Basic Math Questions and Answers

Use the given sets below to find the new set. Enter each number separated by a comma. If there are no numbers in the resulting set, leave the answer blank. A = {-9, 2, 6} and B = {-3, 0, 4} AUB={

1. Mallory bought a computer system to start her business from home for $5,995. It is expected to depreciate at a rate of 8% per year. After how many years will the value of her home computer system depreciate to approximately $2,250. Hint: depreciate means decay

A function f(z) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to fon [a, b]. If so, find all values c in [a, b] guaranteed by the Mean Value Theorem Note, if the Mean Value Theorem does not apply, enter DNE for the c value. C= (Separate multiple answers by commas.) f(x) =z2-1/z²-16 on [0,8]

Geraldo earns $505 from his summer job and deposits it in a savings account that earns 4% simple interest. After 3 years, he moves all his money to another savings account at another ank that earns 6.5% simple interest. What formula below can be used to calculate Geraldo's total account balance after 7 years? (505 x 0.04 x 3) + (565 x 0.065 x 4) [(505 x 0.4 x 3) x 0.65 x 7] [(505 x 0.04 x 3 + 505) x 0.065 x 4]+ (505 x 0.04 x 3 +505) (505 x 0.065 x 7) + (505 x 0.04 x 3)

The Franklins inherited $3,500, which they want to invest for the child's future college expenses. If they invest it at 8.25% with interest compounded monthly, determine the value of the account, in dollars, after 5 years. $5,270.61 $6,200.53 $3,200.47 $5,279.61

A lumber yard has fixed costs of $7259.40 per day and variable costs of $0.07 per board-foot produced. Lumber sells for $1.87 per board-foot. How many board-feet must be produced and sold daily to break even?

A box with an open top has vertical sides, a square bottom, and a volume of 32 cubic meters. If the box has the least possible surface area, find its dimensions. Height = (include units) Length of base= (include units)

The quadratic function R(p)= 70p - 5.2p² models the amount of revenue in dollars R(p), generated from a product priced at p dollars. Question: What price(s) generate a revenue of $250? Enter the two solutions rounded to the nearest penny (hundredth of a dollar) in order from least to greatest. IF there is no valid answer enter N/A in all blanks. *Remember: When calculating, do not do any rounding until the end of Answer: The prices that generate a revenue of $250 are $ your calculations. and $

A computer purchased for $1,100 loses 16% of its value every year. The computer's value can be modeled by the function v(t) = ab^t, where v is the dollar value and t the number of years since purchase. (A) In the exponential model a =__and b =___ (B) In how many years will the computer be worth half its original value? Round answer to 1 decimal place. The answer is ___years

What is the solution to the following system? 3x+10y-12z=40 x-5y=0 X-4z=0 (8, 40, 32) (10, 2, 3) (20, 4, 5) (40, 8, 10)

Gordon invested $100,000 into a CD compounded quarterly with an annual interest rate of 6.00%. Determine how much money Gordon would have after 8 years. Round your answer to the nearest cent. Provide only a numerical answer (For example, if the final amount came to $5,023.97, then you would input 5023.97). Your Answer:

Translate the following verbal statement into an algebraic equation and then solve: Rachael bought a bookcase on sale for $220, which was two-fifths of the original price. What was the original price of the bookcase? Use p for your variable. Equation= p=

Sarah borrows a $300 to purchase a new computer and is charged 12% simple interest. She is not required to make payments on the loan for two years, and she makes one payment to pay off the loan after two years. How much was the payment she made? 172 $372 $720 $327

Last week Marcus travelled 150 miles in 3 hours. This week he wants to go on a 300 mile trip in 5 hours. Will it be possible to make this trip if she travels at the same speed as last week's trip? Show your work and explain why or why not this would be possible.

Grace collected data from twenty of her friends about the number of pets they have. The median number of pets is two. What does the median say about Grace's data set? A. Everyone Grace surveyed has two pets. B. More of Grace's friends have two pets than any other number. C Two is the middle number when the number of pets in the data set is ordered from least to greatest. D. Two is the difference between the greatest and least number of pets Grace's friends have.

In order for applicants to work for the foreign- service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam. # of years,x 2 3 3 4 5 5 6 6 8 Grade on test,y 59 62 70 72 78 85 80 88 92 Find the test value for testing linear correlation. 4.26 7.08 1.97 .937

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 41F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. There is not sufficient evidence to support the claim that the mean temperature is different from 41°F. There is sufficient evidence to support the claim that the mean temperature is different from 41°F. There is sufficient evidence to support the claim that the mean temperature is equal to 41°F. There is not sufficient evidence to support the claim that the mean temperature is equal to 41°F.

