Basic Math Questions and Answers

Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 6 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 98? Show your work and explain how you arrived at your answers. There are sample student explanations in the feedback to questions 1, 3, 5, 9, 11, and 20 that show the level of detail that is expected in your explanations.

Solve the compound inequality. x< 1/1 orx>-1/3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is Ø.

Solve the compound inequality. -5x≤ - 10 or 2x-222 - 12 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is Ø.

The savings in a bank account can be modeled using S=1250e045t, where t is the number of years the money has been in the account. Determine, to the nearest tenth of a year, how long it will take for the amount of savings to double from the initial amount deposited of $1250.

Given the lines I₁: x = 3+t y = 9-2t z = 5t - 8 and I2: x = 6-5t y = 9+t z = 4t - 8 (a) find equations (in general form) for the parallel planes π1 containing I1 and π2 containing I2 π2 : π1 : (b) determine the geometric relation between the lines: they are ?

A bank operates both a drive-up facility and a walk-up window. On a randomly selected day, let X be the proportion of time that the drive-up facility is in use (at least one customer is being served or waiting to be served) and Y be the proportion of time that the walk- up window is in use. The joint PDF is What is the probability that neither window is busy more than one-quarter of the time?

The area of the region that lies to the right of the y-axis and to the left of the parabola x = 2y - y2 (the shaded region in the figure) is given by the integral f (2y - y2) dy. (Turn your head clockwise and think of the region as lying below the curve x = 2y = y² from y 0 to y = 2.) Find the area of the region.

Three million E. coli bacteria are present in a laboratory culture. An antibacterial agent is introduced and the population of bacteria P (1) decreases by half every 3 hr. The population can be represented by (a) Convert the given model to an exponential function using base e. Round the value of k to five decimal places.

Simplify completely, assuming both x > 0 and y> 0: √36x³y⁹ Select the correct answer below: 36xy4√36xy 6xy √xy 36x³y6√36xy2 6x³y6 √6x²y² 6xy √√xy 216xy4√6xy3

Graph the solution of the system of linear inequalities. x 4y x+3y≤6

Compound interest is given by the formula A P(1 + r). Where A is the balance of the account after t years, and P is the starting principal invested at an annual percentage rate of r, expressed as a decimal. Erik invested $7200 in a savings account that pays 11% interest compounded annually and plans to leave it there for 20 years. Determine what Erik 's ending balance will be after 20 years. After 20 years, Erik will have a balance of $ Round your answer to the nearest cent. in his savings account.

Solve the compound inequality. 6-x> 11 and 3x + 1 ≥10 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is Ø.

Graph the solution of the system of linear inequalities. (3x-2y≤6 y≤-5 Use the graphing tool to graph the solution. Click to enlarge graph

We want to know what percent of people get their coffee from a gas station. A random sample of 50 people found that 20% had gotten their coffee from the gas station. All conditions for inference have been met. a) What is the point estimate, the sample size and the critical z value for the sample? a) Find a 90% confidence interval. Show your work.

Together, Kali and Geoff bake 10 pies for the bake sale in 2 hours. Then they make another 6 pies, but Kali works for 45 minutes while Geoff works for an hour and a half. Write and solve a system of equations to find the pie making speed of each person per hour.

Determine all the solutions to √/1+4√x = 1 + √x. x=0 x=4 x = 0 and x = 4 no solution

Solve the compound inequality. 3x+6≤-9 and 2x≤0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set of the compound inequality is B. The solution set is Ø.

Many large farms use center pivot irrigation, which involves a sprinkler rotating around a central point, as shown in the figure. A particular system uses a sprinkler that is 120 meters long and rotates 7 per hour. What is the total area, in square meters, that the sprinkler will water in 5 hours? Enter your answer as a value rounded to the nearest whole number.

The sum of a number and 8 is 14. Write it as an equation. x+8 = 14 5+x=14 x=14+2

A golden rectangle is said to be one of the most visually appealing of all geometric forms. The front of the Parthenon, built in Athens Greece in the 5th century B.C. is a golden rectangle. In a golden rectangle, the length I and the height h of the rectangle must satisfy the equation l/h = h/l - h If a rectangular billboard is to have a height of 10 feet, how long should it be if it is to form a golden rectangle? Round your answer to the nearest tenth of a foot. A) 16.4 ft B) 18.2 ft C) 15.9 ft D) 17.2 ft

Trisha's car cost $10,900. She has enough money to make a down payment of $1,000. Her monthly payments are $250 for 48 months. True or False: The deferred price is $2,100 greater than the original price.

