Basic Math Questions and Answers

Delaney and Erin both leave the college at the same time, but in opposite directions. If Erin travels 5 mph faster than Delaney and after 7 hours they are 203 miles apart, how fast is each traveling?

Given cot A = 9/2 and that angle A is in Quadrant I, find the exact value of sin A in simplest radical form using a rational denominator.

The total profit function P(x) for a company producing x thousand units is given by P(x) = 2x² + 40x- 168. Find the values of x for which the company makes a profit. [Hint: The company makes a profit when P(x) > 0.] A. x is greater than 6 thousand units B. x is between 6 thousand units and 14 thousand units C. x is less than 6 thousand units or greater than 14 thousand units D. x is less than 14 thousand units

A random sample of 159 full-grown lobsters had a mean weight of 18 ounces; the standard deviation of weights of all lobsters is thought to be σ = 2.8 ounces. Use this data to construct a 98 percent confidence interval for the population mean m of weights of all such lobsters.. 16.9 <m< 18.0 18.1 <m< 20 17.48 <m < 18.517 17.48 <m < 19.52

The quadratic function R(p) = -5.2p² +65p - 75 gives the amount of revenue R(p) in dollars generated by a product priced at p dollars. Question: At what price will the maximum revenue be generated?

Alice Coopersmith is moving to a new home. She can rent a 14-foot panel truck for $40.00 a day plus $0.26 a mile or an 18-foot truck for $55.00 a day plus $0.29 a mile. It would take 4 trips to make the move in the 14-foot truck, but only 3 trips in the larger truck. She estimates that gasoline would cost about $45.00 for either truck. A round-trip to her new home is 60 miles Regardless of the number of trips, she would need the truck for only 1 day. To save on expenses, which size truck should Coopersmith rent? How much would it cost per mile to rent each truck?

A college student launches a water balloon from the balcony of a building. The balloon's height off of the ground is a function of the amount of time after it is launched and is described by the equation h(t) = -16t² + 40t + 72 where t is time since launch in seconds and h(t) is the height in feet. Question: When will the balloon reach 60 feet above the ground? Enter your final answer rounded to the nearest tenth (one decimal place.) .Enter the correct units for your answer in the second box. IF there is no valid answer enter N/A in all blanks. Answer: The balloon reaches 60 feet after Why is there only one valid answer?

Select the correct answer. Consider functions fand g. f(x)= x-1/x2+x-1 g(x) = 3² - 2 Using a table of values, what is the approximate solution to the equation f(x)=g(x) to the nearest quarter of a unit?

The ratio of shirts to pants in Sara's closet is 5:2. Which best explains what that means? Sara has 5 shirts for every 2 pairs of pants in her closet Sara only has 7 items of clothing in her closet Sara has 5 more shirts than pants in her closet Sara has 5 pairs of pants for every 2 shirts

Lighthouse Master Olivia is atop her 300 ft lighthouse and spots a boat in the distance at an angle of depression of 18º. Along the same line of sight, she spots another boat at an angle of depression of 62º. How far are the boats from other? Round your answer to the nearest tenth. distance = ft.

Ni Hua is an adventurous traveler. He skydives twice in every island he visits and skydives thrice in every peninsula he visits. In the last decade, Ni Hua went skydiving a total of 45 times in the 19 islands and peninsulas that he visited. How many islands and peninsulas did Ni Hua visit? Choose 1 answer: Ni Hua visited 12 islands and 7 peninsulas. Ni Hua visited 7 islands and 12 peninsulas. There is not enough information to determine the exact number of islands and peninsula Ni Hua visited. The given information describes an impossible situation.

A sandwich shop is ordering apples and grapes to make chicken salad. Apples cost $2.19 per pound and grapes cost $2.60 per pound. If they ordered a total of 20 pounds of apples and grapes and paid $35.80, how many pounds of grapes did they order?

In Exercises 1-4, find the indicated measure. 1. radius of a circle with a circumference of 42π meters 2. circumference of a circle with a radius of 27 feet 3. circumference of a circle with a diameter of 15 inches 4. diameter of a circle with circumference 39 centimeters

In a Northwest Washington County, the speeding fines are determined by the formula: F(s) = 13(s 40) + 35 where F(s) is the cost, in dollars, of the fine if a person is caught driving at a speed of s miles per hour. If a fine comes to $308, how fast in mph was the person speeding? -

Let S be the universal set, where: S = {1,2,3,4,5,6,7,8,9,10} Let sets A and B be subsets of S, where: Set A={1,2,7,9,10} Set B= {1,2,4,5,6,7,8,10} Find the following: LIST the elements in the set (A'): (A) = { } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set (B'): (B')={ } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question.

After a 40% reduction, you purchase a new stereo for $273. What was the price of the stereo before the reduction? A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation. The equation is B) Solve your equation in part [A] to find the original price of the stereo. Answer: The original price of the stereo was dollars.

Claire has received scores of 85, 88, 87, and 95 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 90? A. 95 or greater B. 96 or greater C. 94 or greater D. 93 or greater

The following equation: P = 139t + 9900 gives the total population, P, of a small city t years after 1971. Use the equation to determine when (what year) the population reached a population of 11707 people. Answer: The population reached a total of 11707 people in the year

The perimeter of a rectangle is 48 feet. Describe the possible lengths of a side if the area of the rectangle is to be greater than 95 square feet. A. The length of the rectangle must be greater than 19 ft or less than 5 ft B. The length of the rectangle must lie between 1 and 95 ft C. The length of the rectangle must lie between 5 and 19 ft D. The length of the rectangle must be greater than 19 ft

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.