Basic Math Questions and Answers

Suppose we want to choose 3 letters, without replacement, from the 4 letters A, B, C, and D. (If necessary, consult a list of formulas.) (a) How many ways can this be done, if the order of the choices matters? (b) How many ways can this be done, if the order of the choices does not matter?

Lydia earns $540 per week. Each week, $32 is deducted for federal income taxes, $24.50 for FICA taxes, $29 for state taxes, and $74.50 for health insurance. Find the percentage of gross pay that Lydia takes home to the nearest percent.

Valerie is ordering salads and drinks for her friends. Salads cost $7 each, drinks cost $3 each, and there is a $5 delivery charge per order. She has $50. She buys 3 salads, and wants to figure out the maximum number of drinks she can buy.

Tom bought 8 hamburgers and 5 steaks. Each hamburger weighed 0.35 pounds and each steak weighed 1.25 pounds. How many pounds of meat did Tom buy? * 9.05 pounds 13 pounds. 1.6 pounds 14.6 pounds

Shen is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $83 and allows unlimited mileage. Company B has an initial fee of $65 and charges an additional $0.90 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.

The Clothes Barn is having a 65% off sale on all the dresses, Jennifer paid $43.75 for a dress that was on sale. What was the original price of the dress? $125.00 $28.44 $15.31 $105.00

Maxim has been offered positions by two car companies. The first company pays a salary of $8000 plus a commission of $1100 for each car sold. The second pays a salary of $25600 plus a commission of $300 for each car sold. How many cars would need to be sold to make the total pay the same?

Solve (y-2)³-72=0 where y is a real number. Write your answer in simplified radical form. (If there is more than one solution, separate them with commas.)

Select the reason that best supports Statement 2 in the give 7 proof. A. Substitution B. Division Property of Equality C. Given D. Subtraction Property of Equality

Which of the following is true because of the Associative Law of Addition? 1000 + (2000 + 6) = (1000 + 2000) + 6 1000 + 2000 + 6 = 2000 + 1000 + 6 (1000) + 2000 + 6 = 1000 + (2000) + 6 1000 + 2000 + 6 = 3006

Drake and Josh want to go snowboarding in 3 weeks. Josh is able to save the $520 he needs to go on the trip by saving the pay he received for 5 hours of work at the movie theater each week. Drake must save 8 hours worth of pay from various gigs each week in order to have enough money. How much more money does Josh make than Drake?

An art teacher is hosting a summer art camp. He has a total of $83 to purchase snacks, drinks, and art supplies. He buys 75 bags of chips at $0.30 each and 15 juices at $0.45 each. How much money does he have left to spend on art supplies?

Evaluate the algebraic expression at the indicated values of the variables. (Simplify your answer completely.) 4x² - 5y² - 4xy at x = 3 and y = -5

Gold can be hammered into extremely thin sheets called gold leaf. An architect wants to cover a 100 ft x 85 ft ceiling with gold leaf that is five- millionths of an inch thick. The density of gold is 19.32 g/cm³, and gold costs $1654 per troy ounce (where 1 troy ounce = 31.1034768 g). How much will it cost the architect to buy the necessary gold?

A principal of $4400 is invested at 3.5% interest, compounded annually. How much will the investment be worth after 5 years? Use the calculator provided and round your answer to the nearest dollar.

in the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly 1 ft. An acre is 4840 yd An acre-foot is enough water to supply two typical households for 1.00 yr. Part A It desalinated water costs $1750 per acre-foot, how much does desalinated water cost per liter? Part B How much would it cost one household per day if it were the only source of water?

Hattie had $5750 to invest and wants to earn 4.8% interest per year. She will put some of the money into an account that earns 2.6% per year and the rest into an account that earns 4.9% per year. How much money should she put into each account?

Translate the sentence into an inequality. A number b increased by 5 is less than or equal to 30.

