Math Questions

The difference of two numbers is 5 and the sum of their squares is 53. Find the numbers. List any unique pairs of numbers that satisfy the given conditions. (Type an ordered pair, with the larger number listed first. Use a comma to separate answers as needed.)

Gail, Lucas, and Joel are playing a number game where they must draw a card with a number on it. Then they compare the numbers on the cards. Gail's, Lucas's, and Joel's cards are shown. Gail's Number Card 673.89 Lucas's Number Card 739.86 Joel's Number Card 768.98 Lucas says that the value of the digit 9 in his number is 10 times greater than the value of the digit 9 in Gail's number. Is Lucas's statement correct? Explain why or why not.

According to statistics, a person will devote 35 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 19. Over the lifetime, how many years will the person spend on each of these activities? The person will spend years watching TV and years sleeping. (Type whole numbers.)

An arrow is propelled upward. It is s(t) = - 16t² + 80t + 490 feet off the ground after 1 seconds. Find the velocity of the arrow at 3 seconds. Give appropriate units with your answer. C) 16 ft/s D) 32 ft/s A) - 16 ft/s B) -32 ft/s

Exponential Equations Exponential Equation: y =ab² Continuous Compounding: A =Pert In 2011, there were 8500 cell phone subscribers in Rochester. The number of people getting new cell phone services increased by 28% each year for the next t years. What is the equation that represents the situation?

You are taking out a mortgage to buy a home. After the down payment, you need to borrow $320, 000.If a bank offers you a loan at 5.34 % for 25 years, how much will your monthly payment be? How muchwill you pay in interest? Your monthly payment will be $ 3916.17 x dollars You will pay a total of $ 854851 x in interest

Given the function f(x) = x² - 13x + 40, what is its vertex?

Which of the following would be considered a strength of cross-sectional studies? Select the best answer. Precise measurement is usually possible. They can detect patterns of behavior using relatively few participants. They are inexpensive and require less time investment for researchers and participants.

A bucket on Bridget's porch holds 21/2 cups of water and collects 1/5 cup of rainwater each minute. A bucket on Cassie's porch is empty but collects 1/3 cup of rainwater each minute. Which inequality could be used to determine the number of minutes it would take for Cassie's bucket to have more water than Bridget's bucket?

The Jones want to save $69,000.00 in 5 years for a down payment on a house. If they make monthly deposits in an account paying 5% compounded monthly, what is the size of the payments that are required to meet their goal?

A business pays $68 for a car seat and wants a 24% markup for operating expenses as well as a 6% markup for profit. However, customers think the car seats are ugly, so they are not selling. Management reduces the price of each car seat by $30 to get rid of them. Find: A. the selling price $ B. the reduced price $ C. the percent markdown D. Which one, profit, operating loss, or absolute loss? E. What is the amount of profit, operating loss, or absolute loss? $

A parabola has a vertex at (-1, -2) and opens down. Which of the following equations could represent the equation of this parabola in vertex form? y=2(x+1)2-6 y=-2(x+1)²-6 y= 1/3 (x+1)²-6 y=-6(x+1)²-2

A recent report indicated that twenty percent of the households in a certain community speak a language other than English at home. A reporter will randomly select a household from the community until the first household that speaks a language other than English at home is selected. Let random variable L represent the number of attempts needed until the first household that speaks a language other than English at home is selected. The random variable L has a geometric distribution with p=0.22. What is the expected number of attempts needed until the first household that speaks a language other than English at home is selected?

Nell donated 30 notebooks to a local school and Ronald donated 20 notebooks. Of the donated notebooks, 16 of Neil's notebooks were wide-ruled and 12 of Ronald's notebooks were wide-ruled. Charmaine will randomly choose a notebook from a box containing either Neil's or Ronald's donated notebooks. If she wants to pick a wide-ruled notebook, which box should she choose from? A. Charmaine is equally likely to choose a wide-ruled notebook from Ronald's box or Neil's box. B. There is not enough information to determine whose box Charmaine should choose. C. Neil's box D. Ronald's box

Boris plays a game of tennis. He serves from the base line to his opponent, Steffi. The path of the ball may be modelled by the quadratic curve H(x) = 2.103 +0.1455x -0.01932x² for 0 ≤ x ≤ X. a Find the maximum height of the ball during its motion. (2 marks) b The height of the net is 1.07 m. Boris is standing on the baseline of the court, at a horizontal distance of 11.98 m from the net. Show that the ball just passes over the net. c Suggest a maximum value for X and explain why this would be a sensible value to take.

