Basic Math Questions and Answers

For f(x) as given, write the domain of f. f(x)=x +4/3x - 15

Jacob went bowling over the weekend. On Saturday, he bowled at Bowlero, where he rented shoes for $3.25 and paid $3.75 for each game. On Sunday, he bowled at the Cowtown Bowling Center, where he rented shoes for $2.50 and paid $4.00 per game. If he spent the same amount each day, how many games did he bowl? (Let the number of games played = x.)

Nathan has 102 solid-colored.disks that are red, blue, and green. He lines them up on the floor and finds that there are 3 more red disks than blue and 6 more blue disks than green. How many red disks are there? A. 26 B. 29 C. 31 D. 35 E. 38

In a game, Theodore received a handful of coins (pennies, nickels, dimes, and quarters) as a prize. When he got home, he found that he had managed to get $2.09 in change. He noticed that he had three times as many pennies as dimes, one more nickel than dimes, and twice as many quarters as dimes. How many quarters did Theodore get in his prize? F. 4 G. 5 H. 6 J. 7 K. 8

Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.) f(x) = 3x - 6 (a) [0, 3] minimum (x,y)= maximum (x,y)= (b) [0, 3) minimum (x,y)= maximum (x,y)= (c) (0, 3] minimum (x,y)= maximum (x,y)= (d) (0, 3) minimum (x, y) = maximum (x, y) =

After a 25% reduction, you purchase a new television for $198.75. What was the price of the television before the reduction? A) First write an equation you can use to answer this question. Use a as your variable and express any percents in decimal form in the equation. The equation is B) Solve your equation in part [A] to find the original price of the television. Answer: The original price of the television was dollars.

Marco bought pens and pencils with his company's name and website address to give away to people at a festival. He bought a total of 300 pens and pencils together and spent $62.50. If pencils cost $0.15 each and pens cost $0.25 each, how many pens did Marco buy? A. 175 B. 165 C. 140 D. 130 E. 125

Select the correct answer from the drop-down menu. The two diagonals of an inscribed quadrilateral meet at the center of a circle. The quadrilateral must be a square rectangle rhombus trapezoid

Use only the commutative property of multiplication to rewrite the expression - 12(-15) and then simplify. (Hint: You may use either parentheses or an * to indicate multiplication. For example, multiplying 5 and 8 could be written 5(8) or 5*8.) Rewrite using the commutative property: The simplified expression is:

High levels of cholesterol in the blood increase the risk of heart disease. For 14-year-old boys, the distribution of blood cholesterol is approximately Normal with mean mu = 170 milligrams of cholesterol per deciliter of blood (mg/dl) and standard deviation sigma = 30 mg/dl. Estimate the percent of boys whose cholesterol is below 140

Find the average rate of change of g(x) = 2x³ - 4x² between x = -0.8 and x = 0.8. Enter the exact answer. The average rate of change of g(x) between x = -0.8 and x = 0.8 is i

For the function below, give the units for the Average rate of change=f(b)-f(a)/b - a The cost, C = f(w), in dollars of buying a chemical is a function of the weight bought, w, in pounds. The units are

Goro Unoji's job pays him $14.75 an hour for a 40-hour week. He estimates his fringe benefits to be 32% of his yearly wages. His yearly job expenses are estimated to be: union dues, $575; uniforms, $650; commuting costs, $1,294. a. What is Goro's total annual pay? b. What is the amount of his fringe benefits per year? c. What are his total yearly job benefits? d. What are his total yearly job expenses? e. What are his net yearly job benefits?

Rondo earns $3,750 per month. From those wages, $312 in federal withholding. $245.25 in Social Security, $59 in Medicare, $104 in state income taxes, and $23.75 in health insurance are deducted. Find the percentage of gross pay that Rondo takes home to the nearest percent.

