Basic Math Questions and Answers

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

On the planet of Endor, the Ewoks are building a trebuchet to attack the Storm Troopers. The test their new weapon and decided it can launch 100 kgs of rocks 50 meters, with a margin of error of 7 meters. What is the range of the rocks they can throw?

Dylah is going to invest in an account paying an interest rate of 4.1% compounded continuously. How much would Dylan need to invest, to the nearest cent, for the value of the account to reach $19,000 in 7 years?

A driver filled the gas tank and noted that the odometer read 57,491.9. After the next filling, the odometer read 57,838.4. It took 17.5 gal to fill the tank. How many miles per gallon did the driver get? The driver got mpg. (Type a whole number or a decimal.)

Determine all positive number replacements (less than the modulus) for the question mark that make the statement true. 5 ? (mod 9) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The positive number replacement(s) (less than the modulus) for the question mark is(are) (Use a comma to separate answers as needed.) B. There are no positive number replacements (less than the modulus) for the question mark that make the statement true.

A publisher has fixed costs of $74,968 on a book for development, editing, and advertising. It costs the publisher $4 per copy at the printer. The publisher charges $30 per copy. Write the linear profit function that represents the profit, P(x), for the number of books sold. A. P(x)=-26x + 74,968 B. P(x) = 26x+74,968 C. P(x) = 34x+74,968 D. P(x) = 26x-74,968 E. P(x) = 34x-74,968

A family wants to purchase a house that costs $190,000. They plan to take out a $140,000 mortgage on the house and put $50,000 as a down payment. The bank informs them that with a 15-year mortgage their monthly payment would be $723.49 and with a 30-year mortgage their monthly payment would be $520.82. Determine the amount they would save on the cost of the house if they selected the 15-year mortgage rather than the 30-year mortgage. How much would they save if they selected the 15-year mortgage?

Suppose that $1600 is invested at an interest rate of 2.5% per year, compounded continuously. After how many years will the initial investment be doubled? Do not round any intermediate computations, and round your answer to the nearest hundredth.

A lumber yard has fixed costs of $6,478.7 a day and variable costs of $1 per board-foot produced. The company gets $2.7 per board-foot sold. How many board-feet must be produced daily to reach the break-even point? A. 1,751 board-feet B. 3,811 board-feet C. 2,540 board-feet D. 6,478 board-feet CXXXP

Give an example to show that the commutative property does not hold for the set of integers under the operation of division. Select each of the following that shows that the commutative property does not hold for the set of integers under the operation of division. A. 4+2#2÷4 B. 9+(6+2) # (9÷6)÷(9÷2) C. (10÷5) ÷2# (5÷10) ÷2 D. (18÷6)÷3# 18÷(6÷3)

The difference in frequency between the first and the fifth harmonic of a standing wave on a taut string is f5 - f1 = 50 Hz. The speed of the standing wave is fixed and is equal to 10 m/s. Determine the difference in wavelength between these modes. A5-A1=-0.64 m A5-A1 -1.60 m A5-A1 = 5m A5-A1 = -0.80 m A5-A1 = 0.20 m

Which of the following functions are parallel? I. 2x+4y=9 II. 5x-3y = 10 III. x + 7y=5 IV. 2x+9=-4y O I and IV OI and III OII and IV

Evaluate the following expression without using a calculator. Simplify your answer as much as possible, and enter your answer as a fraction. (27/64)* -1/3

The volume of a rectangular pyramid is 60 cubic feet. The width of the base is then scaled by a factor of 3, the length of the base is scaled by a factor of 2, and the height of the pyramid is scaled such that the resulting pyramid has the same volume as the original pyramid. Find the scale factor used for the height. Leave final answer in fraction form.

The area of a regular pentagon is 50 cm². What is the area of a regular pentagon with sides 6 times the length of the smaller pentagon?

Select all the correct answers. Which two excerpts are written in a third-person omniscient point of view? Long, long ago there lived an old man and his wife who supported themselves by cultivating a small plot of land. (Yei Theodora Ozaki, "The Story of the Old Man Who Made Withered Trees to Flower") Every morning I lay on the floor in the front parlour watching her door. The blind was pulled down to within an inch of the sash so that I could not be seen. (James Joyce, The Dubliners) You may believe me who adore them, who have long given myself to them without reserve. (Anatole France, "The Adventures of the Soul") "The lamp! Put out the flame and bring me the lamp!" Surprised and suspicious, for why should the stranger, out of all such a treasure want only an old lamp, Aladdin wondered. (Brothers Grimm, "The Adventures of Aladdin") He was a man of exuberant fancy, and, withal, of an authority so irresistible that, at his will, he turned his varied fancies into facts. (Frank R. Stockton, "The Lady, or the Tiger")

(a) What positively impacts your persistence, confidence, and/or enjoyment in any class? Why? (b) What can be improved to increase the positive impact of any STEM class to your persistence, confidence, and/or enjoyment of the class? How would one operationalize your idea(s)?

