2, n = // 2n-1-2 3n 2, n = ²/ 47 3n-2, 7-8, 12/0 2n 3n 2,7-8, 3/1

Use logarithmic differentiation to find dy/dx. y = (9 + x)4/x dy dx =

The number of hours needed to complete a trip. . varles inversely with the driving speed. &. A trip can be completed in 5 hours at a speed of 60 miles per hour. Find the equation that represents this relationship.

2. Camille stopped at the grocery store to buy milk. While at the store, she spotted cans of soup on sale for $2.25 each. If the milk costs $3.50 and she can spend no more than $35, how many cans of soup can she buy. b) a) Define your variable Write and solve your equation. c) Answer in a complete sentence.

Find the annual growth rate of the quantity described below. A stock portfolio drops to one-tenth its former value over a 7-year perio Round your answer to two decimal places. The annual growth rate is i %.

(1 point) In a random sample of 90 voters, the proportion of voters in favor of a bond issue is 0.8. Let p = proportion of all voters who favor of the bond issue. (1) Test Ho: p ≤ 0.65 against H₁: p > 0.65. Use a = The test statistic is The critical value is The final conclustion is 0.05. ⒸA. We can reject the null hypothesis that p < 0.65 and accept that p > 0.65. B. There is not sufficient evidence to reject the null hypothesis that p < 0.65

Two cube-shaped containers are filled with beads. Container A has side lengths of 2 inches and contains 142 beads. Container B has side lengths of 3 inches and contains 544 beads. Which container has the greater density in beads per square inch? Both containers have the same density. Container A Container B Impossible to tell from this information

38 A tire has a total of 638.3 pounds of pressure in it. If the inside of the tire has a surface area of 32.61 square inches, what is the tire pressure in pounds per square inch? . Write your answer as a number only. No units. Round your answer to two decimal places if necessary.

Use synthetic division to find the result when 3x³ + 11x² - 10x - 10 is divided by x + 5. r(x) Write your answer in the form q(x) + where g(x) is the quotient, r(x) is the remainder, and d(x) is the divisor. d(x)' Provide your answer below:

When 8 is subtracted from the square of a number, the result is 7 times the number. Find the positive solution. 4 5 7 8 16

Find the real and complex zeros of the function f(x) = 3x³ - 4x² + 11x + 10. Express your answer as a list separated by commas. Do not use a plus minus sign () in your answer; instead, list the zeros separately. Do not include "x =" in your answer. Provide your answer below:

Consider the function f(x) = x5 + 10. If f-¹(x) is the inverse function of f(x), find f¯¹ (42). Provide your answer below: f-¹(42) =

Al and Sarah are raking the yard. Al can rake the entire yard in 5 hours while it takes Sarah 9 hours to rake the yard. How long will it take Al and Sarah to rake the yard together? Choose the equation that should be used to solve this problem and state the solution.

You want to buy a house for $275,000 at 3.5% interest. What would your payment be if you pay it off over 15 years? What would your payment be if you pay it off over 30 years? How much would you end up paying all together for each of those?

Liam bought a plant and planted it in a pot near a window in his house. Let H represent the height of the plant, in inches, t months since Liam bought the plant. A graph of H is shown below. Write an equation for H then state the y-intercept of the graph and determine its interpretation in the context of the problem.

Castle has just finished his thirty-second year with his company and is getting ready to retire. During his thirty-two years, Castle's average annual salary was $62,544. How much can Castle expect to receive from Social Security annually if he were to retire today? (Assume he will receive 55% of his average annual salary.)

