Basic Math Questions and Answers

The gravitational force, F. between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut weighs 207 pounds on the surface of the Earth, what will this astronaut weigh 100 miles above the Earth? Assume that the radius of the Earth is 4000 miles. (Round off your answer to the nearest pound.)

Ivan needs to have a toilet repaired in his house. The cost of the new plumbing fixtures is $140 and the labor is $50/hr. (a) Write a model that represents the cost of the repair C (in $) in terms of the number of hours of labor x. The model that represents the cost of repairs is C = 140 + (b) After how many hours of labor would the cost of the repair job equal the cost of a new toilet of $390? It would take hours of labor for the cost of the repair job to equal the cost of a new toilet.

Miguel has two pet reptiles, Gregory the Gecko and Sammy the Snake. Gregory's tail is two-thirds the length of the rest of his body. Altogether, Gregory is 10 inches long. How long are his body and his tail? Body: Tail: Sammy is two and three-fifths times as long as Gregory. How long is Sammy? Sammy is feet inches. How long are Gregory and Sammy together? feet inches

Determine the exact value(s) for which the rational expression f(x) than one value, list them separated by a comma, e.g. x = 2,3.

Use a tape diagram to model each problem. Solve using a simplifying strategy or an algorithm, and write your answer as a statement. Sammy's bucket holds 2,530 milliliters of water. Marie's bucket holds 2 liters 30 milliliters of water. Katie's bucket holds 2 liters 350 milliliters of water. Whose bucket holds the least amount of water?

An amusement park operator is determining the density of people in the Water Park section of its park. They know that there are 5,000 people in the Water Park at noon and that the Water Park covers 25 acres. What is the density of the Water Park at noon? 0.005 acres per person 200 people per acre 40 people per acre 100 people per acre

A snow cone is 5 inches tall with a 3 inch diameter opening. A scoop of shaved ice is approximately a 2 inch diameter sphere. What is the maximum number of scoops of shaved ice that could melt in the cone and not overflow? No scoops; even 1 scoop would overflow if melted Three scoops Two scoops One scoop

An object thrown directly upward is at a height of s= -16t² + 128t+256 feet after t seconds. (a) What is its initial velocity? (b) When does it reach its maximum height? (c) What is its maximum height? (d) When does it hit the ground? (e) With what speed does it hit the ground? (a) The object's initial velocity is ft/sec. (b) The object reaches its maximum height at time t sec (Round to the nearest tenth as needed.) (c) The object's maximum height is s = ft (Round to the nearest tenth as needed.)

Solve by completing the square and applying the square root property. Express the solution set in exact simplest form. Since the variable terms are already isolated on one side of the equation, we are ready to complete the square.

Solve the inequality. Graph the solution set, and write the solution set in set-builder notation and interval notation. Write numbers as simplified fractions or integers.

Solve by using the quadratic formula. Express the solution set in exact simplest form. x²-7x-3=0

Find the quotient and the remainder. Check your work by verifying that (Quotient) (Divisor) + Remainder = Dividend.

Peanut allergies are becoming increasingly common in Western countries. Some evidence points to the timing of peanuts' first introduction in the diet as an influential factor, raising the question of whether pediatricians should recommend early exposure or avoidance. A study enrolled infants with a diagnosed peanut allergy and randomly assigned them to either completely avoid peanuts or consume peanuts in small amounts regularly until they reached 60 months of age. At the end of the study, 18 of the 51 infants who had avoided peanuts were still allergic to peanuts. In contrast, five of the 47 infants who had consumed peanuts were still allergic to peanuts. (a) What are the two variables described? (Select two options.) percentage of peanuts in diet choice of diaper for infants peanut consumption (avoid or consume small amounts) year the study began peanut allergy at 60 months of age (yes or no) current age in months

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