Math Questions

Drag a value, coordinates, equation, or word to the boxes to correctly complete the statements. Gayle identifies that the vertex of the parabola is! units away from the vertex. The directrix is (3,-1) The directrix of the equation is! (3, 2) Gayle plots the vertex and focus, and graphs the directrix as a dashed line. She then draws the parabola so that the focus sits inside the curve and the directrix does not intersect it.

In a class of 26 students, 17 have a brother and 12 have a sister. There are 5 students who do not have any siblings. What is the probability that a student has a brother given that they have a sister?

The faces of a fair cube are numbered 1 through 6; the probability of rolling any number from 1 through 6 is equally likely. If the cube is rolled twice, what is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll?.

Let a, b, c, d are an increasing A.P. with integer terms and d = a² + b² + c2², then Common difference of A. P. is 2 The value of a + 2b + 3c+4d is 10 The value of 4a + 3b+2c + d is zero Common difference of A.P. is 1

A new computer graphics company employs 10 programmers. The company decides to expand into digital animation and needs to transfer 3 of the programmers into the new department. How many different combinations of 3 programmers can be chosen to transfer to the new department

A particle is moving along a straight line such that the distance traveled (in feet) after t seconds is given by the function s(t) = 8t² + 40t. At t = 6 seconds, what is the velocity of the particle?

A species of snakes studied in a certain area in South America has some exceptionally large individuals, for some reason yet unknown to scientists. The weights of the studied population are strongly right-skewed with mean 36 kg and standard deviation 7 kg. A random sample of 75 snakes is taken. What is the probability that the mean weight of the sample is greater than 37 kg? 0 0.1075 0.4432 cannot say

The water in a pool is evaporating at a rate of 3% per day. If the pool has 21,200 gallons in it today, how many gallons will it have in 10 days? Round your answer to the nearest whole number, if necessary. Answer How to enter your answer (opens in new window) 2 Points

When Bill makes a sandwich, he may choose from among 3 kinds of rolls, 4 varieties of meat, and 2 types of sliced cheese. If he chooses one roll, one meat, and one type of cheese, how many different kinds of sandwiches can he make? (A) 9 (B) 14 (C) 24 3x-420 (D) 288

A carpenter is creating two new templates for his designs. One template will be in the shape of a right triangle, where the longer leg is three inches more than three times the shorter leg. The second template will be in the shape of a rectangle, where one side length is one inch less than three times the length of the triangle's shorter leg, and the other side length is one inch more than twice the width. The carpenter needs the lengths of both diagonals to be the same. Write a system of equations to represent this situation, where y is the length of the diagonals, and x is the shorter leg of the triangle. Which statement describes the number and viability of the system's solutions? A. The system has two solutions, and both are viable because they result in figures with only positive side lengths. B. The system has two solutions, but only one is viable because the other results in a figure with negative side lengths. C. The system has only one solution, and it is viable because it results in a figure with only positive side lengths. D. The system has only one solution, but it is not viable because it it results in a figure with a negative side length.

Karla wants to save up for a prom dress. She figures she can save $9 each week from the money she earns babysitting. If she plans to spend less than $150 for the dress, how many weeks will it take her to save enough money to buy any dress in her price range?

As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 150 milligrams of Medication A with 45 milligrams of Medication B. However this week, the doctor said to only use 6 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?

be worth more or less (including zero) depending on your answer. Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $50, and then they charge her $8 per hour. She has $150 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.) 12 hours 18 hours 13 hours 12.5 hours

You and your classmates create 25 self-portraits to sell at the PTA auction to raise money for your school. In order to pay for the materials you bought to make the self-portraits, you need to sell each of the self- portraits for $1.00. When transporting the self-portraits to the auction, one of your parents accidentally drops three of the self-portraits in the street and they are run over by a school bus. What is the new minimum price you need to set for the remaining self-portraits in order to pay for the materials?