You decide to begin selling caramel apples at the local swap mart. Your cost for each caramel apple is $1.40 plus you have to pay a fixed weekly fee of $230 for the booth. Your plan is to sell each caramel apple for $3.10. 1. Write an expression to represent your total costs for the week if you sell n caramel apples. Total Costs: 2. Write an expression to represent the revenue from the sale of n caramel apples during the week. Revenue: 3. Write an expression that represents the profit for selling n caramel apples in a given week. How many caramel apples must you sell in order to make a positive profit? In order to make a positive profit, you would have to sell.

Alice and Wyatt depart Alice's house at the same time. Alice drives due North at 30 mph and Wyatt drives due East at 40 mph. One hour later, Alice will be 30 miles due north of the house, and Wyatt will be 40 miles due east of the house. At what rate is the distance between Alice and Wyatt changing at this time? Diagrams are included below for your convenience. You are NOT required to use them. Dynamic Diagram Static Diagram

Suppose that the following information is known about a function g(x): (b) (2,4) (c) (2,8) g(1)=2 g(2)=4 g(3) =-1 g'(1) -2 g'(2)=0 g'(3)= Which of the following are critical points of the function f(x)=xg(r)? Choose all that apply. (a) (1,2) (d) (3,-3)

Solve the inequality x +4| < |x| Hint: use the fact that |x| = √² and x + 4 = √(x+4)² so x +4|< x implies √(x+4)² <√x² impying further that (x+4)² < x². Now you finish. A) (-∞, - 2) B) (-∞0, 2) Og) (-4, ∞) D) (-∞, -2]

Solve the inequality |3x2| < 5 A) (3,7) B) (-1,7/3) C) (1,7/3) D) (-1,3/7) E) (-∞, -7/3) U (-1, ∞)

Describe what fixed costs and marginal costs mean to a company. Choose the correct answer below. A. Fixed cost is the rate of change of cost C(x) at the level of production x and is equal to the slope of the cost function at x. Marginal cost is the constant for a particular product and does not change as more items are made. B. The number of units at which revenue just equals cost is the fixed cost. Marginal cost is the constant for a particular product and does not change as more items are made. C. Fixed cost is the constant for a particular product and does not change as more items are made. The number of units at which revenue just equals cost is the marginal cost. D. Fixed cost is the constant for a particular product and does not change as more items are made. Marginal cost is the rate of change of cost Cx) at the level of production x and is equal to the slope of the cost function at x.

A person who exercises regularly has 164 % body fat by mass. If this person weighs 29 pounds, what is the mass, in kilograms, of body fat? Please make sure to include the correct unit symbols with the answer. a. 22 kg b. 57 kg c. 28 kg d. 34 kg e. 36 kg

Graph the following inequality. y≤3 Use the graphing tool to graph the inequality

Solve the compound inequality. -2xs-4 or 2x-142-4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. B. The solution set is Ø.

The formula D = 399t + 5360 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2021. In the year 2021, the total average credit card debt for a U.S. household will be $

Determine all the solutions of the equation x - √11x-24 = 0 A) x = -3,8 B) x = -3, -8 C) x = 3, -8 D) x = 3,8 E) x = 3

c. Use your table to complete the following. At the negative critical value listed in part b, what does your table tell you about the value of the second derivative? f"=(Type integers or simplified fractions.) Consequently, what can be concluded about the graph of f? Select the correct choice below and, if necessary, fill in the answer boxes within your choice. A. The graph of f is concave down and f has a relative maximum at B. The graph of f is concave down and f has a relative minimum at Cc. The graph of f is concave up and f has a relative minimum at D. The graph of f is concave up and f has a relative maximum at ( ion can be made

Jake has 28 coins, some of which are quarters while the remainder are dimes. If the total value of the coins is $5.35, how many of each type of coin does Jake have? 15 quarters and 13 dimes 13 quarters and 15 dimes 16 quarters and 12 dimes 17 quarters and 11 dimes 20 quarters and 8 dimes

A Mississippi riverboat can travel 60 kilometers downstream in three hours and can make the return trip in five hours. Determine the speed of the boat in still water. 32 kph 26 kph 16 kph 20 kph 17 kph

The side of a square is 4 centimeters shorter than the side of a second square. If the sum of their areas is 40 square centimeters, determine the length of one side of the larger square. A) 6cm B) 9cm c) 16cm D) 15cm E) 12cm

Robert scored a total of 25.85 points in a game. Of those points, 3.5 were earned in a bonus round. Find the number of points earned during the game.

