Math Questions

V = πr²h is an equation to calculate the volume of a cylinder, V, where r represents the radius of the cylinder and h represents its height. Which equation allows us to easily find the height of the cylinder because it is solid for h? A. r²h = V/π B. h = V-πr² C. h=V/πr^2 D. πh = V/r^2

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at z = 5 and x=0, and a root of multiplicity 1 at x = -2 Find a possible formula for P(x).

The mean SAT verbal score is 419, with a standard deviation of 96. Use the Empirical Rule to determine what percent of the scores lie between 227 and 515. (Assume the data set has a bell-shaped distribution.) 81.5% 68% 34% 83.9%

Let U = {1,3,5,6,8,9,14,17,18). Determine the complement of the set (1,3,5,8,9,14,17,18). The complement is. (Use a comma to separate answers as needed. Use ascending order.)

When Cara drives to work, it takes her 30 minutes to drive 15 miles. On her days off, she likes to drive to her favorite donut shop. It takes Cara 6 minutes to drive to The Dreamy Donut Shop at the same rate. How many miles away is The Dreamy Donut Shop?

The formula P = 0.35x - 73 models the profit, P, in dollars, for a shoe shiner when he shines x pairs of shoes. Use the formula to find this shoe shiner's profit when he shines 600 pairs of shoes. A) -$69.50 B) $527 C) $137 D) $210

Solve the inequality. State the solution in interval notation. -2x + 20 < 2x + 4

3.25H +2.25C = 32 The above equation is true if Thea buys H pounds of ham slices and C pounds of cheese slices at her local deli. The local deli charges $3.25 per pound of ham and $2.25 per pound of cheese. According to the equation, how much does Thea spend in total on both han and cheese slices?

An average school bus holds 45 people. Sketch a graph showing the relationship between the number of students who need bus transportation and the number of buses required. Be sure to label the axes.

An art student uses a roll of wallpaper to decorate two gift boxes. The student will use 1 1/3 yards of paper for one box and yard of paper for the other box. The paper must be cut into pieces that are yard long. How many pieces will the student cut to use for the gift boxes?

Total revenue is in dollars and x is the number of units. Suppose that in a monopoly market, the demand function for a product is given by the following equation, where x is the number of units and p is the price in dollars. p = 400 - 0.2x (a) Find the total revenue from the sale of 500 units. (b) Find the marginal revenue at 500 units.

Frogs A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment. Previous research had established that this trait is usually found in 1 of every 8 frogs. He collects and examines a dozen frogs. If the frequency of the trait has not changed, what's the probability he finds the trait in a) none of the 12 frogs? b) at least 2 frogs? c) 3 or 4 frogs? d) no more than 4 frogs?

Adrienne and her brother John each inherit ($7,000 that they use to open savings accounts with. Adrienne's account earns 4.7% annual compound interest and John's account earns 4.7% annual simple interest. Neither makes any additional deposits or withdrawals for 10 years. a. Who's account will be worth more at the end of 10 years? b. How much more will the account be worth?

Provide an appropriate response. The scores of the top ten finishers in a recent golf tournament are listed below. Find the mean score. 71 67 67 72 76 72 73 68 72 72 68 71 72 67

Margaret is saving money at a constant rate. Suppose she initially has $80 saved, and after 4 months, she has $180 saved. Which of these expresses the rate at which Margaret is saving? Select the correct answer below: 25 dollars per month 25 months per dollar 100 dollars per month -25 dollars per month 80 months per dollar

In regular polygons, if the number of sides, n, is odd, the lines of symmetry will pass through a ____ and the ____ of the opposite side. If n is even, then the lines of symmetry will pass through two ____ vertices or the of two opposite sides.

The phone company A Fee and Fee has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 280 minutes, the monthly cost will be $142. If the customer uses 650 minutes, the monthly cost will be $290. A. Find an equation in the form y = ma+b, where is the number of monthly minutes used and y is the total monthly cost of the A Fee and Fee plan. y = B. If 907 minutes are used, the total cost will be

A total of 246 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?

