Basic Math Questions and Answers

Among all pairs of numbers whose sum is 20, find a pair whose product is as large as possible. What is the maximum product?

A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 2.5. What are the dimensions of such a cylinder which has maximum volume? Radius= Height =

Consider a student loan of $17,500 at a fixed APR of 9% for 25 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest. a. The monthly payment is $ (Do not round until the final answer. Then round to the nearest cent as needed.)

Two four-sided dice with sides numbered from 1 through 4 are tossed. What is the sample space for the sum of the two dice? a. {4} b. {1, 2, 3, 4) c. {2, 3, 4, 5, 6, 7, 8} d. {1, 2, 3, 4, 5, 6, 7, 8)

Write the following number in decimal notation. Ninety-two and seven hundredths

If all other quantities remain the same, how does the indicated change affect the width of a confidence interval? (a) Increase in the level of confidence (b) Increase in the sample size (c) Increase in the population standard deviation

For the same sample statistics, which level of confidence would produce the widest confidence interval? Explain your reasoning. Choose the correct answer below. 99%, because as the level of confidence increases, Zc decreases. 90%, because as the level of confidence decreases, zo increases. 90%, because as the level of confidence decreases, Zc decreases. 99%, because as the level of confidence increases, zc increases.

The formulas below are the cost and revenue functions for a company that manufactures and sells small radios. C(x)=120,000+ 37x and R(x) = 49x a. Use the formulas shown to write the company's profit function, P, from producing and selling x radios. b. Find the company's profit if 18,000 radios are produced and sold.

Factories often add filler when making meatballs sold by the bag. One factory obtained 90 kg of beef from overseas. They want to add 1.4 oz of filler for each pound of beef. How many ounces of filler will the factory need in order to make meatballs out of this shipment of beef? Use 1 lb = 0.45 kg and do not round any computations.

The Acting Club two-act plays begins at 3:20 P.M. The first act is twice as long as the second act, and there is a 15-minute break between the two acts. The play ends at 4:50 P.M. How long is Act I?

A starship is orbiting Milgram, a large moon of the planet Erdosar. The ship's sensor array detects that the temperature on the surface of the moon is -14.2 °C. What is this temperature in degrees Fahrenheit (°F)? Use the given formulas as necessary, and round your answer to the nearest tenth of a degree. Formulas: C= 5/9 (F-32) F= 9/5C + 32

The population of a bacteria colony triples every hour. If the initial population is 100 a) write an equation that would model the population, where P is the total population and t is time in hours. b) What is the population of the colony in 5 hours?

The Art Club held a show for 2 days. A total of 269 people attended the show. On the second day, 15 more people attended than had come to the show the first day. How many people attended on the first day?

Solve 5 sin(2w) - 4 sin(w) = 0 for all solutions 0≤ W< 2π

Consider a home mortgage of $250,000 at a fixed APR of 9% for 30 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest. a. The monthly payment is $ (Do not round until the final answer. Then round to the nearest cent as needed.) b. The total payment over the term of the loan is $ (Round to the nearest cent as needed.)

If algae grows at a rate that can be modeled by the exponential function A(t) = aert, what is the surface area of algae on a pond if the initial area of the algae (a) is 2 square meters, the growth rate (r) is 10%, and the algae grows for three days (t)? (Use a calcualtor or 2.718 for the value of e.)

For the following loan, make a table showing the amount of each monthly payment that goes toward principal and interest for the first three months of the loan. A home mortgage of $154,000 with a fixed APR of 6% for 30 years. Fill out the table. End of... Month 1 Interest Payment Toward Principal New Principal

Consider a student loan of $10,000 at a fixed APR of 10% for 3 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Find the critical numbers of the function f(x) = -12x^5 + 15x^4 + 100x³ - 5 and classify them using a graph.

Suppose you have a student loan of $25,000 with an APR of 9% for 40 years. Complete parts (a) through (c) below. a. What are your required monthly payments? The required monthly payment is $ 192.84. (Do not round until the final answer. Then round to the nearest cent as needed.) b. Suppose you would like to pay the loan off in 20 years instead of 40. What monthly payments will you need to make? The monthly payment required to pay off the loan in 20 years instead of 40 is $. (Do not round until the final answer. Then round to the nearest cent as needed.)

Consider the following pair of loan options for a $165,000 mortgage. Calculate the monthly payment and total closing costs for each option. Explain which is the better option and why. Choice 1: 30-year fixed rate at 5.5% with closing costs of $2300 and 1 point. Choice 2: 30-year fixed rate at 5.25% with closing costs of $2300 and 4 points. What is the monthly payment for choice 1? (Do not round until the final answer. Then round to the nearest cent as needed.) What is the monthly payment for choice 2? (Do not round until the final answer. Then round to the nearest cent as needed.)

Someone needs to borrow $14,000 to buy a car and the person has determined that monthly payments of $300 are affordable. The bank offers a 3-year loan at 8% APR, a 4-year loan at 8.5%, or a 5-year loan at 9% APR. Which loan best meets the person's needs? Explain. Which loan best meets the person's needs? (Round to the nearest cent as needed.) A. The first loan best meets the person's needs because the monthly payment of $ budgeted amount of $300 per month. B. The second loan best meets the person's needs because the monthly payment of $ budgeted amount of $300 per month. C. The third loan best meets the person's needs because the monthly payment of $ budgeted amount of $300 per month. D. None of the loans meet the person's needs. is less than the maximum is less than the maximum is less than the maximum

An isosceles triangle has a vertex angle of 26°. Two sides of the triangle are each 15 ft long. Find the area of the triangle. A. 49.314 sq ft B. 45.543 sq ft C. 9.931 sq ft D. 98.629 sq ft

A rancher wants to fence in an area of 3,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

Assume you have a balance of $1100 on a credit card with an APR of 24%, or 2% per month. You start making monthly payments of $200, but at the same time you charge an additional $80 per month to the credit card. Assume that interest for a given month is based on the balance for the previous month. The following table shows how you can calculate your monthly balance. Complete and extend the table to show the balance at the end of each month until the debt is paid off. How long does it take to pay off the credit card debt?

