Basic Math Questions and Answers

A rectangular painting measures 14 inches by 16 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 92 inches. Determine the width of the frame. The width of the frame is inch(es).

Which equation represents the line that passes through the points (-1,-2) and (3,10)? y = 3x + 1 y = 3x - 1 y=4x-2 y = 4x+2

Compute the total and annual returns on the described investment. Four years after buying 100 shares of XYZ stock for $70 per share, you sell the stock for $10,900. The total return is 55.7 %. (Do not round until the final answer. Then round to one decimal place as needed.) The annual return is %. (Do not round until the final answer. Then round to one decimal place as needed.)

A water tank that holds 60 L of water can be emptied in 24 min. How long will it take to empty a water tank that holds 280 L of water? A. 82 min B. 96 min C. 112 min D. 128 min

Surveyors counted the number of trees is a popular city park. There were 62 spruce trees, 44 firs, 12 oaks, and 2 maples. What is the theoretical probability that a randomly selected tree is an oak? (Write your answers as a reduced fraction using the / symbol as your fraction bar.)

What's the circumference of a circle with a radius of 5 inches? Use 3.14 for I.

If the rate of inflation is 2.8% per year, the future price p (t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. p(t)=3000 (1.028) Find the price of the item 6 years from today and 10 years from today. Round your answers to the nearest dollar as necessary. Price 6 years from today: Price 10 years from today: $

In how many ways can the expression a5b5c5 be rewritten as a product without exponents? The number of ways a5b5c5 can be written without exponents is ___

Consider the Quadratic function f(x) = x²-3x - 40. Its vertex is Its largest x-intercept is x = Its y-intercept is y =

The original 24 medige length x of a cube decreases at the rate of 3 m/min. a. When x=3 m, at what rate does the cube's surface area change? b. When x=3m, at what rate does the cube's volume change? a. Whenx=3m, the surface area is changing at a rate of (Type an integer or a decimal)

Raise the number to the indicated power and express in trigonometric notation. [3(cos 27+ i sin 27)] 4 81(4cos 27+ i 4sin 2π) 03(cos/271 + 1 sin = 17) 81(cos 87 + i sin 87) 3(cos 27+ i sin 27)

Brendon Walsh wants to borrow $30,000 from the bank. The interest rate is 6% and the term is for 5 years. What is the yearly payment amount? $1,800 $7800 $18,000 $3600

What is the simplest form of ∛24 ? 8 None of the choices are correct. 3∛2 2∛3 12

Factor the following, where n is a positive integer. 6²ⁿ - 2bⁿ +1

Shannon is paid a monthly salary of $1025.02. The regular workweek is 35 hours. (a) What is Shannon's hourly rate of pay? (b) What is Shannon's gross pay if she worked 7(3/4) hours overtime during the month at time- and-a-half regular pay? A) The hourly rate of pay is $------ (b) The gross pay is $----

Subtract the following polynomials. Simplify your answer. (2x² + 2x + 3) - (-4+ 2x – 2x² – 3x³) Provide your answer below:

What is the simplest form of 3√2 + 5√2 ? (Do NOT approximate your answer) 30 16 8√2 None of the choices are correct. 30√2

A piece of wire 19 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Round your answers to two decimal places.) (a) How much wire (in meters) should be used for the square in order to maximize the total area? (b) How much wire (in meters) should be used for the square in order to minimize the total area?

Fred and Wilma purchase a new home for $180,000. The value of the home increases by 4% every 2 years. Determine the value of the home after 23 years. After 23 years, the home is worth $ Round your answer to the nearest cent.

Match the volume of the pyramid to the volume of the prism with the same height and base area.

On average the number of drum sets sold in Texas each year is equivalent to five times the average number sold yearly in Montana. If, on average, there are 46,625 drum sets sold each year in Texas, how many are sold in Montana?

The government conducted a study and collected the given data. Use the data to answer the following questions. Speed (mph) 45 55 65 75 Fuel (mpg) 43 45 38 32 Using the quadratic regression model between speed and fuel, find the residual for the person who drove 65 mph? a. 1.5 b. 0.5 c. 43.5 d. -1.5

Given the equation, y = 3(0.87)^x, where y is the amount of money in thousands in x years, describe what is happening? o The amount of money is decreasing at a rate of 87 per year o The amount of money is decreasing at a rate of 13% per year o The amount of money is decreasing at a rate of 87% per year o The amount of money is decreasing at a rate of 13 per year

Suppose you have the following functions. f(x) = √(x+2) +1 g(x) = x³ – 3x + 1 Which of the following is an approximate solution for f(x) = g(x)? a. x = -1.821, x = 0.347, x = 1.532 b. x = -1.618, x = -0.445, x = 2 c. x = 1.618, x = 2.247, x = 3 d. No Real Answer

Given the equation, y = 3(0.87)ˣ , where y is the amount of money in thousands in x years, describe what is happening? (1) The amount of money is decreasing at a rate of 87 per year (2) The amount of money is decreasing at a rate of 13% per year (3) The amount of money is decreasing at a rate of 13 per year (4) The amount of money is decreasing at a rate of 87% per year

Solve for x: 4+ 5log3 (x + 6) = 8 Round your answer to 3 decimal places. -3.592 no solution -3.345 8.408

The 80% confidence interval for the proportion of students who drink coffee daily is (0.27, 0.50). What point estimate was used to construct the confidence interval? a)0.115 b)0.400 c)0.385 d)0.770

3) A fan of trigonometry is building a right triangular pool in his backyard. The hypotenuse of the right triangle is 30 feet long and the height of the right triangle is 24 feet long. If the fan of trigonometry wants to purchase a pool cover, how many square feet of material should he purchase?