If money can be invested at 3.7% compounded quarterly, which is larger, $659 now or $1000 in 10 years? Use present value to decide. The present value of $1000 in 10 years is $ (Do not round until the final answer. Then round to the nearest cent as needed.) Which value is larger? A. $659 now B. $1000 in 10 years

Haloween is a Holiday that many people observe on the last day of October every year Children and adult's dress in costumes and go door to-door asking for candy. Some people hoste partys and serve Halloween treats such as caramel apples, pop corn, and cidar. Others celebrate by telling scary stories or watching spookey movies.

How long will it take money to double if it is invested at the following rates? (A) 7.3% compounded daily (B) 14.6% compounded daily (A) years (Round to two decimal places as needed.) (B) years (Round to two decimal places as needed.)

Write two decimals that are equivalent to the given decimal. 3.400 Select all that apply. A. 3.04 B. 3.40 C. 3.4 D. 3.040 E. 3.004

Explain why the empty set is a subset of every set. A. If there is at least one element of set A that is not an element of set B, then A is not a subset of B. If A is the empty set, which contains no elements, then there can never be any elements in A, much less elements in A that do not belong to B. B. If all elements in set A are also elements of set B and all elements in set B are also elements in set A, then A and B are subsets. If A is the empty set, then there can never be any elements in A, much less elements in A that belong to B. C. If there is at least one element of set A which is also an element of set B, then A is a subset of B. If A is the empty set, which contains no elements, then there can never be any elements in A, much less elements in A that belong to B.

Drag and drop the reasons into the boxes to correctly complete the table. -6x + 7x + 14 = x + 14 = 3 x = −11

The ratio of a basketball player's completed free throws to attempted free throws is 3 to 8. If she completed 15 free throws, find how many free throws she attempted. Round to the nearest whole number if necessary. A) 5 free throws B) 40 free throws C) 3 free throws D) 6 free throws

Is y = -18x + 58 increasing or decreasing? increasing decreasing

Logan buys white, black, and gray tiles for his bathroom floor. The number of black tiles he buys is 10 more than twice the number of white tiles. He buys 100 gray tiles. If he buys 260 tiles in total, how many of each color did he buy?

Find the x-value of the removable discontinuity of the function. Consider the graph of the function f(x) = x² - 121/x²+x-132 Provide your answer below: The removable discontinuity occurs at x = =

If f(x) is a linear function, f(-4)= -2, and f(5) = 2, find an equation for f(x). f(x) =

The function h is defined as h (x)=3x² - 2x. Find h (x-5). Write your answer without parentheses, and simplify it as much as possible. h(x - 5) =

Consider the graph of the function f(x) = x^2+ 3x - 18 / x^2 - 4x - 21 What are the vertical asymptotes?

Brooklyn needs to order some new supplies for the restaurant where she works. The restaurant needs at least 498 glasses. There are currently 230 glasses. If each set on sale contains 10 glasses, write and solve an inequality which can be used to determine x, the number of sets of glasses Brooklyn could buy for the restaurant to have enough glasses.

A nut wholesaler sells a mix of peanuts and cashews. He charges $2.80 per pound for peanuts and $5.30 per pound for cashews. If the mix is to sell for $4.30 per pound, how many pounds each of peanuts and cashews should be used to make 100 pounds of the mix?

Human skin becomes dry during winter, making it more prone to infections than during summer. How do the sebaceous glands protect the skin normally? A. Sebaceous glands produce a substance that moisturizes and protects the skin. B. Sebaceous glands cause the hair to stand erect, which insulates and protects the skin. C. Sebaceous glands produce keratin, which gives the skin a tough structure and protection. D. Sebaceous glands contain collagen fibers, which provide strength and protection.

