Basic Math Questions and Answers

If refinishing your basement at a cost of $44,141 would add $19,260 to the resale value of your home, what percent of your cost is recouped? (Round to the nearest whole percent.)

A can of beans has surface area 381 cm². Its height is 18 cm. What is the radius of the circular top? (Hint: The surface area consists of the circular top and bottom and a rectangle that represents the side cut open vertically and unrolled.)

A company set aside a certain amount of money in the year 2000. The company spent exactly the same amount from that fund each year on perks for its employees. In 2004, there was still $649,000 left in the fund. In 2006, there was $609,000 left. Let z be the number of years since 2000, and let y be the amount of money left in the fund that year. Use a linear equation to model the amount of money left in the fund after so many years. a. The linear model's slope-intercept equation is b. In the year 2010, there was c. In the year

Daisy has one cucumber that is 3 inches long and another cucumber that is 5 inches long. She cuts the cucumbers into 3/8-inch-thick slices and adds them to a salad. How many 3/8-inch-thick slices does Daisy have? 1. Write division expressions to represent the first steps in the problem. 2. Solve. Then explain your answer.

Decide whether the ordered pair (-8, -2) is a solution of the equation. 7x-7y=0 is (-8,-2) a solution of 7x-7y=0? Select the correct choice below and fill in the answer box within your choice. (Simplify your answer. Type an integer or a simplified fraction.) Yes, because replacing x with -8 and y with -2 and simplifying on the left side results in No, because replacing x with - 8 and y with -2 and simplifying on the left side results in which equals the right side. which does not equal the right side.

Find all excluded values for the expression. That is, find all values of u for which the expression is undefined. If there is more than one value, separate them with commas.

Fill in the blanks below with the correct units. (a) Kala drank about 300 of juice with lunch. (b) The opening of the drinking straw was about 6 ? wide. (c) Alonzo saw an elephant at the zoo. The elephant's mass was about 4000 ?

Each of 8 students reported the number of movies they saw in the past year. This is what they reported: 10, 4, 17, 14, 17, 4, 10, 11 Find the median and mean number of movies that the students saw. If necessary, round your answers to the nearest tenth.

A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind. Find the speed of the wind.

For his phone service, Alonzo pays a monthly fee of $14, and he pays an additional $0.07 per minute of use. The least he has been charged in a month is $106.26. What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes, and solve your inequality for m.

Using the remainder theorem, which binomial divisor of f(x) results in a remainder of -90,916 for the function f(x)=x^5-4x³ +51x² 16? Select the correct answer below: (x-10) (x+10) (x-9) (x+9) (x-8) (x+8)

Keith has $500 in a savings account at the beginning of the summer. He wants to have more than $200 in the account by the end of the summer. He withdraws $25 each week for food, clothes, and movie tickets. Write an inequality that represents Keith's situation. Use w to represent how many weeks that Keith can withdraw money. How many weeks can Keith withdraw money from from his account? Write your answer in standard form.

You are in charge of buying office supplies for your business. Your workers use red and black pens. Red pens cost $5 per box and black pens cost $3 per box. You need at least 10 boxes of pens. You want no more than 7 boxes of black pens and no more than 6 boxes of red pens. You want to minimize the cost to your business. Which of the following is NOT a constraint in the situation?

A rectangular field is four times as long as it is wide. If the perimeter of the field is 440 yards, what are the field's dimensions? The width of the rectangular field is The length of the rectangular field is

A distribution of values is normal with a mean of 198.3 and a standard deviation of 22.3. Find P37, which is the score separating the bottom 37% from the top 63%. Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Jake's water bill is $25.40 per month plus $2.40 per ccf (hundred cubic feet) of water. What is the maximum number of ccf Jake can use if he wants his bill to be no more than $60.00? The maximum number of ccf's Jake can use is

Use synthetic division to divide 2x³ - 6x² - 5 by x - 1. Write your answer in the form g(x) + r(I) where g(x) is the quotient, r(a) is the remainder, and d(x) is the divisor.

