Math Questions

Consider the function f(x) = 5x² - 10x + 1, 0≤x≤ 8. The absolute maximum of f(x) (on the given interval) is at x = and the absolute maximum of f(x) (on the given interval) is The absolute minimum of f(x) (on the given interval) is at x= and the absolute minimum of f(x) (on the given interval) is

From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an answer exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.) x-intercept (x, y) = (0,2 (smaller x-value) x-intercept y-intercept vertical asymptote(s) horizontal asymptote

Sketch the angle and write the sec and tan of the angle if the terminal side of the angle passes through (3, -6). Express each answer as a decimal rounded to the nearest hundredth. Be sure to type your answers to all parts in the answer box. Be sure to show all work on loose leaf as a file upload question at the end.

Suppose the random variable is best described by a normal distribution with μ = 20 and a = 8.2. Find the z-score that corresponds to each of the following a values. Express your answers rounded correctly to the hundredths place. (a) x = 15 z= (b) x = 32 z= (c) x= 10 z= (d) x = 25 z= (e) x= 25 z= (f) x=17 z=

The diagram represents a regular pentagonal pyramid. The measurements unit is feet. (Round your answers to two decimal places.) (a) Find the area of the base. ft² (b) Find the lateral area of the pyramid. ft² (c) Find the surface area of the pyramid. ft² (d) Find the volume of the pyramid. ft3

A person standing close to the edge on top of a 112-foot building throws a ball vertically upward. The quadratic function h(t)=16t² +96t+ 112 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown. a) What is the maximum height of the ball? b) How many seconds does it take until the ball hits the ground?

A simple random sample of size n = 15 is obtained from a population with µ = 67 and σ = 17. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of x. (b) Assuming the normal model can be used, determine P(x < 70.9). (c) Assuming the normal model can be used, determine P(x ≥ 68.3). (a) What must be true regarding the distribution of the population? A. The population must be normally distributed and the sample size must be large. B. Since the sample size is large enough, the population distribution does not need to be normal. C. The sampling distribution must be assumed to be normal. D. The population must be normally distributed.

nSeveral years ago, 51% of parents with children in grades K-12 were satisfied with the quality of education the students receive. A recent poll found that 495 of 1,095 parents with children in grades K-12 were satisfied with the quality of education the students receive. Construct a 90% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed. Find the 90% confidence interval. The lower bound is 0.485 The upper bound is 0.535 (Round to three decimal places as needed.) What is the correct conclusion? A. Since the interval contains the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed. B. Since the interval contains the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed. C. Since the interval does not contain the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed. D. Since the interval does not contain the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed.

Which of the following represents vector t = -8i + 6j in trigonometric form? t= 10 (cos 36.87°, sin 36.87°) t= 10 (cos 143.13°, sin 143.13%) t= 10 (sin 36.87°, cos 36.87°) t= 10 (sin 143.13°, cos 143.13%)

Determine whether the following statement is true or false, and explain why. In a Markov chain, the outcome of an experiment depends only on the present state and not on any past states. Is the statement true or false? A. True. B. False. In a Markov chain, the outcome of an experiment depends on past states found using transition matrice C. False. In a Markov chain, the outcome of an experiment depends on past states found using probability vector D. False. In a Markov chain, the outcome of an experiment depends on both past and present states.

The average daily volume of a computer stock in 2011 was μ = 35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2018 is different from the 2011 level. Based on a random sample of 30 trading days in 2018, he finds the sample mean to be 32.1 million shares, with a standard deviation of s = 12.3 million shares. Test the hypotheses by constructing a 95% confidence interval. Complete parts (a) through (c) below. (a) State the hypotheses for the test. Ho: µ ≠ 35.1 million shares H₁: µ = 35.1 million shares (b) Construct a 95% confidence interval about the sample mean of stocks traded in 2018. million shares and million shares. With 95% confidence, the mean stock volume in 2018 is between (Round to three decimal places as needed.) (c) Will the researcher reject the null hypothesis A. Do not reject the null hypothesis because μ = 35.1 million shares falls in the confidence interval. B. Do not reject the null hypothesis because μ = 35.1 million shares does not fall in the confidence interval. C. Reject the null hypothesis because μ = 35.1 million shares does not fall in the confidence interval. D. Reject the null hypothesis because μ = 35.1 million shares falls in the confidence interval

Graph each of the lines in the following system to find the solution. y = -2x + 6 y=-3x+9

In the figure, m∠1 = (7x+7)°, m∠2 = (5x+14)°, and m∠4 = (13x +9)°. Your friend incorrectly says that m∠4 = 15°. What is m∠4? What mistake might your friend have made?