Express the given set using the roster method. The set of natural numbers less than 6. Express the set of natural numbers less than 6 in roster form. (Use a comma to separate answers as needed. Use ascending order.)

Some water sports are expensive. People with larger incomes are more likely to participate in such a sport. The number of people N (measured in thousands) who engage in a particular water sport can be described by the function N=0.13x² -3.16x + 102.25, where x is the mean income (measured in thousands) and x ≥ 20. Use this information to find N when x = 25, x = 50, x= 75, x = 100, and x = 125. Find N when x = 25, x = 50, x=75, x= 100, and x = 125. When x = 25, N= 104.5 thousand people. When x = 50, N= 269.25 thousand people. When x = 75, N= 596.5 thousand people. When x= 100, N= 1086.25 thousand people. When x = 125, N= thousand people.

A local phone repair company charges $49 for a phone repair. Their operating expenses are, on average $54 per day. The manager calculates the profit of the company by subtracting the operating costs from the money he earns from the phone repairs he gives. In a given day, the manager expects to make a profit of at least 893. If the manager gives r phone repairs in a day, which inequality best models this situation?

A promissory note will pay $47,000 at maturity 6 years from now. If you pay $28,000 for the note now, what rate compounded continuously would you earn?

Graph the following quadratic function. f(x) = -x² + 2x - 7 Find the vertex of the function. The vertex is (Simplify your answer. Type an ordered pair.)

Solve. 3≤2x+3≤ 13 Solve the inequality. Select the correct answer below, and if necessary fill in the answer box to complete your choice. A. The solution set is (Type a compound inequality.) B. There is no solution.

3. Which of the following statements about operations with fractions is not correct? Change a mixed number to a fraction first. To divide, flip the second fraction and then multiply. Add and subtract across fractions with different denominators. Multiply across fractions with different denominators.

Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = x³ y = 0 x = 3 (a) the x-axis (b) the y-axis (c) the line x =

You roll two fair dice. If they land with a sum of 7, you get a $10. If they land with a sum of 6 or 8, you get $5. Everything else earns $0. Which of the following would be the highest value you could set the price and the player would still win? $10 $8 $5 $2

Without a calculator, determine whether the following quantities are positive or negative. 1.-51^-60 2. (−71)^8 3. (−67)^-7 4. (-71)⁰ 5.91^-1

A Food Marketing Institute found that 26% of households spend more than $125 a week on groceries. Assume the population proportion is 0.26 and a simple random sample of 192 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.25? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.25. Round the answer to 4 decimal places, pm

Provide an appropriate response. Find the sample standard deviation. 22 29 21 24 27 28 25 36 1.6 4,2 4,8 2.8

Find the slope of the line that passes through (9, 9) and (1,4). Simplify your answer and write it as a proper fraction, improper fraction, or integer.

A garden measures 24 feet by 21 feet, and the owner of the garden wishes to divide the garden into two parts by installing a fence from corner to corner. Find the cost of the total length of the fence if fence costs $2.00 per foot.

There is a competition at the local movie theater for free movie tickets. You must guess all four employees' ages given a few clues. The first clue is that when added together, their ages total 106 years. Kirk is twice ten years less than the manager's age, Brian is 12 years younger than twice the manager's age, and Matt is 6 years older than half the manager's age. What are all four of their ages? It may help to set up four let statements, one for each employee (including the manager).

A business that manufactures small alarm clocks has weekly fixed costs of $4000. The average cost per clock for the business to manufacture x clocks is described by 0.6x + 4000/X a. Find the average cost when x= 100, 1000, and 10,000. b. Like all other businesses, the alarm clock manufacturer must make a profit. To do this, each clock must be sold for at least 50c more than what it costs to manufacture. Due to competition from a larger company, the clocks can be sold for $1.50 each and no more. Our small manufacturer can only produce 2000 clocks weekly. Does this business have much of a future? Explain. a. The average cost when x= 100 is $