Basic Math Questions and Answers

x²-81 x³+7x² 18x Where is the removable point of discontinuity? Give only the x-value. Consider the graph of the function f(x) =

A gym charges a $615 yearly fee for membership plus $50 for each hour of personal training. What is the average total cost per hour of training if a member works with a personal trainer for 30 hours in a year? Do not include the dollar sign ($) in your answer. Provide your answer below:

The proportion of students in a psychology experiment who could remember an eight-digit number correctly for t minutes was 0.9 0.3 In(t) (for t > 1). Find the proportion that remembered the number for 5 minutes. (Round your answer to one decimal place.) X % 0.4

Consider the function f(x) = 2x¹ − 4x³ + 20x − 100. - What is the remainder if f(x) is divided by (x +11)? Do not include the divisor in your answer. Provide your answer below:

Find the derivative of the function. h'(t) = h(t) = 30 -sinh(-6t)

Find all real and complex solutions to the equation 2³-32²-10x + 24 = 0 Express your answer as a list separated by commas, entering each zero as a separate number.

After walking mile from home, Han is of his way to school. What is the distance between his home and school? 1. Write multiplication and division equations to represent this situation. 2. Use the given diagram to help you answer the question. Mark up and label it as needed.

Select the correct answer. The image of polygon MNOP after a similarity transformation is polygon WXYZ. Each side of MNOP is 2 times as long as the corresponding side of WXYZ. What is the scale factor of the dilation in the similarity transformation? OA. 4 OB. 0.5 OC 2 OD. 0.25

What are the rational zeros of the function f(x) = x³ + 3x²-x-3? List the values separated by commas. Do not include "=" in your answer. Provide your answer below:

Give a third degree polynomial that has zeros of 13, 5i, and -5i, and has a value of -680 when = polynomial in standard form ax + bxn-¹ +... 3. Write the

The physician ordered Platinol (cisplatin) 100 mg/m² IV to infuse over 6 hours once every 4 weeks for a patient who has a BSA of 1.66 m². (a) How many mg of this antineoplastic drug should the patient receive? (b) If the dose of cisplatin were administered in 1,000 mL D5 1/2 NS, at how many mL/h would the IV run?

Given f(x) = 2x³ + 2x - 8 verify that f(x) is invertible and, if so, find the equation of the tangent line to f-¹(x) at the point where x = 12. Note that f(2)= 12. a) O f(x) is not invertible. b) Oy+2=- c) Oy - 2 = d) Oy - 12 = ) Oy - 12 = 1 1 26 26 (x - - 12) (x - 12) 1 26 1 26 (x + 2) (x 2)

The function g is defined as follows. g(x) = -5x² +5 If the graph of g is translated vertically downward by 3 units, it becomes the graph of a function f. Find the expression for f(x). Note that the ALEKS graphing calculator may be helpful in checking your answer.

If the cost, C, for manufacturing x units of a certain product is given by C=x² + 35x + 40, find the number of units manufactured at a cost of $10,240. There are units manufactured at a cost of $10,240.

Divide using long division: Write your answer in the form Q(x) + the given divisor. Provide your answer below: R(x) D(x)' 2x³ - 6x² +5 x-1 where Q(x) is the polynomial quotient, R(x) is the remainder, and D(x) is

Consider the graph of the function f(x) = 2³-x²–2x x²+x Which is a removable discontinuity for the graph? Select all that apply. Select all that apply: 0 x = x = -2 x = −1 x=0 x = 1 ☐ x=2

Add the following rational expressions and make sure to state the restrictions on the variable: 3/x^2-16 + x/x+4 (214)(x-4), 2-4, 4 2+1 214-4 (2-3)(2-1) (14)(x-4), -4, 4 241 = 14,2 -4,4

If the formula y = x³ is changed by adding one as shown in red below. f(x) = (x + 1)³ Which values would be most directly affected by the change? Select an answer < What effect would it have on the graph? D

Diego measured the length of a pen to be 22 cm. The actual length of the pen is 23 cm. Which of these is closest to the percent error for Diego's measurement? O 4.3% O 4.5% O 95.7% O 104.5%

Given that the polynomial f(x) has 3 intercepts, which of the following most accurately describes the degree of f(x)? Select the correct answer below: The degree of f(x) is at most 3. The degree of f(x) is at least 4. The degree of f(x) is at most 4. The degree of f(x) is at most 2. The degree of f(x) is at least 2. O The degree of f(x) is at least 3.

Which function has a remainder of -70 when divided by (x - 9)? Select the correct answer below: O g(x) = x³ - 2x² − 93x + 200 - O g(x) = x³ x² − 93x+20 O g(x) = x³ - 2x² − 90x + 200 - O g(x) = x³ - 2x² − 3x + 20 O g(x) = x³ = x² − 3x + 200

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}