Basic Math Questions and Answers

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 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.

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.

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

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?

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.

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.)

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

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).

Marcus needs to bike at least 80 miles this week for his training. If he has already biked 23 miles this week, then how many miles should he bike on each of the 5 remaining days this week?

Tamika finds some nickels and quarters in her change purse. How many coins does she have if she has 10 nickels and 11 quarters? How many coins does she have if she has a nickels and y quarters?

Suppose that $100,000 from a retirement account is invested in a large cap stock fund. After 25 yr, the value is $183,777.11. (a) Use the model A=Pez^rt to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent.

Victor and his sister have both been saving money to help pay for college. Victor deposited $750 at a local bank 3 years ago, earning a simple interest rate of 4% paid upon withdrawal. His sister deposited $800 at a local bank 3 years ago, earning a simple interest rate of 3% paid upon withdrawal. Compare the interest Victor earned after 3 years to how much interest his sister earned after 3 years?

Catherine earns a yearly salary of $75,000. Lola earns a yearly salary of $80,000. Catherine will receive a salary increase of $4,800 per year, and Lola will receive a salary increase of $3,900 per year. Which equation can be used to find n, the number of years it will take Catherine to earn the same salary as Lola? 75,000+ 4,800n = 80,000+ 3,900n 75,000n +4,800 = 80,000n + 3,900 75,000n + 4,800 = 80,000+ 3,900n 75,000n +4,800n = 80,000n + 3,900n

The equation c = 2.5t represents the cost, c, for t tickets to the school play. Does a value of 3.5 for t make sense in this situation? Explain your reasoning.

Use Hooke's Law to determine the work done by the variable force in the spring problem. Four joules of work is required to stretch a spring 0.5 meter from its natural length. Find the work required to stretch the spring an additional 0.40 meter.

Two lines are cut by a transversal. If you want to show that the lines are parallel, which of the following angle pairs would you show to be congruent? I. Alternate interior II. Vertical III. Consecutive interior IV. Alternate exterior V. Corresponding A I, IV, and V only B I and IV only C I, II, and V only D I, III, and V only

What will a $150,000 house cost 10 years from now if the price appreciation for homes over that period averages 6% compounded annually? The future cost of the house will be $ (Do not round until the final answer. Then round to the nearest cent as needed.).

Use your calculator to find the value of y for the system of equations using matrices. 2x - 3y + 2z = 13 3x+y=z=2 3x - 4y - 3z = 1

A radio station claims that the amount of advertising per hour of broadcast time has an average of 12 minutes and a standard deviation equal to 1.2 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 15 minutes. Calculate the z-score for this amount of advertising time. z = 1.15 z = -2.50 Z=-1.15 z = 2.50

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $90 and you pay 70% of the manufacturer's recommended list price. Plan B offers an annual membership fee of $30 and you pay 90% of the manufacturer's recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?

An investment company pays 8% compounded semiannually. You want to have $17,000 in the future. (A) How much should you deposit now to have that amount 5 years from now? (Round to the nearest cent.) (B) How much should you deposit now to have that amount 10 years from now? (Round to the nearest cent.)

What is -9.2(8x-4) +0.7(2+6.3x) simplified? -69.19x-32.39 -69.19x + 38.2 72.2x + 41.21 75x-338.2