Math Questions

Benji has $3,100 in a savings account which earns 7% interest compounded quarterly. He made no additional withdrawals or deposits. What was the amount in the account after one quarter? O $3,145.25 O $3,255.25 O $3,451.25 O $3,154.25

Select the correct choice that completes the sentences in parts (a) through (c). a) The probability of an event that cannot occur is 0. b) The probability of an event that must occur is 1. c) Every probability must be a number between

Suppose that the joint distribution function of X and Y is given by f(x,y)=x+y If 0<x< 1 and 0 <y< 1, and 0 otherwise, find: a. the marginal density of X b. the marginal density of Y

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

If f(x) = 2² +1, use the limit definition of the derivative to compute f'(z). You can use derivative rules to check your answer, but answers calculated without using the definition of derivative will receive very little credit.

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

The following table shows the age distribution of residents of a certain country. The data are rounded to the nearest million people. If one of these individuals is selected at random, determine the probability that the person is 0-14 years old, given that the person is female.

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, ∞)

If a wagon wheel had 15 more spokes, the angle between spokes would decrease by 54 degrees. How many spokes does the wheel have? A) 11 B) 5 C) 6 D) 2 E) 8

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

Consider the two sets A = {n EN:n is both a perfect square and a perfect cube} and B = {r € N:r = 0mod 7 or r = 1mod 7). If one wishes to prove A = B. then which of the following describes a valid proof strategy? Select only one answer. (a) Suppose z € A and prove r e B, and then suppose r&A and show r & B. (b) Suppose z E A and prove z € B. (c) Suppose z € An B and conclude re AUB. (d) Suppose z € B and conclude z E A. and then suppose z E A and conclude a contradiction. (e) Suppose z B and conclude z € A.

Suppose the total cost C(x) (in dollars) to manufacture a quantity x of weed killer (in hundreds of liters) is given by the function C(x)= x³ - 3x² +9x +50, where x > 0. a) Where is C(x) decreasing? b) Where is C(x) increasing?

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

The power generated by a windmill is related to the velocity of the wind by the formula where P is the power (in watts) and vis the velocity of the wind (in mph). Determine the velocity of the wind when the windmill is generating 600 watts of power. A) v = 965.42 mph B) v = 19.88 mph C) v = 31.07 mph D) v = 173.19 mph E) v = 37.28 mph

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.

Think About the Process In AABC, mZB is 5 times mZA and mZC is 16° less than 4 times mZA. What equation is used to solve for the variable x? Find the measure of each angle. The figure is not drawn to scale. Which of the following is the correct equation used to solve for the measure of each angle? A. MZA+mZB+mZC= 180° B. MZA-mZB-m/C= 180° C. MZA-mZB+mZC = 180° D. MZA+mZB-mZC= 180°

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

Nancy's car cost $14,400. She has enough money to make a down payment of $5,000. Her monthly payments are $210 for 48 months. How much greater is the deferred price than the original price? $4,320 $860 $10,080 $680

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

Consider two electrical components, A and B, with respective lifetimes X and Y in days. Assume that a joint PDF of X and Y is If 0<x< 1 and 0 <y < 2, and 0 otherwise, find: a. the marginal density of X b. the marginal density of Y

Refer to the graph of k(n) to complete the table of values. Determine the formula for the function k(n), then use words to describe the relationship between the input and output variables.

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?

Let'f be a twice-differentiable function with derivative given by f '(x) = 4x³ - 24x². Part A: Find the x-coordinate of any possible critical points of f. Show your work. Part B: Find the x-coordinate of any possible inflection points of f. Show your work. Part C: Use the Second Derivative Test to determine any relative extrema and inflection points. Justify your answers. Part D: Iff has only one critical point on the interval [5, 8], what is true about the function f on the interval [5, 8]? Justify your answers.

Alexia is reviewing for the Algebra End-of-Course exam. She made this graph representing a system of inequalities. (6.2) (5.4) (2,-2) (6,-3) (2, 2) (5, 1) (2.-1) (3.0)

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

Sam borrowed money from a bank to invest in antiques. He took out a personal, amortized loan for $28,000, at an interest rate of 7.55%, with monthly payments for a term of 2 years. For each part, do not round any intermediate computations and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find Sam's monthly payment. (b) If Sam pays the monthly payment each month for the full term, find his total amount to repay the loan. (c) If Sam pays the monthly payment each month for the full term, find the total amount of interest he will pay.

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 high school band trip will require renting buses and trucks to transport no fewer than 150 students and 20 or more large instruments, Each bus can accommodate 60 students plus 3 large instruments; it costs $347 to rent. Each truck can accommodate 15 students plus 7 large instruments and costs $195 to rent. How many of each type of vehicle should be rented for the cost to be minimized? Determine the minimum cost. 2 buses and 2 trucks: $1084 none of these buses and 10 trucks: $1950 4 buses and 0 trucks: $1388 1 buses and 4 trucks: $1127

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:

Complete the table with positive, negative, or 0 to describe g' and g". Justify your answers. positive positive positive positive Part B: Find the x-coordinate of each critical point off and classify each as a relative minimum, a relative maximum, or neither. Justify your answers. Part C: Find all values of x at which the graph of f has a point of inflection. Justify your answers. Part D: Let h be the function defined by h(x) = -2f(x)g(x). Is h increasing or decreasing at x=-1? Justify your answer.

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?

Assume that you want to approximate a function f(x, y, z)=x² + y² +2² by a line function ((x, y, z)= a₁x+ay+at+e such that f(x, y, z)=(x, y. 2) at four points (1,0,0), (1, 1.0), (0, 1, 1), a (1,0,1). Here, means that f(x, y, z) is almost equal to f(x, y, z). Your goal is to find the coefficients a₁.a. and c. Model this problem into an optimization problem of the form that minimizes the sum of squar errors between f and at these four points. Solve the resulting optimization problem.

The weights (to the nearest five pounds) of 34 randomly selected male college students are organized in the histogram. Use the graph to find the median weight.

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

The continuous function g, consisting of two line segments and a parabola, is defined on the closed interval [-3, 6], is shown. Let f be a function such that f(-1)=- and f '(x) =

ATV remote control has keys for channels 0 through 9. a) If a key is selected at random, what is the probability that the key for channel 8 is pressed? b) If a key is selected at random, what is the probability that the key for an even number is pressed? c) If a key is selected at random, what is the probability that the key for a number more than 0 is pressed?

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?