Basic Math Questions and Answers

You are choosing between two health clubs. Club A offers membership for a fee of $11 plus a monthly fee of $22. Club B offers membership for a fee of $29 plus a monthly fee of $19. After how many months will the total cost of each health club be the same? What will be the total cost for each club? In months the total cost of each health club will be the same. The total cost for each health club will be $

Suppose that the local sales tax rate is 4% and you purchase a car for $24,200. a. How much tax is paid? b. What is the car's total cost? a. The amount of tax paid is $. b. The total cost is $.

A small rock sits on the edge of a tall building. A strong wind blows the rock off the edge. The distance, in feet, between the rock and the ground t seconds after the rock leaves the edge is given by d = -16t² - 8t+470. If the answer is not an integer, enter it as a decimal. Round to the nearest hundredth, if needed. How many seconds after the rock leaves the edge is it 443 feet from the ground? seconds How many seconds after the rock leaves the edge does it hit the ground? seconds

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 68.6. You would like to be 98% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? n= Do not round mid-calculation. However, you are encouraged to use a critical value accurate to three decimal places - this is important for the system to be able to give hints for incorrect answers.

Determine the difference in clock 12 arithmetic by starting at the first number and counting counterclockwise on the clock the number of units given by the second number. 2-8

In clock 12 arithmetic, for any elements a, b, and c, (a+b)+c= a + (b+c); therefore, the property holds under the operation of addition. In clock 12 arithmetic, for any elements a, b, and c, (a+b)+c= a + (b + c); therefore, the property holds under the operation of addition.

A school playground is in the shape of a rectangle 800 feet long and 100 feet wide. If fencing costs $22 per yard, what will it cost to place fencing around the playground?

A real estate office handles an apartment complex with 80 units. When the rent is $375 per month, all 80 units are occupied. When the rent is $420, however, the average number of occupied units drops to 77. Assume that the relationship between the monthly rent p and the demand x is linear. (The term demand refers to the number of occupied units.) Predict the number of occupied units when the rent is set at $480. A) 73 B) 74 C) 71 D) 72

What is the meaning and value of the label of "2+50" for a grid survey- A. None of the answers. B. The point is 2.5ft from the origin. C. The point is 25' from the origin. D. The point is 250 ft from the origin.

Fill in the blank with the appropriate word. In clock 12 arithmetic, since 1+11=11+1=12, we say that 1 and 11 are additive

Choose the term that is defined in the given statement. A process that begins with commonly accepted facts and logically arrives at a specific conclusion. Reasoning Inductive Reasoning Counterexample Deductive Reasoning

Suppose the average American's weight increases 1.5 % each year after they turn 40. Uncle Sam just turned 40 and weighs 192 lbs. a. Create an explicit (general) equation to predict Uncle Sam's weight n years after 40. Pn b. Use your equation to predict Uncle Sam's weight at age 80, assuming the same growth applies. Round your answer to at least 3 decimal places, if necessary. Show or explain your calculations below:

Fill in the blank with the appropriate word, phrase, or symbol. The principal (or positive) square root of a number n, written √n, is the positive number that, when multiplied by gives n. The principal (or positive) square root of a number n, written √n, is the positive number that, when multiplied by gives

Use the model 4 = Pert or A=P(1+r/n)nt. where A is the future value of P dollars invested at interest rater compounded continuously or n times per year for t years. If a couple has $50,000 in a retirement account, how long will it take the money to grow to $1,000,000 if it grows by 5.5% compounded continuously? Round up to the nearest year.

Let G be the symmetry group of a regular 10-gon, and let + € G be rotation by 2/5 clockwise. Which of the following sets of integers is equal to (n E Z: rn = r}? Select one: a. {n € Z≥o: 5|n) b. (1) c. {n € Z≥o 10|(n-1)} d. {n € Z≥0:10|n} e. none of the available options

Catherine throws a stone that moves through the air in a parabolic path due to gravity. The height, in meters, of the stone above the ground after t seconds is given by h(t) = -t2 + 13t- 36. Find the maximum height of the stone. 6.5 meters 6.25 meters 6 meters

Use the model A=Pert or A= P ( 1 + r/n)nt where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. If $10,000 is invested in an account earning 6.5% interest compounded continuously, determine how long it will take the money to triple. Round up to the nearest year. It will take approximately years.

A payday loan is made for five weeks, where the amount of interest owed per $100 borrowed is $20. If you borrow $700 for five weeks, how much do you owe at the end of the five weeks?

Halley starts an IRA (Individual Retirement Account) at the age of 36 to save for retirement. She deposits $450 each month. The IRA has an average annual interest rate of 8 % compounded monthly. How much money will she have saved when she retires at the age of 65? Round your answer to the nearest cent, if necessary.

The revenue that a stadium receives from the sale of tickets is given as a function of the ticket price p as follows: R(p) = -450p² + 12600p, where p is in dollars. Find the ticket price that will maximize revenue. Determine the maximum revenue. The ticket price that will maximize revenue is $ The maximum revenue is $

Identify the sample chosen for the study. The number of times 12 out of 25 students on your floor order fast food in a week. All students who order fast food in a week. The 12 students on your floor. The 25 students on your floor.

Determine the simple interest earned on $10,000 after 10 years if the APR is 3%.

A ball is thrown vertically upward from the top of a building 144 feet tall with an initial velocity of 128 feet per second. The distances (in feet) of the ball from the ground after t seconds is s = 144 +128t- 16t2. After how many seconds does the ball strike the ground? 8 sec 145 sec 9 sec 11 sec

Jose will run at most 32 miles this week. So far, he has run 18 miles. What are the possible numbers of additional miles he will run? Use t for the number of additional miles he will run. Write your answer as an inequality solved for t.