Deandre is taking out a mortgage for $249,000 to buy a new house and is deciding between the offers from two lenders. He wants to know which one would be the better deal over the life of the mortgage loan, and by how much. Answer each part. Do not round intermediate computations, and round your answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) An online lending company has offered him a 15-year mortgage loan at an annual interest rate of 4.5%. Find the monthly payment. (b) A savings and loan association has offered him a 15-year mortgage loan at an annual interest rate of 4.7%. Find the monthly payment. (c) Suppose Deandre pays the monthly payment each month for the full term. Which lender's mortgage loan would have the lowest total amount to pay off, and by how much?

Determine the dimensions of a rectangle whose area is 450 cm squared and whose perimeter is 90 cm. A) 20 cm by 22.5 cm B) 10 cm by 45 cm C) 15 cm by 30 cm D) 15 cm by 40 cm E) 20 cm by 30 cm

A farmer drives a tractor from one town to another, a distance of 120 miles. He drives 10 mph faster on the return trip, cutting 1 hour off the time. How fast does he drive each way? A) 40 mph going and 30 mph returning B) 60 mph going and 70 mph returning C) 40 mph going and 50 mph returning D) 30 mph going and 80 mph returning E) 30 mph going and 40 mph returning

In certain population of the herring Pomolobus aestivalis, the length of the individual fish follow a normal distribution. The mean length of the fish is 54.0 mm, and the standard division is 4.5 mm. What percentage of the fish are between 58 and 60 mm long. 40.82% 9.49% 0% 5%

A new sci-fi movie was filmed using a man in rubber monster suit at 7 feet 2 inches tall. The suit was constructed to the scale 1 inch -5 feet. How tall of a monster is the rubber suit designed to depict? A. 430 feet B. 360 feet C. 35 feet 10 inches D. 7 feet 10 inches

Suppose a sample of 950 men found that 642 of them favored the death penalty for capital murder convictions while a sample of 810 women found that 405 of them favored the death penalty for capital murder convictions. Test the claim using a signifiance level of 0.05 that the proportion of men favoring the death penalty is greater tha nthe proportion of women favoring the death penalty. Let p₁ = proportion of men favoring the death penalty Let p2 = proportion of women favoring the death penalty Answer the following questions below based upon the above data and the definitions of p₁ and P2 Which group of statements correctly describe the Claim, the Null Hypothesis, and the Alternative Hypothesis:

Marilyn needs to make a repair. The part costs $165 and labor is 3 hours at $75 per hour. Sales tax is 4%. Sales tax is charged on the parts but not on the labor. How much will it cost for the repair?

A hose can fill a swimming pool in 18 hours. Another hose needs three more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool? A) 9 hours B) 14 hours C) 6 hours D) 12 hours E) 18 hours

Solve the equation. Give the sum of all the solutions. 9m 3/3/2 } – 108m³ 108m A) 761 B) 752 c) 756 D) 758 E) 753

Sean bought a used car with an odometer reading of 15,800 miles. He drove it for 5 years. Now the odometer reading is 65,900 miles. What is the average number of miles that he has driven his car each year?

A cylindrical soup can has the dimensions shown. What is the surface area of the can? Use 3.14 as an approximation for x. Round the answer to the nearest tenth, if necessary. 1614.7 square centimeters 587.2 square centimeters 388.6 square centimeters 777.2 square centimeters

Lacumba, a 228 pound female patient, has a blood volume of 8.7 quarts. If the density of blood is 1.51 grams per milliliters, what is the mass, in kilograms, of Lacumba's blood? Note: 1 quart = 946 milliliters.

In the year 1989, an investment was worth $29400. In the year 1998, this investment was worth $45600. The value of this investment is Select an answer at a rate of