A group of Mathematics faculty at the local college consists of 9 women and 9 men. Five people are to be selected to go to a conference. How many different ways can a group of five people be selected from this group of 18? In how many ways can five women be chosen from the group of 9 women? What is the probability that all women will be chosen to attend the conference? Enter a reduced fraction or decimal.

Kala paid $14.75 for a 2.12-pound bag of shrimp at one store. The following week, she paid $24.99 for a 3.77-pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent. Unit price for the 2.12-pound bag: per pound Unit price for the 3.77-pound bag: per pound The better buy: The 2.12-pound bag The 3.77-pound bag Neither (They have the same unit price)

Find all zeros of f(x) = x³ + 2x² - 6x - 4. Enter the zeros separated by commas. Enter exact value, not decimal approximations.

- Manuel bought 9 pounds of apples. He has eaten 3/4 of a pound so far and has $15 worth of apples left. Write and solve an equation to find the cost of the apples per pound to the nearest dollar. How much did the apples cost per pound?

Arianna invests $5500 in a new savings account which earns 5.6 % annual interest, compounded daily. What will be the value of her investment after 7 years? Round to the nearest cent.

Some species of eagles have been fighting extinction due to environmental hazards such as DDT, PCBS, and dioxin. The problem is with the food chain. Fish or rodents consume contaminated food and/or water. Then the eagles ingest the poison, which in turn affects the durability of the eagles' eggs. It takes only 44 parts per million of certain chemicals to ruin an eagle egg; write this number as a fraction in lowest terms.

A jewelry store sells 168 diamond bracelets per month at $1100 each. The owners estimate that for each $55 increase in price, they will sell 6 fewer diamond bracelets per month. Find the price per diamond bracelet that will maximize revenue.

Four coins are tossed several times. Which of the following represents the outcome on a coin that may not be fair? 1st coin is tossed 50 times and gives 24 heads and 26 tails. 2nd coin is tossed 250 times so that P(heads) = 0.25. 3rd coin is tossed 16 times and gives P(tails) = 9/16 4th coin is tossed 25,000 times and gives 12,505 heads.

A damsel is in distress and is being held captive in a tower. Her knight in shining armor is on the ground below with a ladder. When the knight stands 15 feet from the base of the tower and looks up at his precious damsel, the angle of elevation to her window is 60 degrees. How long does the ladder have to be?

You work as a cashier for a grocery store and earn $5 per hour. You also mow lawns and earn $10 per hour. You want to earn at least $50 per week, but would like to work no more than 10 hours per week. Which system of inequalities, along with y 20 and x20, would you use to solve the real-world problem?

Find the GCF of the given list. x16y5, xy5, x7y8

State the domain and range for the following relation. Then determine whether the relation represents a function. {(3, 1), (4,-1), (5, 1), (6,-1)} The domain of the relation is. (Use a comma to separate answers as needed.) The range of the relation is. (Use a comma to separate answers as needed.) Does the relation represent a function? Choose the correct answer below. A. The relation is a function because there are no ordered pairs with the same first element and different second elements. B. The relation is a function because there are no ordered pairs with the same second element and different first elements. C. The relation is not a function because there are ordered pairs with 1 as the second element and different first elements. D. The relation is not a function because there are ordered pairs with 3 as the first element and different second elements.

Find the average rate of change of f(x) = 2x² +5 over each of the following intervals. (a) From 4 to 6 (b) From 2 to 0 (c) From 0 to 3 (a) The average rate of change from 4 to 6 is. (b) The average rate of change from - 2 to 0 is (c) The average rate of change from 0 to 3 is

Explain what "80% confidence" means in a 80% confidence interval. What does "80% confidence" mean in a 80% confidence interval? OA. The confidence interval includes 80% of all possible values for the parameter. OB. The value of the parameter lies within 80% of a standard deviation of the estimate. OC. The probability that the value of the parameter lies between the lower and upper bounds of the interval is 80%. The probability that it does not is 20%. OD. If 100 different confidence intervals are constructed, each based on a different sample of size n from the san population, then we expect 80 of the intervals to include the parameter and 20 to not include the parameter.

Decide on the procedure to solve the triangle given the following information, then solve the triangle. a = 50.39, b = 37.46, c=66.07 Which of the following procedures should be used to solve the triangle? A. Use the law of cosines to find the third side and the law of sines to find the smaller of the two remaining angles. Use the angle sum formula to find the remaining angle. B.Use the law of cosines to find the largest angle. Use the law of sines to find either remaining angle. Use the angle sum formula to find the remaining angle. C.Use the angle sum formula to find the remaining angle and the law of sines to find the remaining sides. OD. Use the law of sines to find an angle. Then use the angle sum formula to find the remaining angle. Use the law of sines to find the remaining side. Solve the triangle ABC. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Do not round until the final answer. Then round to the nearest minute as needed.) OA. There is one triangle and A = OB. There are two triangles A₁ = OC. There is no triangle. ...... 1 B= B₁ = and C= 1°₁ C₁ = A₂ = B₂= }', C₂ = '.

The marginal revenue function for Hedgemony, a bush planting service, is given by r(x) = 31 - 0.2x dollars per plant, when x bushes are planted. Find the change in revenue for the first 97 bushes planted. (Round your answer to the nearest cent.)

Your alpha level is 0.05. The probability of observing two sample means that you have gathered if the means of the population are the same is 0.04. Which statement below is true? You will accept that the null hypothesis that the means of the populations are the same. You will reject the null hypothesis that the means of the population are the same. There is no conclusion you can make in this situation. Reject both the null and the alternate hypothesis.

Situation: A 50 gram sample of a substance that's used to treat thyroid disorders has a k- value of 0.1113. N = Noe^-kt No initial mass (at time t = 0) N = mass at time t k = a positive constant that depends on the substance itself and on the units used to measure time t = time, in days Find the substance's half-life, in days. Round your answer to the nearest tenth. Enter the correct answer.

A manufacturer produces three products, A, B, and C. The profits for each unit of A, B, and C sold are $1, S2, and $3, respectively. Fixed costs are $17,000 per year, and the costs of producing each unit of A, B, and C are $4, $5, and $7, respectively. Next year, a total of 8000 units of all three products is to be produced and sold, and a total profit of $12,000 is to be realized. If total cost is to be $54,000, how many units of each of the products should be produced next year?

Enrico deposited $2000 in a savings account. Each month he will deposit an additional $25. Which kind of function best models the relationship between time and the total amount in the savings account? Choose 1 answer: Linear Exponential

In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2,..., 36. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot the ball falls into matches the number you selected, you win $35; otherwise you lose $1. Complete parts (a) through (g) below. (a) Construct a probability distribution for the random variable X, the winnings of each spin. x P(x) 35 -1 (Type integers or decimals rounded to four decimal places as needed.)

A machine is valued at $10,000. If the depreciation at the end of each year is 20% of its value at the beginning of the year, find its value at the end of 4 years.

The mean wage at a company is $25 an hour with a standard deviation of $3 an hour. What is the probability that a worker earns between $22 and $34 an hour? Use the 68-95-99.7 normal distribution curve.

Peter wants to buy a sandwich. He can make his sandwich with sourdough, Italian, or whole wheat bread. He can choose turkey, ham, or salami. Each sandwich comes with either Provolone or American cheese. In how many possible ways can Peter make his sandwich if he chooses one item from each group? 6 8 9 18

Consider the following function and express the relationship between a small change in x and the corresponding change in y in the form dy = f'(x)dx. f(x)=e8x

The function y = -16x² + 36 represents the height y (in feet) of an apple a seconds after falling from a tree. Find and interpret the x- and y-intercepts. The x-intercept is x = This means the apple hits the ground after seconds. The y-intercept is y=. This means the apple fell from a height of feet.

