Basic Math Questions and Answers

Complete the statement. If a transversal intersects two parallel lines, then same-side interior angles are supplementary corresponding angles are complementary none alternate exterior angles are supplementary

Find the x & y intercepts. Write the coordinate for each. 2x - 3y = 12 x-intercept: y-intercept

Milan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $114 and allows unlimited mileage. Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.

It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond using a certain bait is f(t)=0.22t+1, for t> 10. Find and interpret f(31). Round your answer to the nearest whole number. A. f(31)= 17 which means that approximately 17 fish can be caught in this pond with this bait in 31 minutes. B. f(31)=8 which means that approximately 8 fish can be caught in this pond with this bait in 31 minutes. C. f(31)=17 which means that approximately 31 fish can be caught in this pond with this bait in 17 minutes. D. 1(31)=8 which means that approximately 31 fish can be caught in this pond with this bait in 8 minutes.

A projectile is launched from ground level with an initial velocity of vo feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s = -16t²+vot. Find the time(s) that the projectile will (a) reach a height of 192 ft and (b) return to the ground when vo= 128 feet per second. (a) Find the time(s) that the projectile will reach a height of 192 ft when vo = 128 feet per second. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. seconds (Use a comma to separate answers as needed.) B. The projectile does not reach 192 feet. (b) The projectile returns to the ground after second(s).

Determine a viewing window that will provide a complete graph of the function. y = 2x4 + 2x³ − 4x² − 3x − 6 A. [-2.2] by [-10,-5] B. [-10,10] by [- 8,8] C. [-3,3] by [-10,5] D. [-5,5] by [-5.5]

Twiigs is an online polling website that allows users to easily create polls and to vote on polls created by other users. A March 2010 poll asked, "Has concern about autism influenced your decision about whether to vaccinate your child?" Of the 182 votes cast, 80% selected "No, I'm not worried about it." Which type of sample was used in this poll? simple random sample stratified random sample multistage random sample voluntary response sample

Complete the sentence below. The polynomial 2x5 -3x4 + 12x3 - 2 is of degree The leading coefficient is

Researchers enrolled a group of 10,892 middle-aged adults and studied them over a period of nine years. They found that smokers who quit had a higher risk for diabetes within three years of quitting than either nonsmokers or continuing smokers. (a) What type of observational study is this? This is a sample survey study. This is a cohort observational study. Actually this is not an observational study, this is a controlled experiment. This is a case-control study. (b) Does this show that stopping smoking causes the short-term risk for diabetes to increase? Should a doctor cite this study to tell a middle-aged adult patient who smokes that stopping smoking can cause diabetes and advise him or her to continue smoking?

We have found f(a+h) = 9a2 + 18ah + 9h² - 11a - 11h + 2 and f(a) = 9a2 - 11a + 2. We utilize these to f(a+h)-f(a), giving the following result. write h f(a+h)-f(a) h = (9a2 + 18ah + 9h² - 11a - 11h + 2) - h

Experiment 1: A study is done to determine which of two fuel mixtures allows a rocket to travel farther over a period of time. Rocket A, which requires additional equipment to keep it stable, is used to test one fuel mixture, and rocket B is used to test the other. Both rockets are identical aside from their mass. The results indicate that rocket B traveled farther than rocket A over the same period of time. Experiment 2: A double-blind experiment is performed to test whether a new drug is effective in lowering blood pressure. A random sample of subjects with high blood pressure is assigned to two groups. One group receives the new drug and the other group does not. Neither group is permitted to take any other medications during the experiment or to change their lifestyles in any way. The results of the experiment show that the drug is effective in lowering blood pressure. Identify the experiment in which confounding occurs and the reason for its occurrence. Experiment 1 has a confounding variable related to the fuel mixtures. Varying the fuel mixture could skew the results of the study and should be kept constant. Neither experiment has a confounding variable. Experiment 2 has a confounding variable related to the type of experiment. A double-blind experiment may increase the risk of the placebo effect and possibly skew the results.

The length, in inches, of a box is 3 inches less than twice its width, in inches. Which of the following gives the length, / inches, in terms of the width, w inches, of the box? F. I = 1/2w + 3 G. I = W+3 H. I= w-3 I. I = 2w + 3 J. I=2w-3

Select the correct answer from each drop-down menu. In a circle with a radius of 7 feet, the radian measure of the central angle subtended by an arc with a length of 4 feet is area of the sector formed by the arc is Assume π = 3.14, and round your answers to the nearest hundredth. square feet.

The mathematical model C(x) = 300x+20,000 represents the cost in dollars for a company to manufacture x items a month. Based on this, how much does it cost to produce 800 items? A. $20,300 B. $16,000,000 C. $260,000 D. $240,000

Aria is ordering a taxi from an online taxi service. The taxi charges $4 just for the pickup and then an additional $1.25 per mile driven. How much would a taxi ride cost if Aria is riding for 2 miles? How much would a taxi ride cost that is m miles long?

State the number of possible real zeros and turning points of f(x) = x² - 6x + 8x5. Then determine all of the real zeros by factoring. 7 real zeros and 6 turning points; 0, 2, and 4 7 real zeros and 6 turning points; 0, –2, and –4 6 real zeros and 5 turning points; 0, 2, and 4 6 real zeros and 5 turning points; 0, -2, and —4

A bike company sells 30,000 bikes in their first year of business. Their business model predicts that sales will increase at 1% each year. How many years after they began business will it take for the company to have sold a total of 200, 000 bikes, (rounding-up to a whole number)?

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