Basic Math Questions and Answers

A pro basketball player has a vertical leap of 42 in. What is his hang time? (Use V=48T2, where V is distance and T is time.) His hang time is

Solve the inequality algebraically. x³-3x²-10x<0

Evaluate the expression P(12, 3), equivalently 12 P3 Your answer is:

According to police sources, a car with a certain protection system will be recovered 92% of the time. If 800 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered after being stolen?

Solve the equation. ex = e 5x +36

Find the 5th term in the expansion of (a + b)8 in simplest form. Answer:

Due to random variations in the operation of an automatic coffee machine, not every cup is filled with the same amount of coffee. Assume that the mean amount of coffee dispensed is 6 ounces and the standard deviation is 0.6 ounce. Use the 68-95-99.7 rule to complete the following. a. What percent of the cups should have at least 6 ounces of coffee? b. What percent of the cups should have less than 4.2 ounces of coffee? a. Approximately % of the cups should have at least 6 ounces. (Type an integer or a decimal.)

A professor has six different tasks to assign, one to each of her six teaching assistants. In how many different ways could she make the assignments?

The endpoints of AB are A(2, 1) and B(4, 2). What are the coordinates of the endpoints of A"B" after a rotation of 450° about the origin, followed by a rotation of 90° about A' ? A" () B" ()

Write the phrase as an expression. a number b squared An expression is Basic

Solve the following inequality. (x-2)(x - 5)(x-6) ≥ 0 The solution is .

Last year, a person wrote 142 checks. Let the random variable x represent the number of checks he wrote in one day, and assume that it has a Poisson distribution. What is the mean number of checks written per day? What is the standard deviation? What is the variance? The mean number of checks written per day is

Recently, about 70 metric tons of soil were removed from under a leaning tower, and the angle the tower made with the ground was increased by about 0.5°. Before that, a point near the top of the tower was 52.6 m from a point at the base (measured along the tower), and this top point was directly above a point on the ground 4.77 m from the same base point. See the given figure. How much did the point on the ground move toward the base point? The point on the ground moved m toward the base point. (Do not round until the final answer. Then round to two decimal places as needed.)

The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r. P = $5000.00, A = $5500.00, t = 2 years % (Round to the nearest tenth of a percent as needed.)

In tennis, a player must win at least 6 games to win a set. If g is the number of games the player won and s is the number of sets the player won, which of the following inequalities must be true? s≤ 6g s ≥ 6g 6s ≤9 6s≥g

The total snowfall in Smithville after a three-day snowstorm was 39.1 inches. The accumulated snow after the second day of the storm was 24.6 inches, two-thirds of which fell on the first day of the storm. How many inches of snow fell each day?

The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and t in seconds. Find the body's displacement and average velocity for the given time interval. s = 3t² + 3t+10, 0st≤2 A. 38 m, 19 m/sec B. 18 m, 9 m/sec C. 12 m, 15 m/sec D. 18 m, 18 m/sec

You measure 25 dogs' weights, and find they have a mean weight of 41 ounces. Assume the population standard deviation is 13 ounces. Based on this, construct a 90% confidence interval for the true population mean dog weight. Give your answers as decimals, to two places

Claire left a 15% tip for the waitress. If Claire's bill was $12.45, how much tip, to the nearest penny, did Claire leave the waitress? A $2.00 B $1.90 C.$1.87 D $1.86

Solve the inequality algebraically. X +8/X-5≤1 List the intervals and sign in each interval. Complete the following table. (Type your answers in interval notation. Use ascending order.)

A car is traveling at a speed of 81 kilometers per hour. What is the car's speed in kilometers per minute? How many kilometers will the car travel in 15 minutes? Do not round your answers. Speed: Distance traveled in 15 minutes: km

Solve for 8cos^20 + 7 = 11 and 0 ≤ 0 < 2π. Provide your answer below:

How many different ways could five distinct days of the week be chosen so that at least one of them begins with the letter T? The number of ways is (Simplify your answer.)

A family went to a baseball game. They parked the car in a parking lot which charged $10. The cost per ticket was $23. Write an equation for the total cost of going to the baseball game, where y is the total cost and x is the total number of people. If the family spent $194, how many people went to the game? Complete the equation: y = (Use integers or decimals for any numbers in the expression.) How many people went to the baseball game if the family spent $194?

Consider the following function. k(x) = -31x1 Step 2 of 2: Find two points on the graph of this function, other than the origin, that fit within the given [-10, 101 by 1-10, 101 gnd. Express each contrate as an integer or simplified fraction.