Ms. Kelly's daughter has 8 stuffed animals that she absolutely loves. a) She is allowed to bring one stuffed animal to school each day for three days in a row. In how many ways can choose to bring her toys? b) She is lining her toys up for a picture, in how many ways can she line up all her toys? c) She is playing "princess" and is using three of her toys as characters. In how many ways can she assign the roles, King, Queen, and Knight? d)While going on vacation she is allowed to bring three stuffed animals with her. In how many ways can she select the toys to bring?

Use a finite sum to estimate the average value of f on the given interval by partitioning the interval into four subintervals of equal length and evaluating f at the subinterval midpoints. f(x)= x³ on [2,4] The average value is. (Type an integer or a simplified fraction.)

The mean of the deviations can not be a measure of dispersion because _________ if a data point is less than the mean X, then the deviation is negative if the data points are more consistent, then it is smaller it is always 0 the sum of the deviations is negative

Approximate the following number using a calculator. 6-2.1

Solve the exponential equation. Write the exact solution and the approximation to the 4 decimal places. Type "DNE" if there is no solution. 109x-9 = 5 1) Exact solution: 2) Approximation:

Car A is traveling at a speed of 61 mph and is increasing its speed 0.2 mph each second. Car B is traveling at a speed of 75 mph and is decreasing its speed 0.5 mph each second. After how many seconds will the cars be traveling the same speed, and how fast will they be going? After 10 seconds, the cars will both be traveling at 66 mph. After 65 seconds, the cars will both be traveling 20 mph. After 18 seconds, the cars will both be traveling at a speed of 70 mph. After 20 seconds, the cars will both be traveling at 65 mph.

To be used safely, a ladder should make no more than a 70° angle with the ground. What is the maximum height a 32 ft ladder can reach? Round answer to the nearest tenth Max height=

In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.4 and a standard deviation of 1.8. Answer parts (a)-(d) below. (a) Find the probability that a randomly selected study participant's response was less than 4. The probability that a randomly selected study participant's response was less than 4 is. (Round to four decimal places as needed.)

The winner of a 10-mile bicycle race finishes 10 minutes ahead of a teammate and travels, on average, 10 miles per hour faster than the teammate. Find the average speed of each racer.

Consider the function f(x)=-42+2 on the interval (0, 4) Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0 Find all such values c and enter them as a comma-separated list. Values of c

A company produces two types of TV stands. Type I has 6 drawers. It requires 3 single drawer pulls and 3 double drawer pulls. The company needs 75 hours of labor to produce the Type I TV stand. Type II has 3 drawers. It requires 6 single drawer pulls. The company needs 50 hours of labor to produce the Type II TV stand. The company only has 600 labor hours available each week, and a total of 60 single drawer pulls available in a week. For each Type I stand produced and sold, the company makes $200 in profit. For each Type II stand produced and sold, the company makes $150 in profit. Part A Identify the constraints as a system of linear inequalities. Let x represent the number of 6 drawer TV stands produced and let y represent the number of 3 drawer TV stands produced.

Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function. If there are multiple values, separate them with commas; enter N if there are no such values. f(x) = x² - 4x + 1, [0,4]

Eddie found a store that sells cell phone cases for $18.50 plus $0.15 per letter engraved on the case. A second store sells cases for $18.00 plus $0.25 per letter engraved on the case. How many letters would Eddie have to engrave on his case for it to cost the same at either store? 5 letters 50 letters 7 letters 10 letters

The data manager for a state political party gathered data to determine how many citizens would support the party's senate candidate. He polled citizens in 30 similarly sized senate districts and found a sample mean of 70,438 citizens. Statewide data shows that the population standard deviation is 645.3. What is the approximate 90% confidence interval for this situation? 70,134 and 70,742 70,403 and 70,473 70,244 and 70,632 70,207 and 70,669

Select the correct answer from each drop-down menu. Marjory works at a commercial bakery. She is conducting an experiment to test the results of two yeast activators for making bread. The Rapid Prove activator claims to increase the rise of dough by at least 30%. The Quick Rise activator claims to increase the rise of dough by at least 26%. Marjory and her team bake 60 loaves of bread, 30 using the Rapid Prove activator and 30 using the Quick Rise activator. After the loaves were baked, Marjory evaluated the rise of the breads as compared to previous doughs with no activator used. She reported that, on average, the rise of those made with the Rapid Prove activator increased by 25% and the rise of loaves made with the Quick Rise activator increased by 28%. The Rapid Prove activator claim is The Quick Rise activator claim is The activator is more effective because the increase in rise was ✓that of the other activator.