The population of India was about 1,380,000,000 people in 2020. Which number best approximates the population as a single digit times a power of 10? OA. 3 x 108 OB. 1 × 109 O C. 1×10-9 O D. 3× 109

The amount of corn yield is normally distributed with a mean of 186.7 bushels of corn per acre, with a standard deviation of 25.6 bushels of corn. In an agricultural study, 100 randomly selected acres were harvested. The mean corn yield of this sample 190 bushels of corn. What is the population mean (μ)? 100 190 186.7 25.6

Find all the real zeros of the following polynomial. Provide your answer below: X = f(x) = x55x³ - 6x

19. A drug must be administered IVPB at the initial rate of 2 mg/min, and the rate may be increased as needed every hour thereafter by 3 mg/min, up to a maxi- mum of 20 mg/min. The strength of the IV solution is 300 mg in 100 ml. DSW. Make a titration table showing the dosage rate (mg/min) and flow rate (ml/h).

The price of a company's stock over the 12-week period at the beginning of 2012 can be approximated by the function f(x) = 35.9x0.1, where x = 1 designates the beginning of week 1. (a) When is the stock increasing in price? (b) At what rate is the stock increasing at the beginning of the 3rd week? (c) At what rate is the stock increasing at the beginning of the 9th week? ▪▪▪▪▪ (a) When is the stock increasing in price? Select the correct answer below, and if necessary, fill in any answer boxes to complete your choice. to week A. The stock is increasing in price from week OB. The stock doesn't increase over the 12-week period.

Of all the rectangles with an area of 900 square feet, find the dimensions of the one with the smallest perimeter. a) 15 ft. x 60 ft. b) O not possible c) O 10 ft. x 90 ft. d) O 30 ft. x 30 ft. 15 2 ft. x 120 ft.

Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the probability that for one such phone number, the last four digits include at least one 0.

Find the domain of the following function. f(x) =1/(x-3)(x-7) Select the correct answer below: O (-∞, -7) U (-3,0) O (-∞, ∞) O (-∞, 3) U (3, 7) U (7, ∞) O (-∞, -3) U (-7,00) O (-∞, -7) U (3, ∞)

Consider f(x) = 2x - 4 and g(x) = (x + 1)² - 6. Identify all points where f(x) and g(x) intersect. Select all that apply. **Hint: Use your Desmos graphing calculator** D (-1,-6) ☐ (0,-44) ☐ (0.-5) □ (1,-2) □ (2.0)

Provide an appropriate response. The ages of five randomly chosen cars in a parking garage are determined to be 7, 9, 3, 4, and 6 years old. If we consider this sample of 5 in groups of 3, how many groups can be formed? O 60 05 30 10

A research firm reported that 15% of those surveyed described their health as poor, 26% as good, 40% as very good, and 19% as excellent. A health professional in Chicago wanted to determine if people in Chicago had similar feelings toward their health. In a sample of 610 people in Chicago, 70 described their health as poor, 180 as good, 220 as very good, and 140 as excellent. Compute the test value.

View Policies Current Attempt in Progress Write an expression representing the given quantity. A population at time t years if it is initially 3 million and growing at 6% per year. NOTE: Enter the exact answer. The population is eTextbook and Media Save for Later million. Attempts: 0 of 3 used Submit Answer

Solve each equation with the quadratic formula. -5n²-2n +72 = 0 2+√6 -2-√6 18 0 {2+ √² 2 = √6} 0 {2+ √² -2-0) 0{-4} 2 0 {= 2 + √² 2 −2+√2 -2- √2 2 ○ {4, −4}

Suppose that the cost for manufacturing n desks is C dollars, so we have C = f(n). Which of the following statements is the best interpretation of 2 f(n)? The cost, in dollars, of manufacturing twice as many desks. The cost, in dollars, has doubled for manufacturing n desks. The cost, in dollars, for manufacturing half as many desks. The number of desks has doubled. The cost, in dollars, for manufacturing n desks has been cut in half.

