Basic Math Questions and Answers

[8 points] Suppose you have invested $2200 at an APR of 3%. Use the Rule of 72 to estimate how long it will be until your investment reaches $4400. It will take approximately Select- years for the investment to reach $4400.

A concrete pillar has the shape of a cylinder. It has a diameter of 8 meters and a height of 6 meters. If concrete costs $106 per cubic meter, how much did the concrete cost for the pillar?

What is the freezing point (°C) of a solution prepared by dissolving 11.3 g of Ca(NO3)2 in 115 g of water? The molal freezing point depression constant for water is (Assume 100% ionization of Ca(NO3)2.) A)-3.34 B) -1.11 C) 3.34 D) 1.11 E) 0.0 B)-1.11 C) 3.34 E) 0.00 A)-3.34 D) 1.11

Which condition makes the statement below false? "If I have an alibi, then I am innocent" Hint: When is a conditional false? I do not have an alibi and I am not innocent I have an alibi and I am not innocent I have an alibi or I am innocent I do not have an alibi or I am innocent

Which segment does not belong with the other three? Explain your reasoning. radius: It is smaller than the other segments. diameter; It is the only segment through the center. tangent, It is the only segment outside the circle. chord; It is the only segment with endpoints on the circle.

The student population in the Greenville school system is increasing about 10% each year. This year there are 3120 students in the Greenville school system. If this trend continues, which of the following is closest to the number of students who will be in this school system 3 years from now? 3400 4000 4200 9400

Air Transportation: A standard M-6 air cargo container is 19.8 feet long, 7 feet wide and 7.3 feet tall. For the purposes of this project, when it is completely filled each container can hold up to 21,500 cellphones, and the transportation cost is $24,000 per container. How much will it cost per cellphone to use this mode of transportation?

A recreational softball league is considering some rule changes. In order to know how the players feel, league officials sent out a survey by email to all the players in the league. What type of sampling method did the league use? Self-selected Stratified Systematic Cluster

A pyramid shaped building is 837 ft tall with a square base that is 156 ft on each side. What is the volume of the pyramid?

John invests $2800 into an investment account described by the equation A = 2800 (e-07-t). If interest is compounded continuously, how much is in his investment account at the end of 5 years? (Round to the nearest penny)

William spends $2,500 on a bedroom furniture set on a store credit account. If he is not required to make payments for three years, but the interest is compounded yearly at 8.5%, how much interest will he owe after 3 years? $2,508.50 $693.22 $212.50

A laptop computer is purchased for $1050. After each year, the resale value decreases by 25%. What will the resale value be after 5 years? Use the calculator provided and round your answer to the nearest dollar. $0 X

Use the given circumference to find the surface area of the spherical object. a pincushion with C = 24 cm The surface area of the pincushion is cm².

A croissant, a cup of coffee, and a fruit bowl from Kelley's Coffee Cart cost a total of $5.25. Kelley posts a notice announcing that, effective next week, the price of a croissant will go up 25% and the price of coffee will go up 35%. After the increase, the total price of the purchase will be $5.74, and a fruit bowl will cost 3 times as much as a croissant. F

Mrs. Travis wants to have a clown deliver balloons to her secretary's office. Clowns R. Fun charges $1.25 per balloon and $6 delivery. Singing Balloons charges $1.95 per balloon and $2 for delivery. What is the minimum number of balloons Mrs. Travis needs to purchase in order for Clowns R Fun to have a lower price than Singing Balloons?

The circumference of a circular field is 273.18 yards. What is the radius of the field?

Based on past experience, a building contractor sets the probability of winning a contract is 30%. The contract is worth $25,000 and the cost to prepare the contract proposal is $2,400. What is the expected value of the contract proposal? $5,100 $6,780 -$5,100 $22,600

The formula v= √2.5r models the safe maximum speed, v, in miles per hour, at which a car can travel on a curved road with radius of curvature, r, in feet. A highway crew measures the radius of curvature at an exit ramp as 810 feet. What is the maximum safe speed? A. 81 miles per hour B. 50 miles per hour C. 42 miles per hour D. 45 miles per hour

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