Using synthetic division, what is the quotient and the reminder for (3x3 + 7x² - 8x +46) ÷ (x+4)? If the remainder is non-zero, express the remainder term as a fraction using the divisor as the denominator.

A ball is dropped from the top of a building that is known to be 784 feet high. The formula for finding the height of the ball at any time is h = 784 -16t², where fis measured in seconds. Step 2 of 3: How many seconds did it take for the ball to reach a height of 528 feet above the ground?

Compute each of the following. Enter your answer simplified, in interval notation. (-9, ∞) ∩ (-∞, 7) = (-9, ∞) ∪ (-∞, 7) =

The function s(t) describes the motion of a particle along a line. s(t)= t² 14t+ 22 (a) Find the velocity function v(t) of the particle at any time t≥ 0. (b) Identify the time interval(s) in which the particle is moving in a positive direction. (Enter your answer using interval notation.) (c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.) (d) Identify the time(s) at which the particle changes direction. (Enter your answers as a comma-separated list.)

A colony of bacteria is of size S(t) = 300e0.1t after t hours. Find the average size during the first 15 hours (that is, from time 0 to time 15). (Round your answer to the nearest whole number.)

Jim Goodman, an employee at Walgreens, earned $38,400, an increase of 16.5% over the previous year. What were Jim's earnings the previous year? (Round to the nearest cent.)

Web Consultants, Inc., pays Alice Rose an annual salary of $55,200. Today, Alice's boss informs her that she will receive a $5,600 raise. What percent of Alice's old salary is the $5,600 raise? (Round to nearest tenth percent.)

Staples pays George Nagovsky an annual salary of $30,000. Today, George's boss informs him that he will receive a $3,500 raise. What percent of George's old salary is the $3,500 raise? (Round to the nearest tenth percent.)

The body mass index, I, can be used to determine an individual's risk for heart disease. An index less than 25 indicates a low risk. The body mass index is given by the I= 700W/H² where W = weight, in pounds, and H= height, in inches. Jerome is 72 inches tall. What weights will keep his body mass index between 19 formula, or model, and 30? Jerome's body mass index will fall between 19 and 30 for the set of all weights such that<W< (Round to the nearest whole number as needed.)

A plane flies 435 miles with the wind and 375 miles against the wind in the same length of time. If the speed of the wind is 10 mph, find the speed of the plane in still air

A rental car company charges $80 per day to rent a car and $0.10 for every mile driven. Luke wants to rent a car, knowing that: He plans to drive 500 miles. He has at most $410 to spend. Write and solve an inequality which can be used to determine d, the number of days Luke can afford to rent while staying within his budget.

Which equation is equivalent to 2 1/4+2/4 = 2 3/4? 7/4 + 2/4 = 9/4 21/4 + 2/4 = 23/4 3/4 + 2/4 = 5/4 9/4 + 2/4 =11/4

For $9.79, Costco sells a box containing 52.5 ounces of Oreo cookies. Target sells a box of Oreos that is 19.1 ounces in size for $3.69. Which is the better purchase? Please explain how you arrived at your answer.

At a carnival, each game has a cost of x dollars to play. Which situation can be represented by this inequality? 8x>5x+6 The cost to play 8 games is less than the cost to play 5 games and a $6 snack. The cost to play 8 games is greater than the cost to play 6 games and a $5 snack. The cost to play 8 games is greater than the cost to play 5 games and a $6 snack. The cost to play 8 games is $6 greater than the cost to play 5 games.

Solve the inequality 5x-4<-8x-69. Write your answer as an inequality and in interval notation, then graph the solution set on the number line.

Out of 4,500 colleges surveyed, 40% reported that SAT scores were not used as a high consideration in viewing their applications. How many schools view the SAT as important in screening applicants?

