Basic Math Questions and Answers

Chris is super hungry and wants to eat an entire pizza. The radius of the pizza is 6 inches. If Chris eats the whole pizza, how many square inches did he consume?

For the polynomial below, 2 is a zero. h(x)=x³ + 4x²8x - 8 Express h (x) as a product of linear factors.

A car is purchased for $43,000. Each year it loses 30% of its value. After how many years will the car be worth $5400 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.

A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (4, -3). What is the vertex of the function defined as g(x) = f(x) - 3?

There is a sales tax of $15 on an item that costs $153 before tax. A second item costs $81.60 before tax. What is the sales tax on the second item?

At a school dance, tickets are sold at the door and each ticket is the same price. The amount of money the school makes from the dance is equal to the total amount of money collected from ticket sales minus the total cost of the DJ and decorations. For this dance, the total cost is fixed and is not dependent on the number of tickets sold. If 75 tickets are sold, the school loses $150. If 100 tickets are sold, the school makes $100. What is the total cost of the DJ and decorations? $250 $300 $900 $1,000

The number of milligrams D (h) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is given by the following function. D(h)=50e-0,25h When the number of milligrams reaches 33, the drug is to be injected again. How much time is needed between Injections? Round your answer to the nearest tenth, and do not round any Intermediate computations.

When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.

Find the surface area of a sphere that has a circumference of 20π cm,, in terms of square centimeters.

Find the volume of a pyramid with a square base, where the side length of the base is 18.5 in and the height of the pyramid is 10.9 in. Round your answer to the nearest tenth of a cubic inch.

You are building a rectangular flowerbed for your back yard. The flowerbed will surround the flowers and sit on the ground. The ground where you want to plant the flowers is 4 ft. by 7 ft. How many feet of boards will you need to build the flowerbed? Your answer should be a number only.

What is the volume of a hemisphere with a radius of 4.8 ft, rounded to the nearest tenth of a cubic foot?

You want to build a sandbox for your little brother. You know you need to buy wood to frame the outside of the box. If the dimensions of the box will be 6 ft. by 8 ft., how many feet of lumber will you have to buy? Your answer should be a number only.

What is the volume of a sphere with a diameter of 6.4 cm, rounded to the nearest tenth of a cubic centimeter?

Which transformation rule below translates points 5 units to the left and 2 units up? A. (x,y) → (x + 5,y + 2) B. (x,y) → (x - 5,y - 2) C. (x,y) → (x + 5,y - 2) D. (x, y) → (x - 5, y + 2)

An online shopping club has 5,200 members when it charges $9 per month for membership. For each $1 monthly increase in membership fee, the club loses approximately 200 of its existing members. Write and simplify a function R to represent the monthly revenue received by the club when x represents the price increase. Hint: Monthly revenue = # members • monthly fee.

In a right triangle the two legs have measurements of 8 inches and 18 inches. Use the Pythagorean theorem to calculate the length of the hypotenuse. 144.00 inches 388.00 inches 12.00 inches 5.10 inches 19.70 inches

A rectangular-shaped window is 200 centimeters long and 5 meters wide. What is the area of the window? A. 1,000 square centimeters B. 250 square centimeters C. 14 square meters D. 10 square meters

A thread is being pulled off a spool at the rate of 61.9 cm per sec. Find the radius of the spool if it makes 123 revolutions per min. r≈cm (Round to two decimal places as needed.)

The formula w=θ/t can be rewritten as =θ wt. Using wt for θ changes s = rθ to s = rwt. Use the formula s = rwt to find the value of the missing variable. s=4π cm, r = 3 cm, w =π/6 radian per sec

Present value. A promissory note will pay $45,000 at maturity 9 years from now. How much should you be willing to pay for the note now if money is worth 4.25% compounded continuously?

A principal of $3800 Is Invested at 7.75% interest, compounded annually. How many years will It take to accumulate $11,000 or more in the account? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.

Travis Thompson uses his credit card to obtain a cash advance of $600 to pay for his textbooks in medical school. The interest rate charged for the loan is 0.04921% per day. Travis repays the money plus the interest after 25 days. a) Determine the interest charged for the cash advance. b) When he repaid the loan, how much did he pay the credit card company?

A forest ranger in an observation tower sees a bear 15 miles to the north. The ranger also knows there are campers located 19 miles due west of her post. To the nearest mile, how far are the campers from the bear?

Write an explicit equation for the nth term of the geometric sequence 3584, 896, 224,.... Find the sixth term of this sequence.

Recently, a certain bank offered a 10-year CD that earns 2.52% compounded continuously. Use the given information to answer the questions. (a) If $20,000 is invested in this CD, how much will it be worth in 10 years? approximately $ (Round to the nearest cent.)

From the top of a building, the angle of depression to a car parked on the street below is 48°. If the building is 75 ft. tall, how far is the car parked from the base of the building? 112.1 ft. 83.3 ft. 100.9 ft. 67.5 ft.

