Basic Math Questions and Answers

Victoria buys a two-gallon bottle of juice for $48.64. What is the unit rate of the cost of the juice per fluid ounce? 1 gallon=4 quarts 1 quart=2 pints 1 pint = 2 cups 1 cup = 8 fluid ounces Before you try that problem, answer the question below. How many fluid ounces of juice did Victoria buy?

The approximate average distances from the sun to Saturn and Venus are listed below: Saturn: 1.43 × 10⁹ kilometers Venus: 1.08 x 108 kilometers How many times farther from the sun is Saturn? Write your answer in standard notation, rounding to the nearest tenth.

A single die is rolled one time. Find the probability of rolling an even number or a number less than 5. 1 5/6 2/3 1/2

Letf(x) = 3x4 – x³ - 24x² + 32x - 8. 1. Using the Rational Zeros Theorem, list the possible rational zeros of f(x). 2. Find all (real/complex) zeros of f(x). You must use synthetic division to find the first two zeros. Any other method will receive no credit. Show all of your work. 3. Determine the X-intercept(s) of f(x). If there are no x-intercepts, write "NONE EXIST."

Solve the problem. 1) A city is growing at the rate of 0.9% annually. If there were 3,619,000 residents in the city in 1994, find how many (to the nearest ten-thousand) are living in that city in 2000. Use y = 3,619,000(2.7)^0.009t

Verify that the equation is an identity. csc θ/ cot θ= sec θ

The cost, in dollars, for a video game developer to code g games can be represented by the function v(g) = 500+ 750g. The number of games produced in w weeks is given by the function g(w) = 3w. Which of the following expressions represents the total cost of games after w weeks? 500 + 750g + 3w 1500 + 2250g 500+2250w 1500w +2250wg

Maria completed 3/4 of her workday. Create a model that represents what percent of the workday Maria has worked.

A real estate sales agent receives a salary of $250 per week plus a commission of 2% of total sales. If the real estate agent sells a house worth $300,000, what would their total income be for the week?

Find the second derivative of the function. f(x) = x sin(x)

Use the counting principle to obtain the answer. A restaurant offered salads with 4 types of dressings and 3 different toppings. How many different types of salads could be offered? A. 12 B. 16 C. 7 D. 9

Let A = {Dirk, Johan, Frans, Sarie}, B = {Frans, Sarie, Tina, Klaas, Henrika}, C = {Hans, Frans}. Does n(CUB) = n(C) + n(B) - n(Cn B)? Yes No

An airplane can travel 365 mph in still air. If it travels 2716 miles with the wind in the same length of time it travels 2394 miles against the wind, what is the speed of the wind?

Parents wish to have $120,000 available for a child's education. If the child is now 4 years old, how much money must be set aside at 3% compounded semiannually to meet their financial goal when the child is 18? Click the icon to view some finance formulas. The amount that should be set aside is $ (Round up to the nearest dollar.)

The denominator of a fraction is five more than three times the numerator. If both numerator and denominator are decreased by five, the simplified result is 1/8. Find the original fraction. (Do NOT simplify.)

Evaluate x² - 4x - 5 /x + 1 when x = -4

The formula for the surface area S of a cone is S = r² + rs, wherer is the radius and s is the slant height. Solve the formula for s. Justify each step. Then find the slant height of the cone when the surface area is 113 square feet and the radius is 4 feet. Approximate to the nearest tenth.

a. Graph the function f(x)= ex on the window [-5,5] by [-10,30]. b. Find f(1), f(-4), and f(4), rounded to three decimal places. c. What is the horizontal asymptote of the graph? d. What is the y-intercept?

The use of calculators in math classrooms has been on the rise over the past 15 years. Is this a good tool that supports students in their learning? Or is it causing too much harm by allowing students to go through life without having mastered basic skills like adding, subtracting, multiplying, etc.? Choose a position and explain why.

A population of rabbits doubles every year and there were 1 million rabbits at the start of 2008. a. How many million rabbits are there in 2013? Hint: How many rabbits are there in 2009? In 2010? b. In what year will there be 10 million rabbits? Hint: Use logs! In the year

The denominator of a fraction is four more than the numerator. If both numerator and denominator are decreased by four, the simplified result is 5/7. Find the original fraction. (Do NOT simplify.)

The odds in favor of Trudy beating her friend in a round of golf are 1:6. Find the probability that Trudy will lose.

Out of a random sample of 65 freshmen at State University, 31 students have declared a major. Use the "plus-four" method to find a 96% confidence interval for the true proportion of freshmen at State University who have declared a major.

Simplify by combining like terms. 75/7 b + 2 2/3 b

A construction worker needs to pour a rectangular slab 20 ft long, 28 ft wide, and 9 in. thick. How many cubic yards of concrete does the worker need? (Assume that the construction worker cannot buy a fraction of a cubic yard of concrete.) The worker needs cubic yards of concrete. (Type a whole number, rounded up to the nearest full cubic yard of concrete.)

A tool rental store charges a flat fee of $6.50 to rent a chain saw, and $3.75 for each day, including the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days.

A scientist uses a submarine to study ocean life. She begins at sea level, which is an elevation of o feet. She descends 48.7 feet. She then rises 38.3 feet. Next, she travels down a second time, 83.6 feet. How many feet must she now ascend to get back to sea level?