Julio Zapata has a job that pays $2,816 a month. He estimates that his fringe benefits are 28% of his annual wages. He also estimates that his yearly job expenses are special tools, $847; union dues, $970; commuting costs, $1,602; uniforms, $450. a. What is Julio's total annual pay? b. What is the amount of his annual fringe benefits? c. What are his total annual job benefits? What are his total annual job expenses? e. What are his net annual job benefits?

Write the sentence as an equation. Let the variable x represent the number. Six less than 5 times a number gives 24.

Ivana Nagy's purchases include a $39.95 blanket, a $24.95 miniblind, an adjustable screen for $15.95, and a 12-foot, eight-outlet power strip for $9.49. The purchases were made in Massachusetts, where the tax rate is 5%. What are the (a) sales tax and (b) total selling price?

Consider the following function. f(x) = (8 - x)(x + 1)² (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) x= (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing decreasing (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = relative minimum (x, y) =

Solve and check the following linear equation. 7x-(3x-8)=36 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. (Type an integer or a simplified fraction.) B. The solution set is {x|x is all real number). C. The solution set is Ø.

Find the derivative of the function. y = 8(5-x²)7

Tomika uses 6 1/9 inches of wire to make a necklace and 3 1/3 inches of wire to make a bracelet. How many necklace and bracelet sets can she make if she uses 28 1/3 inches of wire in all? Enter your answer in the box.

Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator (or computer) to check your work by graphing the curve and estimating the asymptotes. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.)

Use the domain and range of each of the following relations to determine which is a function. {(-4, 3), (-2,-1), (-4, 8)} {(-4, 3), (-2, -1), (-7, 8)} (-4,-2, -7,7} {(-4, 3), (-2, -1), (-2, –8), (-7, 8)}

Find the derivative of the function. f(x) = x³ - 7x² + 6 / x²

Find the second derivative of the function. f(x) = 7x^3/2

a. Rewrite the equation 3x+y+4= 0 in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. a. The slope-intercept form of the equation is y=-3x-4 (Simplify your answer. Use integers or fractions for any numbers in the equation.) b. The slope of the equation of the line is -3 and the y-intercept is (Type integers or fractions.) c. Use the slope and y-intercept to graph the line.

The hard drive on your computer has a capacity of 160 gigabytes (GB). You have used 122 GB. You want to save some home videos to your hard drive. What are the possible sizes of the home video collection you can save? If u represents the amount of space used, write an inequality that determines a, the amount of space available.

The 1st, 5th, and 13th terms of an arithmetic sequence, with common difference d, d # 0, are the first three terms of a geometric sequence, with common ratio r, r ≠ 1. Given that the 1st terms of both sequences is 12, find the value of d and the value of r.

Blake bought a new car and financed $15,000 to make the purchase. He financed the car for 48 months with an APR of 4.5 %. Assuming he made monthly payments. determine the total interest Blake paid over the life of the loan. Round your answer to the nearest cent, if necessary.

Stimulus 4.1 Understanding Systems, Substitution Method Use the system of equations below to answer the following questions. 2x + 3y = 15 x - 3y = 3 Using the equation you chose from part 1, rewrite the equation isolating the variable you determined was the easiest to isolate.

In Jaden's yard, there is a triangular garden patch. He wants to plant a geranium in the patch at a point equidistant from all its vertices. Where should Jaden plant the geranium? A in the center of the inscribed circle of the triangle B. in the center of the circumscribed circle of the triangle C. at the point of intersection of the angle bisectors of the triangle D. at the point of intersection of an angle bisector and a perpendicular bisector of the triangle

Find the second derivative of the function. f(x) = CSC X

What is 7,000,000+ 900,000+20,000 + 7,000 + 400 + 40 + 2 in standard form?

In Lixue's garden, the green pepper plants grew 5 inches in month. At this rate, how many feet can they grow in one month? (Let 5 inches = 5/12 feet)

Lin spent 80 minutes doing homework on Monday. Each day from Tuesday through Friday, Lin spent half as much time doing homework as the day before. How much total time did Lin spend doing homework, from Monday through Friday? Explain how you know.