Evaluate the expression with the given replacement values. 8 7x2; x = -3 7x² O A. O B. O C. O D. - 4 21 8 63 4 21 8 63

Internet tax: The Gallup Poll asked 1031u.S. adults whether they believed that people should pay sales tax on items purchased over the internet. Of these, 443 said they supported such a tax. Does the survey provide convincing evidence that less than 45% of U.S. adults favor an internet sales tax? Use the a= 0.05 level of significance. Part: 0/5 Part 1 of 5 State the appropriate null and alternate hypotheses. Ho: H₁: This hypothesis test is a (Choose one) test. O<0 0>0 0-0 X P S

Use polynomial long division to write each of the following ratios in polynomial and r is the remainder. (a) (c) x² - 6x +11 x-4 3x² +17x+25 x+4 (b) (d) x²+2x-25 x+7 5x²-41x+3 x-8 x-a form, where q(x) is a

Create a table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer!

pose that the distribution of scores of 1,000 students who take a standardized intelligence test is a normal distribution. Also suppose that the distribution's mean is 450 and its standard deviation is 25. a) How many scores do we expect to fall between 400 and 500? b) How many scores do we expect to fall below 400? a) It is expected that score(s) fall between 400 and 500. (Round to the nearest whole number as needed.) .....

. Atmospheric pressure decreases by about 12% for every 1000 meters you climb. The pressure at sea level is about 1.013 bars. a. Construct a model to represent the atmospheric pressure at a given altitude in thousands of meters.

rt (a) Use the model A-Pet to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. Avoid rounding in intermediate steps. The average rate of return under continuous compounding is approximately %. X

Find the focus and directrix of the parabola with the given equation. x = 6y² O focus: (1,0) directrix: x = - O focus: (4,0) directrix: x = O focus: (0,1) focus: s: (,0) directrix: y = - 4 24 1/6 directrix: x = 2/ 1 24

Curt and John play one basketball game every night of the week. Each night's game is won by either Curt or John; there is no draw. The probability that John wins any game is 0.75 and the result of each game played is independent of any other game played. Let X denote the number of games won by John. Find the expression showing the probability that Curt wins exactly 2 games out of 7?

If a, b, c are real and a² + b² + c²= 1, then ab + bc + ca lies in the interval: 1 (A) (B) [0, 2] 9[-2] ON (D)

Where does the tangent line to y = e* at x = 1 cross the y-axis? At x -

The area of a rectangular living room is 300 square feet. The length of the room is 10 feet less than twice the width. What is the width of the living room in feet? Do not include units in your answer. Provide your answer below:

I want to buy a car, but I have two options. Option 1: I can pay it off over 6 years at an interest rate of 3.8%. Option 2 I can pay it off over 7 years at 2.5%. What would the payment for each of those be? Which option would cost me more over time?

Solve the exponential equation by using the property that b = by means that x = y whenever b> 0 and b 1. 2x-1 A= = 9 25

Use the pop up below to find the area under the standard normal curve from 0 to - 2.01.

Create an Amortization table using the following: I am buying a Tesla for $75,000. I am paying it off over 7 years, and I have an interest rate of 1.8%. What is my monthly payment? How much of the first payment is going toward interest?

To begin a bacteria study, a petri dish had 2600 bacteria cells. Each hour since, the number of cells has increased by 4.1%. Let t be the number of hours since the start of the study. Let y be the number of bacteria cells. Write an exponential function showing the relationship between y and t.

Current Attempt in Progress The given function describes the value in dollars of an investment in year t. What does the given function tell you about the investment? V = 9100(0.929)' Enter the exact answers. Enter only positive values in the answer areas. The initial value of the investment is $ % per year. 9100 , and it decreases by i

The formula A-Pe describes the accumulated value, A, of a sum of money, P, the principal, after t years at annual percentage rate r (in decimal form) compounded continuously. Complete the table for a savings account sub to continuous compounding. Amount Invested Annual Interest Rate 8% $9000 Accumulated Amount Time t in Years Double the amount invested ? to years (Do not round until the final answer. Then round to one decimal place as needed)

Consider the following function. -2x-6 if x ≤ -3 11/2² if x > -3 Step 2 of 3: Identify the general shape and direction of the graph of this function on the interval (-3,00). An 15/25 Correct (4(3)