Use the Monotonicity Thoerem to find the intervals where the given function is increasing and w g(t) = -21²-3t+4 Select the correct choice below and, if necessary, fill in the answer box within your choice. (Type your answer in interval notation.) A. The function g is increasing on B. The function g is not increasing on any interval. Next Que

Sarah left Minneapolis heading east on the interstate at a speed of 70 mph. Her sister followed her on the same route, leaving 2 hours later and driving at a rate of 80 mph. How long will it take for Sarah's sister to catch up to Sarah?

Solve for u. 5u²+15u=0 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

A biochemist carefully measures the molarity of calcium ion in 89.3 mL of cell growth medium to be 68.2 µM. Unfortunately, a careless graduate student forgets to cover the container of growth medium and a substantial amount of the solvent evaporates. The volume of the cell growth medium falls to 12.7 mL. Calculate the new molarity of calcium ion in the cell growth medium. Round each of your answers to 3 significant digits.

A package of aluminum foil contains 50. ft² of foil, which weighs approximately 8.0 oz. Aluminum has a density of 2.70 g/cm³. What is the approximate thickness of the foil in millimeters?

Elena collects 112 specimens of beetle and records their lengths for an ecology research project. When she returns to the laboratory, Elena finds that she incorrectly recorded one of lengths of the beetles as 122 centimeters (about 4 feet). What should she do with the outlier, 122 centimeters, when she analyzes her data?

Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying x-intercepts. 2x² + 10x = 0 Rewrite the equation in factored form. The solution set is (Use a comma to separate answers as needed. Type each solution only once.)

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. Parallel to the line x-2y = -9; containing the point (0,0) The equation of the line is. (Simplify your answer. Use integers or fractions for any numbers in the equation.)

Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how compression hosiery, typical shoes, and medical shoes affect range of ankle motion. Click to download the data in your preferred format. CrunchIt! CSV Excel JMP Mac Text Minitab PC Text R SPSS TI Calc In particular, note the variables Barefoot and Footwear1. Barefoot represents a subject's range of ankle motion (in degrees) while barefoot, and Footwearl represents their range of ankle motion (in degrees) while wearing typical shoes. Use this data and your preferred software to calculate the equation of the least-squares linear regression line to predict a subject's range of ankle motion while wearing typical shoes, ŷ, based on their range of ankle motion while barefoot, x. Round your coefficients to two decimal places of precision. ŷ=

Find the least common multiple of 6w³ and 7n².

An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 90 miles from the point and has a speed of 270 miles per hour. The other is 120 miles from the point and has a speed of 360 miles per hour. Exercise (a) At what rate is the distance between the planes changing? Exercise (b) How much time does the controller have to get one of the airplanes on a different flight path? Step 1 In part (a), it was found that the two planes were 150 miles apart and getting closer at the rate of 450 mph. Use the formula Time = Distance/Speed to find the time that the air traffic controller has to get one of the planes on a different flight path.

Suppose it has been determined that the sales at a gallery decline after the end of an advertising campaign, with daily sales given by where S is in dollars and x is the number of days after the campaign ends. What are the daily sales 10 days after the end of the campaign?

You invest $3000 into an account that has a 3.7% annual interest rate and is compounded monthly. How long will it take until you have doubled your money? A. 231.29 years B. 18.76 years C. 1.6 years D. 38.56 years

Victor Haddad sold 8 pumpkins for $2.75 each, 9 for $2.00 each, 24 for $1.50 each, and 15 for $1.00 each. He receives $0.35 for each pumpkin sold plus a $10.00 bonus if his sales total $75.00 or more. How much did he receive?

The true price of a gift you purchase by mail-order is $18.85, but you are billed for $19.27. Find the absolute and relative errors.

An object's velocity is given by v(t) = 0.5(t + 3)(t-1)(t - 5)2, where t is time, in seconds. What is the total distance traveled by the object in the first 5 minutes? A. 37.500 B. 41.667 C. 59.733 D. 77.800

For intervals of values, enter your answer using interval notation. Here are some examples of how interval notation relates to inequalities: With inequalities, we use "less than" (<) or "greater than" (>) to exclude the endpoint of the interval. With interval notation, we use use round parentheses: (, ). With inequalities, we use "less than or equal to" (s) or "greater than or equal to" (2) to include the endpoint of the interval. With interval notation, we use use square brackets: [ ]. To combine two intervals, use U (an uppercase letter u) for union: U. Use oo (two lowercase letter o's) for infinity: 00. Try it now. Enter the interval equivalent to 2 < x < 5 or x > 7.