Find the exact value of the logarithm without using a calculator. log 5 125

A researcher for a travel company is looking into the prices people are willing to pay for airplane tickets. The company has communicated that the overall population mean is $265 with a standard deviation of $40.93. The researcher has a sample of 130 ticket purchases from one location By the Central limit theorem, which interval can the researcher be 95% certain that the sample mean will fall within? A. $264.37 and $265.63 $254.23 and $275.77 $261.41 and $268.59 $257.82 and $272.18

Which statement about the graph of y = 8(0.25)x is true? F The coordinates of the x-intercept are (0.25, 0). G The coordinates of the y-intercept are (0, 8). H The equation of the asymptote is x = 0. J The graph includes the point (2, 1).

If 26200 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent. (a) Annual: $ (b) Semiannual: $ (c) Monthly: $ (d) Daily: $

What is the image point of (9, 0) after a translation left 2 units and up 5 units?

What is the solution to the following system? 3x+3y+6z=9 x+3y+2z=5 3x+12y+ 12z = 18 (3, 1, 0) (0, 1, 0) (2, 1, 0) (-2, 1, 0)

In order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the average time it takes to replace a fuel pump in a car. How large a sample must he select if he wants to be 99% confident that the true average time is within 15 minutes of the sample average? Assume the standard deviation of all times is 30 minutes. 27 5 26 6

A student took out a simple interest loan for $2200 for 2 years at an annual rate of 5.6%.. (a) What is the interest on the loan? $ (b) How much will the student have to repay at the end of 2 years? $

Susan is conducting a survey about the electric bills of households in her city. From the electric company, she found that the population mean is $98.75 with a standard deviation of $10.45. Susan has a sample size of 60. Complete the equation that Susan can use to find the interval in which she can be 68% sure that the sample mean will lie. 88.3 10.45 7.75 109.2 60 98.75

-X Answer the following questions about the function whose derivative is f'(x) = (x+3) e ¯X. a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values? a. Find the critical points, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical point(s) of f is/are x = (Simplify your answer. Use a comma to separate answers as needed.) B. The function f has no critical points.

Convert the complex number 1 - 8i into polar form. Express the angle using degrees over the interval 0° ≤ 0 < 360°. You may round the argument to the nearest tenth of a degree (if necessary), but you must express your modulus in it's exact form.

Find the open intervals on which the function h(x)= x³ + x² is increasing and decreasing. Identify the function's local and absolute extreme values, if any, saying where they occur. (a) On what open interval(s), if any, is the function increasing? Select the correct choice below and fill in any answer boxes within your choice. A. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The function is never increasing.

The parent function f(x) = x² is reflected across the x-axis, vertically stretched by a factor of 3, and translated right 7 units to create g. Use the description to write the quadratic function in vertex form. g(x) = 7(x+3)² g(x)=-3(x-7)² g(x) = -3(x+7)² g(x) = 3(x-7)²

Eric's bicycle tires have a 29-inch diameter and Maggie's bicycle tires have a 26-inch diameter. How much farther do Eric's tires travel compared to Maggie after 10 complete revolutions? Use = 3.14 Enter your answer correct to one decimal place.

A college believes that 26% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 3% with 99% confidence? 473 2129 2413 1419

Consider the following scenario: Joe woke up one morning and found he was bitten all over by some sort of mystery bug. The next night, he felt itchy, especially on his torso, near where he'd gotten the other bites. He did not feel the same sensation on his legs, and he knew it must be psychosomatic. He treated his bed for a variety of different bugs, and the bites stopped, but he associated his bed with feelings of itchiness for several weeks. Eventually the response went away, only to suddenly show back up six months later! l

Ronald and his friends are at an arcade and are redeeming their tickets for prizes. The number of prizes they can get is calculated based on how many tickets they have won. p= the number of prizes the friends can get t = the number of tickets the friends have won Which of the variables is independent and which is dependent? t is the independent variable and p is the dependent variable p is the independent variable and t is the dependent variable

Four starting youth basketball players are ages 8, 10, 9, and 11. Solve for the number of samples if a sample of two is randomly chosen. Show your work and explain the steps you used to solve.

The city transit authority surveyed 1,000 citizens who regularly use public transportation. Of those surveyed, 658 users said they paid using a monthly subscription as opposed to paying for each ride individually. The transit authority's report claims, "We can be 95% confident that the percentage of citizens using public transportation with a monthly subscription is between 63.33% and 68.27%. " Which statement best describes this claim? A. There is not enough information to evaluate the report's claim. B.The report's claim is false because the margin of error is 3.87%. C. The report's claim is true. D. The report's claim is false because the margin of error is 2.94%.

Which of the following is true? It is never good to have sampling bias. Statistics are not used to help understand the data collected. A random sample includes only specific people. The best results come from sampling bias.