The population of a small town in North Carolina is 4,000, and it has a decay rate of 3% per year. Which expression can be used to calculate the town's population x years from now? 4,000x1.03 4,000x³ 4,000(1.03)* 4,000(.97)*

A poll of 1567 adults in a certain country found that 23% identified themselves as the followers of some religion. The margin of error was 4 percentage points with 90% confidence. Which of the following represents a reasonable interpretation of the survey results? A. In 90% of samples of adults in a certain country, the proportion who identify themselves as the followers of some religion is between 19% and 27%. B. There is 90% confidence that 23% of adults in a certain country identify themselves as the followers of some religion. C. There is 90% confidence that the proportion of adults in a certain country who identify themselves as the followers of some religion is between 19% and 27%. D. There is between 86% and 94% confidence that 23% of adults in a certain country identify themselves as the followers of some religion.

A 10-foot ladder is to be placed against the side of a building. The base of the ladder must be placed at an angle of 72° with the level ground for a secure footing. Find, to the nearest inch, how far the base of the ladder should be from the side of the building and how far up the side of the building the ladder will reach.

Carolyn was not able to sell her house for $220,000, so she lowered the price to $195,000. What was the percent of decrease? Round to the nearest tenth of a percent.

Solve and check the linear equation. 5(x-2)+17= 4(x+3) What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is {x|x is a real number}. C. The solution set is Ø.

In 1984, the population of Greensboro, N.C. was 197,910. According to the U.S. Census Bureau, Greensboro has been decreasing at the rate of 6.9% annually since 1984. What equation models the population of Greensboro t years after 1984? 197, 910(1 - 6.9)t 197, 910(1 - 0.69)t 197,910(1-0.069)t 197, 910(1 - 69)t

Is the equation A = 21000(1-0.12)t a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period? exponential decay and 88% exponential decay and 12% exponential growth and 12% exponential growth and 88%

Mr. Smith invested $2,500 in a savings account that earns 3% interest compounded annually. He made no additional deposits or withdrawals. Which expression can be used to determine the number of dollars in this account at the end of 4 years? 2500(1+0.04)³ 2500(1+0.3)4 2500(1+0.03)4 2500(1+0.4)³

A psychologist wants to estimate the standard deviation of IQ scores. It is widely believed that IQ scores follow a normal distribution. Her random sample of 20 IQ scores has a mean of 101.3 and a standard deviation of 16.9. Find the 90% confidence interval for the population standard deviation based on this sample. Then give its lower limit and upper limit. Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list of formulas.)

Order the investments below from 1 to 4, with the investment labeled "1" being theriskiest and the investment labeled "4" being the safest. Foreign Stocks U.S. Government Bonds Fixed-Income Bank Account U.S. Stocks

There are 800 toothpicks in a regular-sized box. If a jumbo box is made by doubling all the dimensions of the regular-sized box, how many toothpicks will the jumbo box hold?

Paul purchased a $2450 bond paying 3.5% annual simple interest after graduating from college. It is now 21 years later and he decides to cash in the bond. What is the value of this bond now? Round your answer to the nearest dollar. $1808 $4251 $4125 $18,008 $1800.75

Given that f(x)= x²(x+3)². Which of the following is correct? As x→∞, f(x)→∞o; as x→∞, f(x)→-∞0. As X →∞, f(x)→-o; as xxx, f(x) →∞. As x→∞, f(x)→∞o; as x→ ∞, f(x) →∞. AS X →∞o, f(x) →∞o; as x→∞o, f(x)→ ∞.

A 15-foot ladder leans against the side of a house with its base 4 feet from the house. Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house. Round your answer to the nearest hundredth. The ladder reaches feet high.

Samantha wants to start a college fund for her daughter Taylor. She puts $37000 into an account that grows at a rate of 2.14% per year, compounded monthly. Write a function, C(t), that represents the amount of money in the account t years after the account is opened, given that no more money is deposited into or withdrawn from the account C(t) =

2. An educator was trying to determine the effect of remote learning on middle school aged children. They randomly selected 250 students who spent a full year with in person learning and 190 of them showed similar or improved scores on a set of metrics. They also randomly selected 350 student who spent the year remotely learning and 252 of them showed similar or improved scores. a. Construct a 95% confidence interval for the difference of proportions. Show all intermediate calculations to receive full credit. b. Based on the confidence interval can you conclude there is a difference between the two groups?