A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. If n represents the number of nickels and d represents the number of dimes, which of the following systems of equations can be used to represent this situation. n+d=4.45 0.05n+ 0.10d = 60 0.05n+ 0.10d = 60 0.05n+ 0.10d = 4.45 n+d=60 5n+ 10 d = 4.45 n+d=60 0.05n+ 0.10d = 4.45

The area of a circle with a radius of 3.65 cm is cm² Round answer to nearest tenth.

Use the remainder theorem to find P (2) for P(x)=2x³-2x² - 2x+4. Specifically, give the quotient and the remainder for the associated division and the value of P (2).

Jayla bought a table and some chairs at a furniture store. The equation that models this situation is y= 35x + 30, where y is the amount of money she spent and x is the number of chairs she bought. What does the y-intercept mean in this situation? A. She paid $30 for the table. B. She paid $35 for each chair. C. She paid $30 for each chair. D. She paid $35 for the table.

Directions: Complete the following statements. 1. The standard form of a quadratic equation is 2. The curve formed by a quadratic equation is called a 3. The formula for the axis of symmetry is 4. If the vertex is the highest point on the graph, it is called a 5. If a vertex is the lowest point on a graph, it is called a

Manuel wants to buy new carpet for his living room floor. The floor is in the shape of a rectangle. Its length is 19 feet and its width is 12 feet. Suppose carpet costs $8 for each square foot. How much will carpet cost for the floor?

Let 8 be an angle such that sinθ=-12/13 and tanθ>0. Find the exact values of cot and sec8.

Solve the equation over the interval [0,2π), then support your solutions graphically. 2 cos 2x + 2 cos x = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. (Use a comma to separate answers as needed. Type exact answers, using as needed.) B. The solution is the empty set.

A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 54 square feet of material to build the cube. What is the volume inside the giant sugar cube? *

What is the volume of a sphere with a diameter of 43.5 cm, rounded to the nearest tenth of a cubic centimeter?

When members of the military are in a combat zone, they often eat meals-ready-to-eat (MRES). A typical MRE contains 1,800 calories. If the average soldier eats 3 MREs per day and is deployed for 6 months, approximately how many calories will be consumed by a 44-member platoon of soldiers? The platoon will consume million calories. (Round to the nearest hundredth as needed.)

Use the formula w=θ/t to find the value of the missing variable. θ= radians, t= 5 sec w= radians per sec (Simplify your answer. Type an exact answer, using as needed.)

A student who is driving home for the holidays averages 38 miles per hour. Set up the problem below and calculate how many miles the student would travel if the trip home took 6.70 hours.

A clock is malfunctioning. The minute hand of the clock only moves and indicates correct time every 12 minutes. For instance, the clock indicates 12 pm between 12 pm to 12:11 pm and indicates correct time at 12:12 pm. How many times does the clock indicate correct time between 12:10 pm and 5:35 pm?

Flying against the wind, an airplane travels 7760 kilometers in 8 hours. Flying with the wind, the same plane travels 8470 kilometers in 7 hours. What is the rate of the plane in still air and what is the rate of the wind?

The tangent line to the graph of function h at the point (-2,-4) passes through the point (1,5). Find h'(-2). h'(-2)=[

If a line of one billion people standing shoulder-to-shoulder stretches 333,181 miles long, what is the average shoulder width, in feet, of the people in the line?

Norman's checking account reconciliation information is as follows: Bank balance $304.79 Checkbook balance $206.19 Unreturned checks $110.17 Unprocessed deposits $12.58 When the account is reconciled, the checkbook balance is a. $206.19 b. $207.20 c. $303.78 d. $304.79

(1) Solve this system using the substitution method: y = 2x-3; y = (1/2)x-4 (2) Solve this application problem using a system of equations: The owner of Jeremy's Garage wants to fill a 55-gallon drum with a 20% winter mixture of antifreeze for is customers. How many gallons of 100% antifreeze should he mix with some 12% antifreeze mixture in order to fill the drum?

Use the formula v= rw to find the value of the missing variable. r = 15 m, w = 3π/5 radians per sec The missing variable is v= m per sec. (Type an exact answer.)

Adam needs to buy a solar blanket for his rectangular pool. The blanket will sit on the surface of the water and keep it warm. If the dimensions of the pool are 15 ft. by 18 ft., how many square feet of water will the solar blanket cover? Your answer should be a number only.

On the blueprint of a house, 28 millimeters represents 6 meters. The actual length of the living room is 9 meters. What is its length on the blueprint? millimeters

Nicole wants to build a circular deck in her yard. If she needs the radius of the deck to be 7 feet, how many square feet of her yard will be covered by the deck? Your answer should be a number only. Use 3.14 for pi. Round your answer to the nearest hundredth.