Basic Math Questions and Answers

Solve the exponential equation by using the property that bx = by means that x = y whenever b> 0 and b ≠1. 3x = 243

g(x) = -x-5 h(x) = 4x+2 Find (g. h)(x) A) -x³-6x² - 8x B) -4x²-22x-10 C) -4x³2x²-12x-6 D) -4x² +22x-10

The cost of a soccer ball to Soccer Line Sports Goods is $45. They sell the same soccer ball for $54. Determine the percent markup in the price of the soccer ball The markup is.

A vehicle purchased for $27,500 depreciates at a constant rate of 4%. Determine the approximate value of the vehicle 11 years after purchase. Round to the nearest whole dollar.

Find the value of the expression. 8² + 20

On Monday, Harold picked up five donuts and six large coffees for the office staff. He paid $7.85. On Tuesday, Melinda picked up six donuts and four large coffees for the office staff. She paid $6.70. What is the cost of one donut? What is the cost of one large coffee?

Light spheres are designed to measure, in lumens, visible light or the flux of different lights, lamps, etc. A particular institute establishes standards for how these commercial spheres are calibrated. These spheres are sold in different diameters that determine the lamp length that can be tested. Find the surface area of a 58-inch light-measurement sphere, rounded to the nearest square unit.

A baseball is hit so that its height in feet after t seconds is s(t) = -2t² +40t+6. (a) How high is the baseball after 1 second? (b) Find the maximum height of the baseball.

A man earned wages of $52,000, received $2600 in interest from a savings account, and contributed $3700 to a tax-deferred retirement plan. He was entitled to a personal exemption of $3800 and had deductions totaling $6430. Find his gross income, adjusted gross income, and taxable income.

Recall the GRE example. Students' scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation 8.8. Suppose n= 16 randomly selected students take the GRE on the same day. a. What is the probability that one randomly selected student scores above 147 on the quantitative portion of the GRE?

Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax²+bx+c = 0. The solutions are - 6 and 2.

Cabot Creamery Cooperative tried three times and was able to concoct the world's largest smoothie. It was 400 gallons. How many servings of 16 fluid ounces did this make?

There are 63 students in the cafeteria. There are 9 students at each a. At how many tables are the students seated? b. Write a division equation to represent your answer.

The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts (a) through (d) below.

Modeling Data In Exercises 81-84, determine which of the following functions f(x) = cx, g(x) = cx², h(x) = c√x, and r(x) = c/x can be used to model the data and determine the value of the constant c that will make the function fit the data in the table.

Write a third-degree equation having the given numbers as solutions. -4, 3, 8 The third-degree equation, has solutions - 4, 3, and 8. (Simplify your answer. Type an equation using x as the variable. Type your answer in standard form.)

Mr. Jones wants to buy 6 tickets to a play. Each ticket costs $10. Mr. Jones has $45 in his pocket. How much more money does he need to buy all 6 tickets?

Nestled deep in a particular rainforest, these wooden spheres, called "Free Spirit Spheres," are hung from the trees by small networks of ropes. The exterior of a sphere has a diameter of about 9 feet 10 inches. Find the volume of the exterior of the sphere to the nearest whole cubic inch.

Two angles form a linear pair and their measures have a ratio of 2 : 5. Select the angle measures (rounded to the nearest hundredth). 130.00 51.42 128.55 2.00 25.71 5.00 104.84

What is the image point of (2,6) after a translation right 5 units and down 3 units?

Gul can run 800 meters in 139 seconds. About how long would it take her to run 6 times as far if she runs at the same speed? Choose the best estimate. About 140 seconds About 600 seconds About 1,200 seconds About 6,000 seconds

Solve the inequality algebraically. X+5/ x-5 > 0 The solution is (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

In January, each of 60 people purchased a $500 washing machine. In February, 5% fewer customers purchased the same washing machine that had increased in price by 20%. What was the change in sales from January to February? Select the correct choice below and fill in the answer box within your choice. A. The change in sales from January to February is a $ B. The change in sales from January to February is a $ C. There is no change in the sales from January to February.