The path of the object thrown above the ground level is given by the function s(t) = 2t2 + 5t + 3. Rewrite it in factored form. (2t+3)(t-1) (2t+3)(t+1) (2t-3)(t+1)

Solve for x and write the solution set using set-builder notation: 1.5-0.25x ≤ 6 {x|x ≥-18} {x|x ≥-10} {x|x ≤ 8}

Function W gives the weight of a cat t weeks after it was born. The weight is measured in pounds. Use function notation to represent this statement: 10 weeks after the cat was born, it weighed 8 pounds. t=8, W=10 10(8) = W W(10)=8 W(8)=10

Find all real solutions of the equation (b + 3)² = 294 After simplifying, the solutions should look like b = A +- B√C where A = B = C =

Dan traveled to his friend's house and back. The trip there took two hours and the trip back took three hours. What was Dan's average speed on the trip there if he averaged 20 mph on the return trip? 25 mph 50 mph 42 mph 43 mph 30 mph

A spinner has an equal chance of landing on each of its five numbered regions. You spin twice. The first spin lands in region two and the second spin lands in region one. 21/55≈ 0.382 1/25≈0.04 1/4≈0.25 4/15≈0.267 7/22≈0.318

Write an equation for a line perpendicular to y = 2x - 5 and passing through the point (2,2) y =

A bike shop rents bikes for $4 per hour, and helmets for $8 per day. Justin has less than $ 20 to rent a helmet and a bike for x hours. Which of following inequality represents this situation? 4x+8 = 20 4x+8<20 4x-8<20

If a couple has $50,000 in a retirement account, how long will it take the money to grow to $1,000,000 if it grows by 6% compounded continuously? Write your answer as an exact value.

The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its width Find the length and width of the pool. I=30, w = 30 I=52, w = 25 I=25, w = 35

Simplify the following expressions completely. Assume all variables represent non-negative numbers. A)√16p26 B)√81m22 =

The following problem refers to triangle ABC. Solve it. Round your degrees and minutes to the nearest whole number. Round the sides to the 3 decimal places. b = 0.75, c = 0.507, A = 46°20'

The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 21.25 minutes, complete parts (a) through (f). (a) What is the probability that a randomly selected time interval between eruptions is longer than 94 minutes? The probability that a randomly selected time interval is longer than 94 minutes is approximately 0.3192 (Round to four decimal places as needed.) (b) What is the probability that a random sample of 14 time intervals between eruptions has a mean longer than 94 minutes? The probability that the mean of a random sample of 14 time intervals is more than 94 minutes is approximately noruptions has a mean longer than 94 minutes?

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = -4.9t² +241t+ 178. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak?

Construct a confidence interval of the population proportion at the given level of confidence. x= 120, n= 1100, 98% confidence The lower bound of the confidence interval is

Which is the equation of a circle with diameter AB where A(5, 4) and B(-1,-4)? Select one: a. (x + 2)² + y² = 5 b. (x + 5)² + (y - 4)² = 100 c. (x-2)² + y² = 25 d. (x - 5)² + (y-4)² = 10

An object is thrown upward at a speed of 132 feet per second by a machine from a height of 17 feet off the ground. The height of the object after t seconds can be found using the equation s(t) = 16t² + vot + so, where is the initial velocity and so is the initial height. Give all numerical answers to 2 decimal places. (a) When will the object reach its maximum height? (b) What is its maximum height? (c) When will the object reach the ground?

Consider Ho: = 29 versus H₁: #29. A random sample of 16 observations taken from this population produced a sample mean of 24.89. The population is normally distributed with a = 7. (a) Compute . Round the answer to four decimal places. % = 1.75 (b) Compute z value. Round the answer to two decimal places. (c) Find area to the left of z-value on the standard normal distribution. Round the answer to four decimal places. (d) Find p-value. Round the answer to four decimal places.

Which of the following points lies in the solution region for y> 3 and y < -3. (3,-3) No solution (0, 0)

Suppose a simple random sample of size n = 11 is obtained from a population with μ-66 and o=14 (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? As the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(x <69.3). (c) Assuming the normal model can be used, determine P(x ≥ 67.9). (a) What must be true regarding the distribution of the population? A. The population must be normally distributed. B. There are no requirements on the shape of the distribution of the population C. The population must be normally distributed and the sample size must be large D. Since the sample size is large enough, the population distribution does not need to be normal.

