Basic Math Questions and Answers

Cole has a cylinder that fits within a cube. The height and diameter of the cylinder are each equal to x. Each side of the cube is also equal to x. Cole wants to know the volume of water that can be poured inside the rectangular prism yet outside the cylinder. Which expression will help Cole solve for this volume?

For the following compound inequality, give the solution set in both interval and graph form. x+4> 12 or - 2x+325 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer in interval notation.) B. The solution set is Ø.

Chet needs to buy 4work shirts, all costing the same amount. After he uses a $25 gift certificate, he can spend no more than $75. Write an inequality to find the possible costs for a shirt. Identify what your variable represents.

Identify the critical points. Then use (a) the First Derivative Test and (if possible) (b) the Second Derivative Test to decide which of the critical points give a local maximum and which give a local minimum. f(x)=x4-50x²+625 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The function has critical points at x B. The function has no critical points.

There was 1/2 yd of purple and pink striped fabric. Jessie said she could only make 1/24 of a purse using that fabric as the trim. Is she correct? Use what you know about the meanings of multiplication and division to defend your answer.

For the compound inequality, give the solution set in both interval and graph form. 5x-8-33 or 3x+1≤19 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. www. A. The solution set is (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The solution set is Ø.

Approximate the given number (a) rounded and (b) truncated to three decimal places. 68.1688 (a) The given number rounded to three decimal places is (b) The given number truncated to three decimal places is

Solve the inequality algebraically. Express your answer using set notation or interval notation. Graph the solution set. Verify your results using a graphing utility. -6≤10-4x≤7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. The solution is the empty set.

Evaluate the function f(x) = 5x-4 at the given values of the independent variable and simplify. a. f(8) b. f(x+5) c. f(-x)

Haley is responsible for buying a week's supply of food and medication for the pigs and cows at a local co-op. The food and medi each cow costs four times as much as those supplies for a pig. She needs to feed 20 cows and 10 pigs. Her budget is $990. Let represent the cost per pig and c represent the cost per cow. How much does Haley spend on each cow at the co-op?

Let f be continuous on the closed interval [a, b] and differentiable on the open interval (a, b). If f(a) = f(b), then there is at least one number c in (a, b) such that f'(c) As with the application of any theorem to a specific instance, we first check that the initial conditions are met. From the graph and our knowledge of the tan function, we determine that the given function has these qualities. (Select all that apply.) Continuous on the closed interval Differentiable on the open interval Discontinuous on the closed interval Non-differentiable on the open interval

Find the perimeter of the parallelogram with these vertices. (4, 3), (-2, 3), (2,-2), (-4,-2) Give an exact answer (not a decimal approximation). Simplify your answer as much as possible.

Express the set in the simplest interval form. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The set in simplest interval form is B. The answer is the empty set.

Solve the compound inequality. Give the solution set in both interval and graph forms. x<-3 and x>-8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval form is (Type your answer in interval notation.) B. The solution set is Ø.

Rewrite the equation 12x-3y-9-0 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

Use graphs to find the set. (-6,6) n[-1,8] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The set is B. The set is the empty set. (Type your answer in interval notation.)

If we are classifying psychiatric patients as having one or another of five different psychological disorders - major depressive disorder, bipolar disorder, generalized anxiety disorder, obsessive compulsive disorder, and phobic disorder - what kind of measurement scale are we using?

Erica claims if a cylinder has an equal radius and height, and its surface area it 64π square inches, what is its volume? 128π 32π 64π 48π

Rate is inversely proportional to time or a given distance. Samantha drives to work averaging 30 mph for (on way ½ hour. On the way back she travels the same way and does it in 1/3 hour, what is her average rate?

Complete the sentence below. In the expression 35, the number 3 is called the and 5 is called the In the expression 35, the number 3 is called the and 5 is called the

Write the following decimals in expanded notation. Write 1.368 in expanded notation. Write 4.092 in expanded notation. Write 21.98 in expanded notation. Write 90.45 in expanded notation. Write 0.379 in expanded notation.

Sean is shipping a box in the shape of a rectangular prism to his brother at college. The box will need to hold 465 cubic inches. The dimensions of the box need to be such that the length is 2 inches less than 3 times the width and the height is half the width. What is the height of the box that Sean is shipping? 14 inches 3.5 inches 7 inches 19 inches

Solve the following inequality algebraically. Express your answer using set notation or interval notation. Graph the solution set. Verify your results using a graphing utility. 5x-9=11 Express the solution in interval notation. 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 is the empty set.

A company designs a model pyramid with a square base that has side lengths equal to 5 inches and a height of 10 inches. To save costs in production, the lengths of the sides of the base are each reduced by one inch while the pyramid's height remains the same. What are the volumes of the original and the reduced size pyramids? Original volume: 53.3 cubic inches; Reduced volume: 30 cubic inches Original volume: 417.7 cubic inches; Reduced volume: 213.3 cubic inches Original volume: 83.3 cubic inches; Reduced volume: 53.3 cubic inches Original volume: 41.8 cubic inches; Reduced volume: 21.3 cubic inches

Statins are used to keep cholesterol in check and are a top-selling drug in the U.S. The equation: S - 1.7x = 5 gives the amount of sales (S) of statin in billions of dollars a years after 1998. According to this equation, how much will/did people in the U.S. spend on statins in the year 2013? Answer: People in the U.S. will spend billion dollars on statins in 2013.

Sam wants to build a toy box in the shape of a rectangular prism that will hold 36 cubic feet. If the height needs to be 1 foot less than the width and the length is twice the width, find the height of the toy box. Height of 2.5 feet Height of 2 feet Height of 3 feet Height of 4 feet

Find the average rate of change of g(x) = 4x³ + 2 from x = - 4 to x = 3.

A company wants to sell spherical piñatas and will use 3,000 square inches of material for each one. What will be the volume of each piñata in cubic inches? (Use 3.14 for π. Round to the nearest interger at the end of your work.) 1000 15,455 123,609 15.451

To calculate simple average, add all your scores and the sum by the number of exams. Your scores are 82, 75, 85 and 93 out of 100 maximum score. 1. What is your current average for the four exams?

The volume of a prism is given by the formula V = lwh, where I is the length, w is the width, and his the height of the pl a. Solve the formula for 1. b. A prism has a volume of 819 cubic feet, a width of 7 feet, and a height of 9 feet. What is the length of the prism rounded to the nearest foot?

Tell whether the lines are parallel, perpendicular, or neither. Line 1: (4,1) and (3,5) Line 2: (8,6) and (4, 5) Line 1: (-4,-5) and (9,3) Line 2: (3,5) and (-1,2)

How many terms are in this expression? -x³ + 2x² - 3x + 54 A.1 B. 2 C. 3 D. 4

During a 6-hour period, the air temperature at the zoo dropped by 48°F. If the temperature dropped at a steady rate, how much did the air temperature drop each hour? -6°F -12°F -48°F -8°F

Suppose you took 17 credit-hours this past semester, your third semester in college. You earned an A- in psychology (3 hours), a C+ in economics (3 hours), a B+ in chemistry (4 hours), a B in English (3 hours), and a B- in mathematics (4 hours). 8. a. Use the first four columns of the following table to record the information regarding the courses you took. As a guide, the information for your psychology course has been recorded for you.

What is the solution set? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The solution set is (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The solution set is Ø.

Solve the following system of equations using ELIMINATION. 2x + 2y = 34 3x - 4y = -89 Solution: x = y =

For the demand equation, express the total revenue R as a function of the price p per item. 9 = -4p + 80

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?