Find the equation of the horizontal line that contains the point (-9,-5). Express the equation using either the general form or the slope-intercept form of the equation of a line. The equation of the line is. (Type an equation.)

A museum charges $14.50 for a one-day youth admission and $18.50 for a one-day adult admission. One Friday, the museum collected $1723 from a total of 110 youths and adults. How many admissions of each type were sold? The museum sold youth admissions and adult admissions.

In triangle ABC, the measure of angle B is 34° more than three times the measure of angle A. The measure of angle C is 56° more than the measure of angle A. Find the measure of each angle. Angle A measures

Find the absolute and relative errors in the following situation. The actual distance to a certain town is 32.8 miles, but your odometer reads 32.7 miles. The absolute error is The relative error is mile(s). (Type an integer or decimal rounded to the nearest tenth as needed.) %. (Type an integer or decimal rounded to the nearest tenth as needed.)

Each course at college X is worth either 2 or 3 credits. The members of the men's swim team are taking a total of 47 courses that are worth a total of 105 credits. How many 2-credit courses and how many 3-credit courses are being taken? 2-credit courses and 3-credit courses being taken. There are

The length of a rectangle is 1 m more than double the width, and the area of the rectangle is 45 m². Find the dimensions of the rectangle.

This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 20+b=15.7 can be used to find the side lengths. If one of the longer sides is 6.3 centimeters, what is the length of the base? Icm

Fred earns $45 mowing the lawn. He spends $5 on music, and puts half of what's left in a savings account. He then gets another $5 for washing his neighbor's car. First, write the expression that represents the number of dollars Fred keeps (and does not put in his savings accbunt), and then simplify.

Write each of the following numbers in scientific notation. a. 6800 b. 0.00431 c. 247,120 a. 6800 = (Use the multiplication symbol in the math palette as needed.) b. 0.00431 = (Use the multiplication symbol in the math palette as needed.) c. 247,120= (Use the multiplication symbol in the math palette as needed.)

Select the correct answer from each drop-down Point O is the center of a circle passing through points A, B, and C. Bis a right angle. The center of the circumscribed circle lies on line segment of the circle.and the longest side of the triangle is equal to the

Xavier Zermeno worked through 174 pages of a 408-page computer training manual. It took him 2 days to work through the remaining pages. If he worked through the same number of pages each day, how many pages did he work through each day?

Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 31 cups of coffee, using 444 ounces of coffee, while collecting a total of $36.60. How many cups of each size did Kyle fill? Kyle filled 10-oz cup(s). 14-oz cup(s), and 20-oz cup(s).

Round the following numbers to the nearest tenth and nearest ten. a. 699.34 b. 764.148 c. 668.9 d. - 47.517 a. 699.34 rounded to the nearest tenth is and rounded to the nearest ten is b. 764.148 rounded to the nearest tenth is and rounded to the nearest ten is c. 668.9 rounded to the nearest tenth is and rounded to the nearest ten is d. -47.517 rounded to the nearest tenth is and rounded to the nearest ten is.

Give the slope and the y-intercept of the line with the given equation. Then, graph the linear equation. y = 2x + 3 What is the slope? Select the correct choice below and fill in any answer boxes within your choice. A. The slope is (Simplify your answer.) B. The slope is undefined.

Do the following operations without a calculator. Be sure to express answers in scientific notation. You may round your answers to one decima a.(3x10³) × (2×10⁹) b. (5x106) + (9x105) c. (4×10⁹) + (2x10³) a.(3x10³) x (2x 10) = 6x10 (Use the multiplication symbol in the math palette as needed.) b. (5x106) + (9x10³) = (Use the multiplication symbol in the math palette as needed.) C.(4x109) + (2x103) =0