Suppose you want to purchase a house. Your take-home pay is $2630 per month, and you wish to stay within the recommended guidelines for mortgage amounts by only spending 1/4 of your take-home pay on a house payment. You have $15,300 saved for a down payment and you can get an APR from your bank of 3.7 %, compounded monthly. What is the total cost of a house you could afford with a 30-year mortgage? Round your answer to the nearest cent, if necessary.

If you leave a 100°C pot of tea at room temperature (25°C) and an identical pot in the refrigerator (5°C), with k=0.02, the tea in the refrigerator reaches a drinkable temperature (70°C) more than minutes before the tea at room temperature. True False

Suppose that $15,000 is deposited for seven years at 5% APR. Calculate the interest earned if interest is compounded monthly. Round your answer to the nearest cent.

In the mathematical system of clock 12 arithmetic, under the operation of addition the set of elements is {1,12}. {12}. {1,2,3,4,5,6,7,8,9,10,11,12}. {0,1,2,3,4,5,6,7,8,9,10,11}.

The formula v = √2.6r models the maximum safe 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 on a highway as 670 feet. What is the maximum safe speed? For this problem, round your answer DOWN to the nearest whole number. (Think: Why is this type of rounding appropriate for this scenario?) max safe speed=

Joshua is going to invest $680 and leave it in an account for 19 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Joshua to end up with $1,680?

Two cell phone plans offer differing text packages. The two plans are outlined below: Plan A: $6.00 per month charge along with a charge of $0.05 per text. Plan B: No per month charge, but a charge of $0.20 per text. Is there a certain number of texts, when the two plans cost the same amount? Determine your answer by setting up a system of equations that model the two plans.

Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value. At a boating and sports store, the cost of renting a personal watercraft is $47.70 per half hour, which includes a 6% sales tax. Determine the cost of a half hour rental before tax. The equation is The cost of a half hour rental is $45 per half hour. (Type an equation using x as the variable.)

Jen collects toy sports cars. She has 784 red cars and 224 black cars. She wants to line up the cars in groups so that each group has the same number of cars and contains only red cars or only black cars. What is the largest number of cars that she can have in a group? The largest number of cars that Jen can have in a group is. (Simplify your answer. Type an integer.)

A publishing company sold 26,265,591 books last year. Round the number of books sold to the nearest ten million. A. 30,000,000 B. 26,000,000 C. 20,000,000 D. 26,270,000

Give the associative property of addition and illustrate the property with an example. Choose the correct answer below. A. For any elements a and b, a+b=b+a. An example of this is 4+7=7+4. B. For any element a, a +(-a)= -a+a=0. An example of this is 2+(-2)=-2+2=0. C. For any element a, a +0=0+a=a. An example of this is 8+0=0+8=8. D. For any elements a, b, and c, (a+b)+c= a + (b+c). An example of this is (3+2)+6=3+(2+6).

A rectangular kitchen has an area of 160 square feet. The length is 12 feet more than the width. a. Write an equation that represents the area of the kitchen. b. Find the dimensions of the kitchen by completing the square.

Calculate the monthly payment needed to pay off a $200,000 loan at 4% yearly interest over a 20 year period. Recall that r is the monthly rate. Show your work and carefully evaluate the above formula for m.

The population is decreasing at a rate of 4 % per year. If the population is 28,000 today, what will the population be in 12 years? Round your answer to the nearest whole number, if necessary.

The HMS Sasquatch leaves port on a bearing of N29°E and travels for 7 miles. It then changes course and follows a heading of S31°E for 4 miles. How far is it from port? Round your answer to the nearest hundredth of a mile. What is its bearing to port? Round your angle to the nearest degree. Distance = miles Bearing with angle rounded to the nearest degree is ?

Given the vector u equal to 5 (cos 255°, sin 255°) and vector v equal to 7 (cos 150°, sin 150°), find the sum u + v and write your answer in magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree, 0° ≤0 < 360°.

Brenda cuts her grass every 10 days and trims her shrubs every 24 days. If Brenda cut her grass and trimmed her shrubs on June 1, how many days will it be before she cuts her grass and trims her shrubs on the same day again? It will be days before Brenda cuts her grass and trims her shrubs on the same day again.

The sales in thousands of a new type of product are given by S(t)=180-50 e -0.3t, where t represents time in years. Find the rate of change of sales at the time when t=3. Round to the nearest tenth. A. 6.1 thousand per year B.-36.9 thousand per year C.-6.1 thousand per year D. 36.9 thousand per year

Juan is going to invest $1,700 and leave it in an account for 14 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Juan to end up with $3,700?

Alexa invested $54,000 in an account paying an interest rate of 4% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $106,200?

At the beginning of an experiment, a scientist has 180 grams of radioactive goo. After 255 minutes, her sample has decayed to 5.625 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t)= How many grams of goo will remain after 17 minutes?

Josiah invested $96,000 in an account paying an interest rate of 3.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $153,400?

Bella is going to invest $94,000 and leave it in an account for 9 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Bella to end up with $156,000?

Police use the formula: v = √20L to estimate the speed of a car, v, in miles per hour, based on the length, L, in feet, of its skid marks when suddenly braking on a dry, asphalt road. At the scene of an accident, a police officer measures a car's skid marks to be 208 feet long. Approximately how fast was the car traveling? Round your answer to the nearest tenth (one decimal place) of a unit. Answer: The car was traveling at approximately miles per hour.

Find the volume of a hemisphere with a great circle circumference of 37.7 centimeters. r= V =

Anne and Nancy use a metal alloy that is 18. 141% copper to make jewelry. How many ounces of an alloy that is 14% copper must be mixed with an alloy that is 25%, copper to form 85 ounces of the desired alloy? Round to the nearest whole number. A. 53 ounces B. 37 ounces C. 55 ounces D. 32 ounces