The following equation is given. Complete parts (a)-(c). x³-3x²-25x+75=0 a. List all rational roots that are possible according to the Rational Zero Theorem. (Use a comma to separate answers as needed.) b. Use synthetic division to test several possible rational roots in order to identify one actual root. One rational root of the given equation is (Simplify your answer.) c. Use the root from part (b) and solve the equation. The solution set of x³-3x²-25x+75=0 is O. (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as neec

Pedro has scores of 92, 85, 68, and 73 after four tests. What score must he make on his fifth test to have an average of 78 or greater? The score that Pedro needs on his fifth test to get an average of at least 78 is (Round to the nearest integer as needed.)

Drag each step and justification to the correct location on the table. Each step and justification can be used more than once, but not all steps and justifications will be used. Order each step and justification that is needed to solve the equation below.

Graph the polynomial function f(x) = -2(x-3)²(x²-16) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = -2x for large values of [x]. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are 3,4,-4. The y-intercept is 288. (Simplify your answer. Type an integer or a fraction.) (c) Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The real zero(s) of f is/are 3,4,-4.

Given f(x)=3x+6, (a) Find f(x+h) and simplify. (b) Find f(x+h)-f(x)/h and simplify.

Determine the total amount and the interest paid on $3000 with interest compounded semiannually for 5 years at a) 1%. b) 2%. c) 4%. d) Is there a predictable outcome in either the amount or the interest when the rate is doubled?

In a recent year, person A and person B had the two top-grossing concert tours, together generating about $314 million in ticket sales. If person B took in $28 million less than person A, how much did each tour generate?

Sarah Yost took out a 48-month fixed installment loan of $17,000 to open a gift shop. She began making monthly payments of $423.05. Sarah's business does better than expected and instead of making her 12th payment, Sarah decides to repay her loan in full. How much interest will Sarah save (use the actuarial method)? $1926.35 $1872.84 $2205.29 $1907.97

An island has some portion submerged in water. Point A on the island is at -5/4 feet from the surface of the sea. Point B on the island is at -2/3 feet from the surface of the sea. Because -2/3 feet > -5/4 feet what is true about the distance of the two points from the surface of the sea? Point A is closer to the surface of the sea than point B. Point B is closer to the surface of the sea than point A. Both points are 1 11/12feet from the surface of the sea. Both points are 7/12feet from the surface of the sea.

Construct a Binomial probability distrubtion table using n= 5 and p = 0.22. Next, record the mean a standard deviation of the distribution below. Where necessary, round all numbers to four decimal place

Analyze the polynomial function f(x) = 2x (x² - 9) (x + 4) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = for large values of |x|.

Two ships leave a port at the same time. The first ship sails on a bearing of 39° at 18 knots (nautical miles per hour) and the second on a bearing of 129° at 12 knots. How far apart are they after 1.5 hours? (Neglect the curvature of the earth.) After 1.5 hours, the ships are approximately (Round to the nearest nautical mile as needed.) nautical miles apart.

Use the substitution method to solve the system -x+y=2 4x-3y=-8 Your answer is x= y=

Luggage Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65. a) Are the first flight leaving on time and the luggage making the connection independent events? Explain. b) What is the probability that her luggage arrives in Denver with her?

Which is an equation with a degree of 4, zeros located at (5, 0), (−8, 0) and (3, 0) and a y- intercept located at (0, -120)? Select the correct answer below: y = (x - 5)(x + 8)(x − 3)(x - 1) y = (x - 5)(x + 8)(x − 3)(x + 1) y = (x + 5)(x + 8)(x − 3)(x - 1) y = (x + 5)(x-8)(x+3)(x + 1)

Admission to a baseball game is $4.00 for general admission and $6.00 for reserved seats. The receipts were $6120.00 for 1348 paid admissions. How many of each ticket were sold? (Round to nearest integer if necessary.)

Multiply 9.5 x 1.3 First, write your factors as whole numbers to multiply: 95 13 Now write your final answer with your decimal: