Basic Math Questions and Answers

Solve the equation 5(5x-1)= 75. Be sure to check your proposed solution by substituting it for the variable in the original equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. (Simplify your answer.) B. All real numbers are solutions. C. The equation has no solution.

A movie theater charges $6.00 for adults and $2.00 for senior citizens. On a day when 320 people paid for admission, the total receipts were $1116 How many who paid were adults? How many were seniors? There were adults and senior citizens.

If a pair of sunglasses costs x dollars, the expression x + 0.11(x) means "increase the price of the sunglasses by 11%. What is another expression for the sale price? 11x 1.1x 1.11x 0.11x

If Maria designs a function to predict the amount of revenue, r, generated as a function of the number of people, n, who attend a fundraiser, explain why 13.5 would not be a member of this function's domain?

Find the average rate of change of g(x) = 3x³ The average rate of change of g(x) between x = -0.8 and x = 0.8 is

Express the set in the simplest interval form. (-∞, -5]∩[-7,∞) 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 (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The answer is the empty set.

Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (2x+6)(x+6)

Point P has coordinates (-2.5, 3). Point Q is a reflection of point P across the x-axis. What are the coordinates of point Q? Which quadrant is it in? Draw a graph to show how you know.

The length of a rectangle is 3 yd more than twice the width x. The area is 377 yd². (a) Write an equation in terms of x that represents the given relationship.

An object thrown directly upward is at a height of s= - 16t² +96t +288 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= (Round to the nearest tenth as needed.) (c) The object's maximum height is s = (Round to the nearest tenth as needed.)

Fernando invested money in a 3-yr CD (certificate of deposit) that returned the equivalent of 4.1% simple interest. He invested $2000 less in a 30-month CD that had a 2% simple interest return. If the total amount of interest from these investments was $592.00, determine how much was invested in each CD.

I am going to invest my money into two different accounts. The first account gives 4% interest. The second account gives 8% interest. I have $100,000 to invest. After 1 year, I have $6800 in interest. How much did I invest into each account?

Solve the equation. 1/3-2/3c=4/c The solution set is all real numbers. The solution set is the empty set, {}. The solution set is a finite set. The solution set is

Use the Pythagorean Theorem and the square root property to solve the following problem. Express your answer in simplified radical form. Then find a decimal approximation to the nearest tenth. A rectangular park is 9 miles long and 3 miles wide. How long is a pedestrian route that runs diagonally across the park? miles long. In simplified radical form, the pedestrian route is Rounded to the nearest tenth, the pedestrian route is miles long.

The density of quartz is 2.65 grams per cubic centimeter. If you find a piece of quartz that measures 60 cubic centimeters, how many grams of quartz did you find? 159 grams 0.04 grams 15.9 grams 22.6 grams

Suppose a survey of 1000 students is obtained from a college whose population is 10,000 students. The sample was obtained by selecting at random from the population without replacement, meaning that no student could be selected twice. This survey represents a sample that is not random because the probability of being selected depends on the previous selections. a sample that is not random because the probability of selecting each student is 1/10,000 a random sample because the sample size is large relative to the population. a random sample because each student is unique and cannot be selected more than once. a random sample because the probability of selecting any one particular student is equal to the probability of selecting any other particular student.

One safe investment pays 8% per year, and a more risky investment pays 14% per year. a. How much must be invested in each account if an investor of $94,000 would like a return of $8,780 per year? b. Why might the investor use two accounts rather than put all the money in the 14% investment? a. is invested in the 8% account.

A beverage company is creating a can to hold 25 cubic inches of diet cola. What is the radius of the can that will use the minimum amount of material? radius 1.6 inches radius= 1.3 inches radius = 1.1 inches radius= 0.9 inches

Jotham needs 24 liters of a 60% alcohol solution. He has a 10% and a 90% solution available. How many liters of the 10% and how many liters of the 90% solutions should he mix to make the 60% solution?

Factor the polynomial by removing the common monomial factor. x6 + x5 +X Select the correct choice below and, if necessary, fill in the answer box within your choice. A. x6 +x+x= B. The polynomial is prime.

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?