Consider the following inequality: 25 <(x + 1)^2 + (y+ 6)^2. The shaded solution on the coordinate plane includes all of the area outside the circle, which is bordered by a dotted line. True False

Determine where the graph of f is below the graph of g by solving the inequality f(x) sgtx). f(x)=x^4 +3 g(x) = x + 3 f(x) ≤ g(x) if x ≤ 0 or x≥ 1 f(x) ≤ g(x) if x ≤ -1 or x≥ 1 f(x) ≤ g(x) if-1 ≤ x ≤ 1 f(x) ≤ g(x) if 0 ≤ x ≤ 1

Read the following description: An organization that provides networking and collaboration for American Indian and Alaska native psychological professionals Which of the following organizations best matches the description? Select the best answer. AAPA NLPA SIP Keyboa

Person A who is 20 years old, gives $6000 to their stock fund and continues to do so for the next 10 years. Person B started contributing $6000 to the same stock and continues until he is 65. Person B invested a total of $210,000 and person A only contributed $60,000. At age 65, which of the 2 people had the most money assuming they earned an average rate of return equal to 7% (by how much??) Use Future value= P{(1+r)^t -1}

Since January 2005 the population of Brownsville has grown according to the mathematical model y = 778500 . (1.018)x, where x is the number of years since 2005 a) What is the percent growth for this situation? b) What would the population be in the year 2015 according to the equation above? (round to the nearest whole number)

Solve and check the following linear equation. 8x − (5x – 3) = 27 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an integer or a simplified fraction.) B. The solution set is {x|x is all real number}. C. The solution set is Ø.

In a junior track and field meet, Jennifer jumped a height of 1.873 meters in the high jump. Samantha jumped a height of 1.807 meters. A. Use <, >, or = to write a number sentence comparing the heights of the girls' jumps. Whose jump was higher? Explain how you know. B. In the boys' long jump, Kevin jumped a distance of (6 × 1) + (9x) + (8 × 100)+(3× 1,000) meters. Leon jumped a distance of 6.093 meters. Kevin said he jumped farther than Leon. Is Kevin correct? Explain why or why not. C. Ben and Michael also participated in the long jump. Michael jumped 334 thousandths of a meter less than Kevin. Ben jumped farther than Michael but not as far as Kevin. Write a decimal to the thousandths that is greater than Michael's distance and less than Kevin's distance. Explain the reasoning you used.

The difference of two numbers is 5 and the sum of their squares is 53. Find the numbers. List any unique pairs of numbers that satisfy the given conditions. (Type an ordered pair, with the larger number listed first. Use a comma to separate answers as needed.)

Gail, Lucas, and Joel are playing a number game where they must draw a card with a number on it. Then they compare the numbers on the cards. Gail's, Lucas's, and Joel's cards are shown. Gail's Number Card 673.89 Lucas's Number Card 739.86 Joel's Number Card 768.98 Lucas says that the value of the digit 9 in his number is 10 times greater than the value of the digit 9 in Gail's number. Is Lucas's statement correct? Explain why or why not.

According to statistics, a person will devote 35 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 19. Over the lifetime, how many years will the person spend on each of these activities? The person will spend years watching TV and years sleeping. (Type whole numbers.)

Exponential Equations Exponential Equation: y =ab² Continuous Compounding: A =Pert In 2011, there were 8500 cell phone subscribers in Rochester. The number of people getting new cell phone services increased by 28% each year for the next t years. What is the equation that represents the situation?

You are taking out a mortgage to buy a home. After the down payment, you need to borrow $320, 000.If a bank offers you a loan at 5.34 % for 25 years, how much will your monthly payment be? How muchwill you pay in interest? Your monthly payment will be $ 3916.17 x dollars You will pay a total of $ 854851 x in interest

Given the function f(x) = x² - 13x + 40, what is its vertex?

Which of the following would be considered a strength of cross-sectional studies? Select the best answer. Precise measurement is usually possible. They can detect patterns of behavior using relatively few participants. They are inexpensive and require less time investment for researchers and participants.

A bucket on Bridget's porch holds 21/2 cups of water and collects 1/5 cup of rainwater each minute. A bucket on Cassie's porch is empty but collects 1/3 cup of rainwater each minute. Which inequality could be used to determine the number of minutes it would take for Cassie's bucket to have more water than Bridget's bucket?

The Jones want to save $69,000.00 in 5 years for a down payment on a house. If they make monthly deposits in an account paying 5% compounded monthly, what is the size of the payments that are required to meet their goal?

A business pays $68 for a car seat and wants a 24% markup for operating expenses as well as a 6% markup for profit. However, customers think the car seats are ugly, so they are not selling. Management reduces the price of each car seat by $30 to get rid of them. Find: A. the selling price $ B. the reduced price $ C. the percent markdown D. Which one, profit, operating loss, or absolute loss? E. What is the amount of profit, operating loss, or absolute loss? $