At the beginning of an experiment, a scientist has 244 grams of radioactive goo. After 105 minutes, her sample has decayed to 7.625 grams. What is the half-life of the goo in minutes? Find a formula for G(t)G(t), the amount of goo remaining at time tt. G(t)=G(t)= How many grams of goo will remain after 2 minutes? You may enter the exact value or round to 2 decimal places.

In many cases the Law of Sines works perfectly well and returns the correct missing values in a non-right triangle. However, in some cases the Law of Sines returns two possible measurements. Statement of the Law of Sines. Helpful Hint: Draw a unit circle and think about the range of arcsin. Also, recall that the trigonometric functions in iMathAS use radians as the default, so you may need to change units. Consider the diagram below, and assume that mZB= 61, AB= 4.25 cm, and AC = 3.9 cm. 3.9 cm a. Using the Law of Sines, determine the value of mLC. You should notice that there are actually neo possible values-list both of them (separated by a comma). b. If we assume the diagram is to scale, which value of mLC makes more sense? Enter the appropriate value. mLC= c. Using your answer to part (b), determine the length of BC. BC= cm

An asymptote is a line that the the graph of a function will get closer and closer to, but never reach. a) True b) False

Graph the equation. Let x= -3, -2, -1, 0, 1, 2, and 3. y=2x+2 x y -3

A bacterial population doubles every 4 months. If there were originally 2000 cells in the sample, how many will there be in 2 months? a) 512 000 b) 2828 c) 2519 d) 8000

Graph the equation y = -5|x|. Let x = -3, -2, 1, 0, 1, 2, and 3. Find the following y -values. Then choose the correct graph of the equation to the right. X y -3 -15 -2

Use the critical value method to solve the rational inequality. Write the solution set in interval notation. x-9/x+8 ≥5

Solve the equation. Check your solution(s). 3x³/4 - 14 = 67 a)x = 9x = 3(81) ³/4 b)x = 81 c)no real solution d)x = ±81

In a village there is a farmer, carpenter, and a tailor, who provide the three essential services: food, shelter, and clothing. Suppose the farmer himself consumes 40% of the food he produces, and gives 40% to the carpenter, and 20% to the tailor. Thirty percent of the carpenter's production is consumed by himself, 40% by the farmer, and 30% by the carpenter. Fifty percent of the tailor's production is used by himself, 30% by the farmer, and 20% by the tailor. What 'prices' should the providers get if the equilibrium condition of a closed economy is to be satisfied, and if the lowest-price is $720?

If Solution A has a pH of 5.0 and Solution B has a pH of 3.0, which statement below is true? a) Solution A is twice as acidic b) Solution B is 100 times more acidic c) Solution B is twice as acidic d) Solution A is 100 times more acidic

Solve the equation. Check your solution(s). √6x+1=x-9 a) X = 4 b) x = 4 and x = 20 c) x = 20 d) x = -4 and x = -20

Solve the equation. 2/3x+1/5x-1/4=4/5x The solution is x = (Type an integer or a simplified fraction.)

We are now going to work with Conditional Probability with Percentages. We will use the information from question 1. This time you will take the number of men divided by the total group. Next we will take that percentage of men who prefer chocolate chip cookies which is 5.67% and divide it by the percentage of men. Show your work.

Simplify the expression. 4³√2+³√2 a 10 b 5³√2 c 5⁶√2 d 5³√4

Chase had $100 in his wallet. He spent $5.56 on lunch one day and $1.75 on coffee a few mornings a week. Write and solve an inequality to determine how many mornings he got coffee if he now has at most $85 in his wallet.

A man bought a length of rope at the hardware store. He used one-third of it to make a bow painter (a rope located at the front of the canoe) for his canoe and then used one-fourth of the remaining piece to tie up a roll of carpet. He now has 24 feet of rope left. What was the length of the rope he had originally purchased? Since it is often helpful to visualize a problem, obtain your answer pictorially by adding additional marks and labels to the following drawing. He had originally purchased (Type an integer or a simplified fraction.) feet of rope.

At a track-and-field meet, the winner of the pole vault event cleared a height of 3.25 meters. This was 0.1 meters more than the height cleared by the second-place pole- vaulter. The second-place height was 0.05 meters more than the third-place height. What height did the third-place pole-vaulter clear?

Samuel invested $28,000 in an account paying an interest rate of 5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 5 years?

Which property is demonstrated by the following equation? (12+8) + 11 = 12 + (8 +11) Select the correct answer below: Commutative Distributive Identity Inverse Associative

Valerie is deciding on her schedule for next semester. She must take each of the following classes: English 102, Music 101, History 102, and Math 120. If there are 15 sections of English 102, 10 sections of Music 101, 13 sections of History 102, and 13 sections of Math 120, how many different possible schedules are there for Valerie to choose from? Assume there are no time conflicts between the different classes.

How much material would be needed for the rungs of a ladder of 30 rungs, if the rungs taper uniformly from 20 inches to 30 inches? inches of material would be needed. (Simplify your answer.)

A particle moves in a straight line and has velocity given by v(t) = -6t² + 7t-2 m/s. Its initial displacement is s(0) = 4 m. Find its position function s(t). Provide your answer below: