Basic Math Questions and Answers

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)

3. Many communities today are concerned with their local government's ability to appropriately manage the taxes it collects. If a government spends more money on expenditures than it collects in taxes, it may end up with not enough money, called deficit. Which of the following could result in a county government budget in Deficit? a. The government raises sales and property taxes without adjusting expenditures. b. The county closes a fire station, reducing expenditures, without adjusting taxes. c. The county gives all public-school teachers a $2,000 raise without adjusting taxes. d. The count collects donations to build a fountain in city hall.

An object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second. The height h of the object after t seconds is given by the quadratic equation h = - 16t² + 128t+144. When will the object hit the ground? The object will hit the ground when the time is seconds.

Advice from most financial advisers states to spend no more than 28% of one's gross monthly income for one's mortgage payment, and to spend no more than 36% of one's gross monthly income for one's total monthly debt. Suppose a family has a gross annual income of $39,600. a. What is the maximum amount the family should spend each month on a mortgage payment? b. What is the maximum amount the family should spend each month for total credit obligations? c. If the family's monthly mortgage payment is 70% of the maximum they can afford, what is the maximum amount they should spend each month for all other debt? a. The maximum monthly mortgage payment should be $ .....

An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 5 inches, and the length of the base is 2 inches. Find the triangle's perimeter. Round to the nearest tenth of an inch.

The costs of general admission and student tickets to a high school football game are $7 and $4 respectively. The ticket sales for one game totaled $11,200. Write an equation which models the situation.

A baseball is dropped from a stadium seat that is 79 feet above the ground. Its height s in feet after t seconds is given by s(t)=79-22t2. Estimate to the nearest tenth of a second how long it takes for the baseball to strike the ground.

If a person shoots a basketball overhand from a position 8 feet above the floor, then the path of the basketball through the hoop can be modeled by the parabola y=- ball in ft/sec, y is the height of the ball and x is the distance away from the person. (a) If the basketball hoop is 10 ft high and located 15 ft away, what initial velocity v should the basketball have? (b) What is the maximum height of the basketball? (a) The initial velocity of the basketball should be approximately 23.32 ft per sec. (Round to the nearest hundredth.) (b) The maximum height of the basketball is approximately ft. (Round to the nearest hundredth.) -16x² 0.434v² ..... +1.15x+8, where v is the initial velocity of the

In 2012, the population of a city was 6.55 million. The exponential growth rate was 1.94% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 10 million? d) Find the doubling time.

A farmer has 400 feet of fence to enclose a rectangular area. What dimensions for the rectangle result in the maximum area enclosed by the fence? The rectangle with the maximum area enclosed by the fence has a length of ft and a width of ft.

900 11.29fd18son side rool box dam has 9. You are playing a board game with a spinner that has numbers 1, 2, 3, and 4 on it. You get to spin the spinner twice. What is the probability that you land on number 2 given that your first spin landed on number 1?

Classify the quotient as positive, negative, zero, or undefined. 5+5 Select the correct choice below. A. The quotient is zero. B. The quotient is undefined. C. The quotient is positive.. D. The quotient is negative.

What value of n makes this proportion true? 2n=1 = 1 10 O 1/2 03 06 O 2/3

The probability is (Type an integer or a simplified fraction.) HW Score: 75%, 6 of 8 points O Points: 0 of 1 A "trifecta" is a particular horse race in which you win by picking the "win," "place," and "show" horses (the first-, second-, and third-place winners), in their proper order. If five horses of equal ability are entered in a trifecta race, and Tracy selects an entry, what is the probability that she will be a winner?

A car manufacturer announced that next year the price of a certain model car would increase by 3.5%. This year the price is $17,015. Find the increase and the new price.