Mary has $18.50 to buy pizza. A cheese pizza costs $14. Each extra topping cost $0.75. How many extra toppings can she buy? 4 toppings 6 toppings 3 toppings

Solve this equation using the square root property. If possible, simplify radicals. All answers should be exact. (c - 9)² = 29 The solution(s) to this equation have the form c = A ± √B

According to a food website, the mean consumption of popcorn annually by Americans is 63 quarts. The marketing division of the food website unleashes an aggressive campaign designed to get Americans to consume even more popcorn. Complete parts (a) through (c) below. (a) Determine the null and alternative hypotheses that would be used to test the effectiveness of the marketing campaign. (b) A sample of 866 Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department. A. There is sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. B. There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. OC. There is not sufficient evidence to conclude that the mean consumption of popcorn has risen. D. There is sufficient evidence to conclude that the mean consumption of popcorn has risen.

A website uses the formula above to calculate a seller's rating, R, based on the number of favorable reviews, F, and unfavorable reviews, N. Which of the following expresses the number of favorable reviews in terms of the other variables?

The radius of a circular oil spill after t minutes is given by r(t) = √4t. Find the instantaneous rate at which the radius is growing after 31 minutes. Give your answer as a decimal approximation with at least 3 decimal places.

Is the hypothesis test left-tailed, right-tailed, or two-tailed? The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested? Ho μ = 125 H₁: μ < 125 Right-tailed test Left-tailed test Two-tailed test Submit test

Find the Z-scores that separate the middle 75% of the distribution from the area in the tails of the standard normal distribution The Z-scores are

Determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ∞ or -∞, as appropriate. Determine the equation of the horizontal asymptote that corresponds to the limit as n → ∞. Equation of horizontal asymptote: No horizontal asymptote corresponds to the limit as n→∞. Determine the equation of the horizontal asymptote that corresponds to the limit as n → -∞. Equation of horizontal asymptote: No horizontal asymptote corresponds to the limit as n→-8

Given oblique triangle ABC, side a = 12 ft., side b = 17 ft., side c = 10 ft., find the degree of the smallest angle (round to the nearest whole degree). DO NOT FIND ALL THREE ANGLES AND THEN CHOOSE THE MALLEST. Remember that the smallest angles is across from the smallest side. Be sure to type your answers to all parts in the answer box. Be sure to show all work on loose leaf as a file upload question at the end. This question is worth 8 points total. 1 for the answer and 7 for the work.

The graph of y=g (x) is given. (a) Find g (2). (b) Find g (0). (c) Find g (-3). (d) For what value(s) of x is g (x)=4? (e) For what value(s) of x is g(x)=-3? (f) Write the domain of g. (g) Write the range of g.

Let x)=x², and compute the Riemann sum off over the interval [4, 51, choosing the representative points to be the midpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.) (a) two subintervals of equal length (n=2) (b) five subintervals of equal length (n = 5) (c) ten subintervals of equal length (n = 10) (d) Can you guess at the area of the region under the graph of fon the interval [4, 5]?

In a survey, it was found that 78% of the population of a certain urban area lived in single-family dwellings and 22% in multiple housing. Five years later, of those who had been living in single-family dwellings, 91% still did so, but 9% had moved to multiple-family dwellings. Of those in multiple housing, 96% were still living in that type of housing, while 4% had moved to single-family housing. Assume that these trends continue. Answer parts (a) through (f).

Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a mathematician, she suggests building fences described by y = 112² and y = x² + 4. Farmer Jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. What is the area of the enclosed region?

Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N= 1,500,000 and whose population proportion with a specified characteristic is p = 0.44. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. A. Approximately normal, μ = 0.44 and o≈ 0.0004 B. Approximately normal, μ = 0.44 and ≈ 0.0157 C. Approximately normal, μ = 0.44 and o.≈ 0.0002 (b) What is the probability of obtaining x = 470 or more individuals with the characteristic?

How many real and imaginary solutions does the equation x² + x = 11 contain? 1 real solution; 1 imaginary solution No real solutions; 2 imaginary solutions 1 real solution; no imaginary solutions 2 real solutions; no imaginary solutions

A certain forest covers an area of 1800 km². Suppose that each year this area decreases by 3%. What will the area be after 13 years? Use the calculator provided and round your answer to the nearest square kilometer.

Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided. Lower bound = 0.201, upper bound = 0.469, n = 1000