Math Questions

Person A who is 20 years old, gives $6000 to their stock fund and continues to do so for the next 10 years. Person B started contributing $6000 to the same stock and continues until he is 65. Person B invested a total of $210,000 and person A only contributed $60,000. At age 65, which of the 2 people had the most money assuming they earned an average rate of return equal to 7% (by how much??) Use Future value= P{(1+r)^t -1}

You are flying a kite on a line that is 350 feet long. Let's suppose the line is perfectly straight (it never really is) and it makes an angle of 65 degrees with the horizontal direction. The kite is flying at an altitude of feet. Hint: Draw a picture. Look for a right triangle.

A competitive knitter is knitting a circular place mat. The radius of the mat is given by the formula r(t) = 5- 605/(t + 11)² with 7 in centimeters and t in seconds. A. Find the rate at which the area of the mat is increasing. Select an answer B. Use your expression to find the rate at which the area is expanding at t = 3.

A genetic experiment involving peas yielded one sample of offspring consisting of 433 green peas and 142 yellow peas. Use a 0.01 significance level to test the claim that under the same circumstances, 25% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

Select ALL the correct answers. Two friends worked together on an entry for a poetry contest and won; however, there is only one prize and it cannot be split. Some methods of determining who receives the prize are given below. Select all the fair methods for determining who receives the prize. ask a stranger to flip a coin throw a stone closest to an object place both names in equal amounts into a hat and draw one without looking ask a random friend to choose roll a die and evaluate the outcome as either even or odd

Since January 2005 the population of Brownsville has grown according to the mathematical model y = 778500 . (1.018)x, where x is the number of years since 2005 a) What is the percent growth for this situation? b) What would the population be in the year 2015 according to the equation above? (round to the nearest whole number)

A large corporation sent out four groups of people to conduct observational studies on the average walt time at four different restaurants in its restaurant group. The restaurants have approximately the same ratings in terms of quality and popularity. In their reports to the company board, each of the four groups described different methods used to conduct their studies, as shown in the table. Which group's method will give the most accurate, unbiased results? Northeast Researchers observed and recorded the average wait times each day between the hours of 8 a.m. and 11 a.m. South Researchers used a phone survey to ask residents of the restaurants' city about the wait times they've experienced. A. B. Northeast C. Midwest D. West Coast South West Coast Researchers surveyed restaurant-goers on their wait times as they left the building over the course of one full business day. Midwest Researchers observed and recorded the average wait times during random time periods over the course of a week.

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 11 cm and the width is 5 cm, how fast is the area of the rectangle increasing? cm²/s

You order ten burritos to go from a Mexican restaurant, six with hot peppers and four without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability that at least one has hot peppers 2/15 5/6 29/30 4/5 41/42

A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f on [a, b]. If so, find all values c in [a, b] guaranteed by the Mean Value Theorem Note, if the Mean Value Theorem does not apply, enter DNE for the c value. f(x) = 4 sin-1x on [-1,1] (Separate multiple answers by commas.)

P-value is the A. probability, when the null hypothesis is false, of obtaining a sample result that is at least as unlikely (or as extreme) as what is observed B. probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely (or as extreme) as what is observed C. t test statistic (that is, P-value = t test statistic) D. Both B and C.

Solve and check the following linear equation. 8x − (5x – 3) = 27 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an integer or a simplified fraction.) B. The solution set is {x|x is all real number}. C. The solution set is Ø.

Polonium-210 is a radioactive substance with a half-life of 138 days. If a nuclear facility is handling 110 grams of polonium-210, then how many grams of polonium- 210 will be left in 270 days. Round your answer 4 decimal places and remember to use labels.

In a junior track and field meet, Jennifer jumped a height of 1.873 meters in the high jump. Samantha jumped a height of 1.807 meters. A. Use <, >, or = to write a number sentence comparing the heights of the girls' jumps. Whose jump was higher? Explain how you know. B. In the boys' long jump, Kevin jumped a distance of (6 × 1) + (9x) + (8 × 100)+(3× 1,000) meters. Leon jumped a distance of 6.093 meters. Kevin said he jumped farther than Leon. Is Kevin correct? Explain why or why not. C. Ben and Michael also participated in the long jump. Michael jumped 334 thousandths of a meter less than Kevin. Ben jumped farther than Michael but not as far as Kevin. Write a decimal to the thousandths that is greater than Michael's distance and less than Kevin's distance. Explain the reasoning you used.

A scatterplot is used to display data where x is the amount of time, in minutes, one member can tolera sauna, and y is the temperature, in degrees Fahrenheit, of the sauna. Which interpretation describes a line of best fit of y=-1.5x + 173 for the data? The member can tolerate a temperature of 173° Fahrenheit for 0 minutes. The amount of time the member can tolerate the heat in a sauna is 173 minutes. The time increased 1.5 minutes for every degree Fahrenheit the temperature increased. The time decreased 1.5 minutes for every degree Fahrenheit the temperature decreased.

A travel association claims that the mean daily meal cost for two adults traveigling together on vacation in San francisco is $105. A random sample of 20 such couples has a mean daily meal cost of $110 and a standard deviation of $8.50. At the α = .05 significance level, is there enough evidence to reject the claim? There is significant evidence that the claim is false, because p = .0165. There is not significant evidence to refute the athletic association's claim because 2.63 is not in the rejection region. Since p = 0.0165, there is evidence that the association's claim is true. No answer text provided.

The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible items are chosen at random, one at a time, until one is found who purchased the extended warranty. Let the random variable P represent the number of customers it takes to find one who purchased the extended warranty. Assume customers' decisions on whether to purchase the extended warranty are independent. What is the probability that it takes more than 4 customers who buy an eligible item to find one who purchased the extended warranty?

According to a recent survey, forty percent of the people living in a certain region carry a certain genetic trait. People from the region will be selected at random one at a time until someone is found who carries the genetic trait. Let the random variable X represent the number of people selected to find one person who carries the genetic trait. On average, how many people from the region will need to be selected to find one person who carries the genetic trait?

Graph the given functions, f and g, in the same rectangular coordinate system. Describe how the graph of g is related to the graph of f. f(x) = - 4x g(x)=-4x-2

Find the contrapositive of the conditional "You are a vegetarian if you do not eat meat." . Caution: What is the antecedent of the conditional? If you eat meat, then you are not a vegetarian If you are not a vegetarian, then you eat meat If you are a vegetarian, then you do not eat meat If you do not eat meat, then you are a vegetarian

The perimeter of a rectangle is 20 inches and its area is 16 square inches. What are its dimensions? What are the dimensions? inches (Use a comma to separate answers as needed.)

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