Ray Flagg took out a 60-month fixed installment loan of $12,000 to open a new pet store. He paid no money down and began making monthly payments of $221. R business does better than expected and instead of making his 36th payment, Ray wishes to repay his loan in full. Complete parts a) through c). a) Determine the APR of the installment loan. APR=

There were 401 tickets sold for a basketball game. The activity cardholders' tickets cost $1.75 and the non-cardholders' tickets cost $2.25. The total amount of money collected was $880.75. How many of each kind of ticket were sold?

In a game of dice, a player throws two regular dice and records their sum. This is repeated 50 times. Find the expected number of times when the player records a prime number. Give your answer as a fraction in fully simplified form or as a decimal rounded to three significant figures.

A principal of $3500 is invested at 3.75% interest, compounded annually. How much will the investment be worth after 12 years? Use the calculator provided and round your answer to the nearest dollar.

Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that for the afternoon shift 5% of all welds done will be substandard. If Smith checks 300 of the 7500 welds completed that shift, what is the probability that he will find more than 25 substandard welds? 0.4960 0.9960 0.0040 0.5040

Maritza is baking cookies to bring to school and share with her friends on her birthday. The recipe requires 3 eggs for every 2 cups of sugar. To have enough cookies for all of her friends, Maritza determined she would need 12 eggs. If her mom bought o cups of sugar, does Maritza have enough sugar to make the cookies? Why or why not?

Here are several recipes for sparkling lemonade. For each recipe describe how many tablespoons of lemonade mix it takes per cup of sparkling water. (Lesson 2-1) Recipe 1: 4 tablespoons of lemonade mix and 12 cups of sparkling water Recipe 2: 4 tablespoons of lemonade mix and 6 cups of sparkling water Recipe 3: 3 tablespoons of lemonade mix and 5 cups of sparkling water

Use the laws of logarithms, the fact that the exponential and logarithmic functions are inverses of each other and the table on the last page to find an approximation to the nearest tenth of the log of the following values. (a) log(251) (b) log(0.00398) (c) log(16/320)

1. Harper is going to create a graph of the equation y = -0.5x + 12. Which of the following will be true about the graph? a.The graph will contain the origin. b. The graph will increase from left to right. c. The graph will cross the x-axis at (12, 0). d. The graph will have a slope of -0.5.

To start a new business Beth deposits $1500 at the end of each six-month period in an account that pays 7%, compounded semiannually. How much will she have at the end of 8 years? At the end of 8 years, Beth will have approximately $ (Do not round until the final answer. Then round to the nearest hundredth as needed.)

On the April 2 billing date, Michaelle Chappell had a balance due of $1423.58 on her credit card. From April 2 through May 1, Michaelle charged an additional $482.18 and made a payment of $600. a) Find the finance charge on May 2, using the previous balance method. Assume that the interest rate is 1.4% per month. b) Find the new balance on May 2. a) The finance charge on May 2 is $ (Round to the nearest cent as needed.)

A line goes through the points (8,11) and (-2,7). (a) What is the slope of the line? Show your work. (b) Write the equation of the line in point-slope form. Show your work. (c) Write the equation of the line in slope-intercept form. Show your work.

Jeff and Sargon are saving money to go on a road trip. After looking at all the costs, they determine they need at least $2050 to go on the trip. Jeff shovels snow from driveways and Sargon salts the sidewalks to raise money. Jeff charges $15 each time he shovels a driveway and Sargon charges $10 each time he salts a sidewalk. The number of sidewalks that Sargon has scheduled is no more than three times the number of driveways Jeff has scheduled to shovel. Sargon plans to salt at least 35 sidewalks through the winter season. Write a set of constraints to model the problem, with x representing the number of driveways shoveled and y representing the number of sidewalks salted.

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.)