According to the Original Tipping Page, www.tipping.org, it is appropriate to tip waiters and waitresses 15%-20% of the pre-tax restaurant bill. The Leeseburgs' dinner costs $49.00 before tax, and the tax rate is 6%. a) What is the tax on the Leeseburgs' dinner? b) If the Leeseburgs decide to tip 20% of the pre-tax bill, how much is the tip? c) What is the total cost of the dinner including the tax and tip?

Complete the tables, and graph the corresponding ordered pairs. Draw the line defined by the points to represent all solutions to the equation. x-y=-3

Malik uses an app on his phone to track how far he rides his bike. Yesterday, he biked a new trail in a total of 57.5 minutes, including a 2.5-minute water break. The app notified Malik that he rode 10 miles. What was Malik's average pace while biking? Write your answer as a whole number or a decimal. minutes per mile

Does the function y(t) = 4e-6t satisfy the following initial value problem? y' (t)-6y(t) = 0, y(0) = 4 Choose the correct answer below. No, because the initial condition does not satisfy the original function, so the original function cannot satisfy the initial value problem. Yes, because the initial condition satisfies the original function, so the original function must satisfy the initial value problem. No, because when y and y' are substituted into the equation, the result is not a true statement. Yes, because when y and y' are substituted into the equation, the result is a true statement.

Audrey Graco plans to conduct book signings in several cities to promote her new novel. She wishes to visit Knoxville, Chattanooga, Chapel Hill, Charlotte, Raleigh, and Richmond. How many different ways can she visit each of these cities and return to her starting point in Wilmington? A. 120 B. 720 C. 29 D. 30

A principal of $4900 is invested at 3.25% interest, compounded annually. How much will the investment be worth after 8 years? Use the calculator provided and round your answer to the nearest dollar.

MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $983 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin $13,400. Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car.

2. Kirsten has $500 in her savings account. She is able to save $50 each month. The function S(m) = 50m + 500 represents the amount of money in her savings account S as a function of time in months m. 2.a. Find S(2). Explain what this represents in this problem.

Calculate the surface area of each pyramid with the following values. (P = perimeter, b = one side of the base, s=side, h-height). Number of sides is given in each problem. The first two have hints to let you know what the shape of the base is P = 12 ft, s = 4 ft, b = 4 ft, h=2 ft, 3 sides (base is a triangle)

Suppose a life insurance policy costs $20 for the first unit of coverage and then $5 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost? $70 $30 $50 $65

A large rectangle has a total area of 102 square feet, and is divided into two portions. If one portion of the rectangle has an area of 36 square feet, what is the area of the other portion of the rectangle, in square feet?

Ramon's calculator screen is not working correctly. It displays the correct digits, but it does not display any decimal points. For each of the following examples, the digits from Ramon's calculator are shown below the expression. Use estimation to determine where (if anywhere) to place a decimal point in each result to end up with a reasonable answer. a. (2.95)(414) b. 7.16.5.38-10.6748 c. 9.21² +19.08

An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tile has length 1/3 in. and width 1/4 in. The actual tiles have length 1/4 ft and width 3/16ft What is the ratio of the length of a tile in the model to the length of an actual tile? What is the ratio of the area of a tile in the model to the area of an actual tile? Use pencil and paper. Describe two ways to find each ratio. The ratio of the length of a tile in the model to the length of an actual tile is (Type the ratio as a simplified fraction.)

A book publisher claims that its mean book length is 250 pages with a standard deviation of 70 pages. What is the probability that for a sample of 45 randomly selected books, the mean length of a book is less than 230 pages?

Consider the function below. f(x) = -5x² + 30x + 3

For the following initial value problem, compute the first two approximations u₁ and u₂ given by Euler's method using the given time step. y' (t)=t+y. y(0) = 3; At=0.3

For the function f(x) = 1/10x,construct and simplify the difference quotient f(x+h)-f(x) / h

A water park has pools, slides, and rides that, in total, make use of 4.1 × 106 gallons of water. They plan to add a ride that would make use of an additional 91, 000 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.

Jon recently drove to visit his parents who live 270 miles away. On his way there his average speed was 24 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 12 hours driving, find the two rates.

Each day, Caleb feeds his horse 2.25 lb of oats. He also feeds it hay. The weight of hay is 6.5 times the weight of oats. What is the combined weight of oats and hay Caleb feeds his horse in one week? A 61.250 lb B 102.375 lb C 118.125 lb D 259.875 lb Naomi chose C as the correct answer. How might she have gotten that answer?

Researchers in Antarctica discovered a warm sea current under a glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate of 0.06 m per day. Which function can be used to find the thickness of the ice shelf in meters x days since the discovery? t(x)= 450 -0.06x t(x)= -0.06(x+450) t(x)= 450+ 0.06x t(x)= 0.06 (x+450)

Use f(x) and g(x) to find each composition. Identify its domain. (Use a calculator if necessary to find the domain.) (a) (fog)(x) (b) (gof)(x) (c) (fof)(x) f(x)=x². g(x)=√1-x (a) (fog)(x) = 1-x (Simplify your answer.) The domain of (fog)(x) is (-∞0.1). (Type your answer in interval notation.) (b) (gof)(x) = (Simplify your answer.)

You earn $11 per hour working at a grocery store during the summer. The function p(x) = 11x represents the amount you earn for working x hours. a. You work 18 hours. How much do you earn? b. How many hours do you have to work to earn $275?