Consider the following quadratic function. Identify the vertex and axis of symmetry (2 points). Then, in your own words, describe the definition of the axis of symmetry (1 point). f(x) = -4x² - 28x

Suppose that the distribution of scores of 1,000 students who take a standardized intelligence test is a normal distribution. Also suppose that the distribution's mean is 450 and its standard deviation is 25. a) How many scores do we expect to fall between 400 and 500? b) How many scores do we expect to fall below 400? a) It is expected that score(s) fall between 400 and 500. (Round to the nearest whole number as needed.)

Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is -6. If the smaller number is subtracted from the larger number, the result is 8. Find the numbers List the two numbers. (Use a comma to separate answers.)

At a concession stand, seven hot dogs and two hamburgers cost $16.75; two hot dogs and seven hamburgers cost $19.25. Find the cost of one hot dog and the cost of one hamburger. The cost of one hot dog is and the cost of one hamburger is $.

If 0 ≤ θ < 2π and 1 - 7cos θ = 8, determine the values of θ. Enter your answer(s) in radians. If necessary, separate multiple values by commas.

Samir is preheating his oven before using it to bake. Samir created the following linear graph to predict the final temperature after a minutes. What is the meaning of the point (1,90)?

In what form is the following quadratic function? f(x) =3x²-7x+4 Vertex Form Standard Form Maximum Form Intercept Form

What is the image point of (2, 9) after the transformation T-1,-4° ry=x ?

For each pair of functions and g below, find f(g(x)) and g(/(x)). Then, determine whether fand g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the compos You do not have to indicate the domain.)

Teagan likes to play golf. He has budgeted $60 next month for the driving range. It costs him $10.55 for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?

Subtract the following rational expressions and make sure to state the restrictions on the variable:

Brent Pickett borrowed $3000 from his brother Dave. He agreed to repay the money at the end of 4 years, giving Dave the same amount of interest that he would have received if the money had been invested at 3.75% compounded quarterly. How much money did Brent repay his brother?

Use the present value formula to determine the amount to be invested now, or the present value needed. The desired accumulated amount is $85,000 after 10 years invested in an account with 6% interest compounded semiannually. The amount to be invested now, or the present value needed, is $ (Round to the nearest cent as needed.)

Use the compound interest formula to compute the total amount accumulated and the interest earned. $2500 for 3 years at 6% compounded quarterly

If P(E)= 0.19, find the odds against E. What are the odds against E? Select the correct choice below and fill in the answer box(es) to complete your answer. A. The odds are to (Type integers or decimals.) B. The odds are (Type an integer or a decimal.)

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Wind farms are a source of renewable energy found around the world. The power P (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v (in meters per second). If a turbine generates 500 kW in a 10 m/s wind, how much power does it generate in a 12 m/s wind?

Match each of the following equations according to their slope and y-intercept. y=-1.5x-4 m = -1.5, b = -4 y = 3x m = -3, b = 4 y = 1.5x-7 m = 0, b = 7 y=-3x+4 m = 3, b=0 y=7 m = 1.5, b = -7

Find the average value of the function f over the interval [0, 10]. f(x)=5/x+1

Enter the next three numbers of the repeating decimal produced by the fraction 3/9. 0.333333...

A large snowball is melting so that its radius is decreasing at the rate of 4 inches per hour. How fast is the volume decreasing at the moment when the radius is 5 inches? [Hint: The volume of a sphere of radius r is V = 7³.] (Round your answer to the nearest integer.)

The function h (t) = -25 cos(4nt) + 29 represents the height above the ground of a chair on a Ferris Wheel where t=0 represents the time the ride started. If h(t) is in feet and t is in minutes, answer the following: Be sure to include units and justify your answers. A. How long does it take to complete one full revolution? B. What is the highest point on the ride? C. If the ride stops after 15 seconds, how high is the chair above the ground? D. What is the radius of the Wheel?

Write a rule for 9 described by the transformations of the graph of f(x) = x² A vertical stretch by a factor of 3 and a reflection in the x-axis, followed by a translation 5 units down. a. g(x) = 3x² + 5 b. g(x) = (-3x)² - 5 c. g(x) = (3x)² - 5 d. g(x) = -3x² - 5

Solve the following inequality. (x - 1)(x-2)(x-4) ≤0 The solution is (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.)

Nick's telephone company charges $0.04 per minute for weekend calls and $0.08 per minute for calls made on weekdays. This month Nick was billed for 627 minutes. The charge for these minutes was $37.84. How many minutes did he talk on weekends and how many minutes did he talk on weekdays?

A national fast food company has just analyzed the effect of the latest sales promotion. It has determined that the sales decay for its milkshakes is given by S = 405, 000e-0.32, where S is the weekly sales and is the number of weeks that have passes since the end of the sales promotion. Round each answer to 2 decimal places. a) What will the sales 5 weeks after the end of the promotion? $ b) How many weeks after the end of the promotion will sales drop below 15,000, if no new campaign is started?