Suppose there are two routes from North Point to Boulder Creek, four routes from Boulder Creek to Beaver Dam, four routes from Beaver Dam to Star Lake, and three routes directly from Boulder Creek to Star Lake. (Hint: Draw a sketch. Assume each route can pass through a city at most one time.) (a) How many routes from North Point to Star Lake pass through Beaver Dam? To answer this question, think of creating a route from North Point to Star Lake that passes through Beaver Dam as a 3-step process. Step 1: Choose a route from North Point to Step 2: Choose a route from Step 3: Choose a route from Beaver Dam to Star Lake. There are 2__choices for step 1, 4__to Beaver Dam. (b) How many routes from North Point to Star Lake bypass Beaver Dam? choices for step 3. Thus, the answer is 32

A company estimates that the marginal cost (in dollars per item) of producing x items is C'(x) = 1.7 -0.008x. If the cost of producing one item is $754, find the cost of producing 154 items. (Round your answer to the nearest cent.)

Andrew Merrill, owns a mobile sandwich and pretzel stand. Andrew borrows $5,200 for 135 days at ,9% ordinary simple interest. What total will Andrew need to repay for both interest and principal? (Use a 360-day year.) $175.50 $5,300.50 $5,375.50 $5,373.10

Sketch the region enclosed by x + y² = 2 and x + y = 0. a) Favoring convenience, should you integrate with respect to x or y? b) What are the limits of integration? lower limit and upper limit c) Find the area of the region by integrating.

Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 4.25% compounded quarterly. The annual percentage yield is %. (Do not round until the final answer. Then round to two decimal places as needed.)

A beverage company tested a new flavor of fruit drink on a random, representative sample of consumers. The company found that 47 percent of consumers surveyed liked the new flavor, with a margin of error of 6 percent. Which of the follow- ing is the most appropriate conclusion about how consumers in general will like the new flavor? A) More than half of consumers will dislike the new flavor. B) The researchers who conducted the sampling are between 41% and 53% certain that customers will like the new flavor. C.) It is likely that the percentage of consumers who like the new flavor will be between 44% and 50%. D.) It is likely that the percentage of consumers who like the new flavor will be between 41% and 53%

Jack bought a car for $17,500. The car loses $750 in value each year. Which equation represents the situation? an 18250n - 750 an= 750n + 18250 an = 18250n + 750 an= -750n + 18250

In a piano recital, Toby has to perform one piece from each era of western classical music. There are eight pieces from the Baroque period, five pieces from the Classical period, and six pieces from the Romantic period to choose from. How many possible choices could Toby perform in his recital? 40 48 200 240

Using data starting with 1950 and projected to 2050, the number of women (in millions) in the workforce is given by the function P=0.79x+20.86, where x equals the number of years after 1950. (a) Find the value of P when x=65. Explain what this means. (b) What value of x represents 2030? Use the model to find the number of women in the workforce in 2030. (a) The value of P when x= 65 is million. (Type an integer or decimal rounded to two decimal places as needed.) What is the meaning of this value of P? A. The value of P represents the number of women who will join the work force between the years 1950 and 2015. B. The value of P represents the number of women in the workforce in the year 1965. C. The value of P represents the number of women who will join the work force between the years 1900 and 1965. D. The value of P represents the number of women in the workforce in the year 2015. (b) The value of x that represents 2030 is x = The number of women in the workforce in 2030 will be million. (Type an integer or decimal rounded to two decimal places as needed.)

Inverse variation can be applied in physics. The relationship between wavelength and frequency of light are closely related. The equation λv=c where λ is the wavelength, v is the frequency and c is the speed of light represents the relationship between wavelength and frequency of light. When written as an inverse variation equation, we can write λ=c/v or we can write v=c/λ In this formula, which variable represents the constant of variation k? Is it logical that this variable represents the constant of variation? Explain your answer.