A 5000-seat theater has tickets for sale at $26 and $40. How many tickets should be sold at each pric $148,200?

Solve the system by the addition method. 5x - 4y = 2 2x + 5y = 14 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. There are infinitely many solutions. C. There is no solution.

A 6000-seat theater has tickets for sale at $25 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $190,500?

A radioactive isotope decays rapidly with a half-life of 4 minutes. For a 12 minute test, technicians need at least 6 grams of the isotope to remain at the end of the test. How much must they start with? a) 48 grams b) 12 grams c) 24 grams d) 96 grams

Find the value of z in the solution of the following system: 2x+2y+3z = -107 3x + 2y - 5z = 16 -5x – 2y - 5z = 180

You are planning to make an open rectangular box from a 6-in. by 6-in. piece of cardboard by cutting congruent squares from the corners and folding up the sides. What are the dimensions of the box of largest volume you can make this way, and what is its volume? Use must use calculus to determine the desired optimal solution to the problem.

Solve the system by the addition method. 5x + 3y = 4 10x+6y=8 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. There is exactly one solution. The solution set is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. The solution set is {(x,y) |5x+3y=4} or {(x,y)| 10x+6y=8}. C. The solution set is Ø.

A farmer finds that if she plants 90 trees per acre, each tree will yield 60 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 2 bushels. How many trees should she plant per acre to maximize her harvest?

Using the formula A(t) = ae^rt, what is the value of an investment with an initial value (indicated by the variable a) of $1,000 that continuously compounded at 8% (r) over 50 years (t)? (Use 2.718 for the value of e.)

A fence 6 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

Suppose that on January 1 you have a balance of $2800 on a credit card whose APR is 14%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1. a. Calculate your monthly payments. b. When the card is paid off, how much will you have paid since January 1? c. What percentage of your total payment from part (b) is interest?

Let f(x) = x³ + 3x² - 9x + 15. (a) Use the definition of a derivative or the derivative rules to find f'(x)= (b) Use the definition of a derivative or the derivative rules to find f''(x) = (c) On what interval is f increasing (include the endpoints in the interval)? interval of increasing = (d) On what interval is f decreasing (include the endpoints in the interval)? interval of decreasing = (e) On what interval is f concave downward (include the endpoints in the interval)? interval of downward concavity = (f) On what interval is f concave upward (include the endpoints in the interval)? interval of upward concavity =

8. Suppose you have borrowed two calculators from friends, but you do not know whether they are set to work in radians or degrees. You ask each calculator to evaluate cos 3.14. One calculator replies with an answer of -0.99999; the other calculator replies with an answer of 0.998499. Without further use of a calculator, how would you decide which calculator is using degrees? Explain your answer.

Find the coordinates of point L that lies along the directed line segment from N(14, 4) to M(2, 8) and partitions the segment in the ratio of 1:3. A. (16, 12) B. (8,6) C. (11,5) D. (-3,1)

Find the midpoint of the segment between the points (8,-10) and (-10,-8). A. (-1,-9) B. (0,0) C. (-1,2) D. (0,-6)

The population of Suka is currently 34.88 million people. Suka's current growth rate is 1.1% per year. What will Suka's population be in 5 years? a) 58 774 828 b) 19 477 199 c) 33 003 343 d) 36 841 072

A triangular field has sides of 218.5 m and 213.3 m, and the angle between them measures 58.96°. Find the area of the field. A. 24,032 m² B. 19,966 m² C. 12,016 m² D. 14,332 m²

Which of the following is NOT the equation for a conic section? Enter a, b, c, d, or e. a. 2x² + 5y² - 2x + 7y - 8 = 0 b. y = 3x² + 7x-3 c. y = 2^x + 5 d. x²/9 - (x-3) ²/ 16 =1 e. (x - 2)² + (y + 3)² = 25

While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 40 degrees. After walking 450 ft closer, he guessed that the angle of elevation had increased by 18 degrees. Approximately how tall is the hill? A. 236 feet B. 794 feet C. 496 feet D. 608 feet

Find the midpoint of WX. W = (-1, 5) X = (7,3)

Which of the following would be a good idea as you prepare for a test? A. Stay up late the night before studying. B. Eat a big breakfast right before. C. Put new batteries in your calculator. D. Don't study until the morning of the test.

Jon has quarters, dimes, and nickels in his pocket. The value of his money is $1.75. There are two more dimes than quarters and twice as many nickels as dimes. How many nickels does he have?

If 1800 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

If a virus spreads at a rate that can be modeled by the exponential function A(t) = ae^rt, how many people will be infected after 5 days if the initially 3 people are infected and the growth rate is 40%? (Use your calculator for a precise version of e. If you are not able to use a calculator, you can approximate e as 2.718. Round your answer to the nearest person.)

Solve the following system of equations. If there is no solution, write DNE in each coordinate of the ordered triplet. If there are an infinite number of solution, write each coordinate in terms of z. x-14=y-13 z+6=x+2 y-10=z-7