Find the slope of the line X+ 9 = 14. zero 14 undefined

A particle moves along a line with a velocity v(t) = -4t + 2, measured in meters per second. Find the total distance the particle travels from t = 0 seconds to t = 2 seconds. Enter an exact answer.

What are the transformations performed in the function y = |x +41-8? 8 units to the right and 4 units up. 4 units to the left and 8 units down. 4 units to the right and 8 units down.

If a system of two equations in two variables is solved graphically, a unique solution exists when: The lines are parallel Both equations yield the same line The lines intersect at two distinct points The lines intersect at one point

What is the name of the transformation of the function f(x) = - tan(x)? Reflection about the x-axis Reflection about the y-axis Horizontal shift

Suppose in order for a bill to pass in Congress, 50% of voters must be in favor of it. In a random sample of 200 voters, 98 said that they were in favor of a new bill. State the p-value assuming the alternative hypothesis is Ha #.50 (Round to the nearest hundredth)

Chase invested $39,000 in an account paying an interest rate of 3.2% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $66,100?

Emma is going to invest in an account paying an interest rate of 2.6% compounded quarterly. How much would Emma need to invest, to the nearest cent, for the value of the account to reach $66,000 in 7 years?

If y is directly proportional to the square root of x and y = 98 when x = 144, find y if x = 20736. (Round off your answer to the nearest hundredth.)

Joseph invested $16,000 in an account paying an interest rate of 5.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 14 years?

Jamal is watching the wood in a fire pit burn. Jamal started with 35 pounds of wood, and 30% of the wood is burning every hour. Which equation models the amount of wood remaining after t hours? A = 35(0.7)t A = 35 (0.3)t 35 = P(1 -0.3)t A=35t (1-0.3)

The engine in a car is started at time t = 0 and it consumes gasoline at the rate of r(t) = 8 + t - 2t3, measured in gallons per hour. How much gasoline is consumed in the first 2 hours? Provide your answer below:

Brittany's annual salary is $73,800. She pays 23% in taxes. After taxes, she pays 4% into retirement. How much does Brittany pay into retirement? What is Brittany's annual salary after taxes and retirement?

A YouTube star knows that 56% of her viewers are under the age of 24. She wants to expand to other age groups, so she updates her content to be more universal. Then, she collects a simple random survey of her her followers and finds that 36 of 67 of her viewers are still under the age of 24. Using a 5% significance level, can she conclude that updating her content expanded her viewers' age group? Yes, because .7 < .05 Yes, because .53 > .56 No, because.53 <.56 No, because .7 > .05

Cooper invested $1,100 in an account paying an interest rate of 3.8% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 10 years?

Ariana invested $7,500 in an account paying an interest rate of 2.9% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 14 years?

Determine whether the following statement is true or false. Modify each false statement to make it a true statement. 63 is a divisor of 9.

Determine whether the following statement is true or false. Modify each false statement to make it a true statement. 16 is divisible by 8.

Landon is going to invest in an account paying an interest rate of 4.3% compounded continuously. How much would Landon need to invest, to the nearest hundred dollars, for the value of the account to reach $11,300 in 14 years?

Victoria is going to invest in an account paying an interest rate of 1.5% compounded quarterly. How much would Victoria need to invest, to the nearest hundred dollars, for the value of the account to reach $3,300 in 13 years?

Determine whether the statement is true or false. Modify each false statement to make it a true statement. Every whole number is an integer.

Fill in the blank with an appropriate word, phrase, or symbol. With the quotient rule for exponents, the expression x^8/x^5 can be simplified to ___.

A landscaper is designing a display of flowers for an area in a public park. The flower seeds will be planted at points that lie on a circle that has a diameter of 8 feet. The point where any seed is planted must be at least 2 feet away from the seeds on either side of it. Part A What is the maximum number of flower seeds that can be planted using the design? Part B After planting the flower seeds, the landscaper has 20 seeds left over. The landscaper wants to plant all of the remaining seeds in another circle so that the seeds are 2 feet apart. To the nearest tenth of a foot, what is the diameter of the smallest circle that the landscaper can use to plant all of the remaining seeds?

Determine whether the number used is a cardinal number or an ordinal number. Jim B. Brown has directed 8 movies. Choose the correct answer below. A. In this context, the number 8 is used as an ordinal number because it describes the relative position that an element occupies. B. In this context, the number 8 is used as a cardinal number because it describes the relative position that an element occupies. C. In this context, the number 8 is used as a cardinal number because it answers the question "How many movies has Jim B. Brown directed?" D. In this context, the number 8 is used as an ordinal number because it answers the question "How many movies has Jim B: Brown directed?"

Simplify. Enter the result as a single logarithm with a coefficient of 1. log9(7x^5)+log9(6x^4)

Suppose the binomial expansion of (2x−3y)^n includes the term -15120x^4y^3 The x^4y^3 term in the expansion will be The x^5y^3 term in the expansion will be