Bucky's hourly wage is $18 and his net pay is 78% of his earnings. Bucky spends about $2,000 on his monthly expenses. If Bucky works 40 hours per week and has no other sources of income, what is his total monthly cash inflow? (Hint 1: Assume that there are 4 pay periods per month) (Hint 2: Read the question carefully)

Bob Ross bought a Blackberry on the Web for $90.69. He saw the same Blackberry in the mall for $119.76. How much did Bob save by buying on the Web? (Round your answer to the nearest cent.)

Mark Ogara rented a truck from Avis Rent-A-Car for the weekend (2 days). The base rental price was $30.75 per day plus 16.5 cents per mile. Mark drove 418.85 miles. How much does Mark owe? (Round your answer to the nearest cent.)

Roger bought season tickets for weekend games to professional basketball games. The cost was $945.70. The season package included 46 home games. a. What is the average price of the tickets per game? b. Marcelo, Roger's friend, offered to buy four of the tickets from Roger. What is the total amount Roger should receive?

Write the equation of the line with slope 1/7 and y-intercept 6. The equation of the line is (Simplify your answer. Type an equation using x and y as the variables. Use integers or fractions for any numbers in the equation.)

You give up a full time salary of $58,000 a year to go to school for 2 years. The total cost of going to school is $32,000. If you want to be able to recover your investment in 4 years or less, what is the minimum salary you would need to earn upon earning your degree?

Write the equation of the line with slope 8 and y-intercept 1/9 The equation of the line is (Simplify your answer. Type an equation using x and y as the variables. Use integers or fractions for any numbers in the equation.)

Find the derivative of the exponential function. y = x²e^-5x

The following data show the lengths of boats in a marina. A) Provide the 5-Number-Summary of the Data in the textbox given below.

Find the average rate of change of g(x) = 2x³ - 3x² between x = 3 and x = 5. The average rate of change of g(x) between x = 3 and x = 5 is

A scientist needs to make 5.4 liters of saline solution (salt water), in which the salt level must be at 28% concentration (meaning 28% of the water is salt). Unfortunately, the scientist only has two types of saline solution in his possession. He has saline solution with a 12% concentration level and saline solution with a 30% concentration level. How much of each type of saline solution should the scientist mix together to achieve 5.4 liters of saline solution at a concentration level of 28%? Let x represent the amount 12% saline solution and let y represent the amount of 30% saline solution. Determine how many liters of each should be mixed to get the desired solution. *Enter a numerical value only. The amount of 12% saline solution needed is liters and the amount of 30% saline solution needed is

Which question is a statistical question? How many students are in Mrs. Johnson's math class? How old is a typical student in the school? How many students are on the basketball team? How old are you?

The flag of Colombia is a rectangle that is 6 ft long with three horizontal strips. The top stripe is 2 ft tall and is yellow. The middle stripe is 1 ft tall and is blue. The bottom stripe is also 1 ft tall and is red. a. Create a scale drawing of the Colombian flag with a scale of 1 cm to 2 ft. b. Create a scale drawing of the Colombian flag with a scale of 2 cm to 1 ft.

Fred and Winnie O'Callahan have put themselves on a very strict budget. Their goal at the end of the year is to buy a car for $14,100 in cash. Their budget includes the following per dollar: Fred earns $2,190 per month and Winnie earns $2,770 per month. After 1 year will Fred and Winnie have enough cash to buy the car?

Gracie went to Home Depot to buy wall-to-wall carpeting for her house. She needs 104.86 square yards for downstairs, 17.43 square yards for halls, and 168.71 square yards for the upstairs bedrooms. Gracie chose a shag carpet that costs $13.98 per square yard. She ordered foam padding at $2.78 per square yard. The installers quoted Gracie a labor cost of $5.78 per square yard in installation. What will the total job cost Gracie? (Do not round intermediate calculation. Round your answer to 2 decimal places.)