Math Questions

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1200 miles. What is the probability a certain tire of this brand will last between 57,480 miles and 57,840 miles? 0.4649 0.0180 0.4920 0.9813

Curing diabetes: Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that less than 77% of those with diabetes who undergo this surgery will recover from diabetes? Use the α= 0.10 level of significance and the critical value method. State the appropriate null and alternate hypotheses. Ho: H₁: This hypothesis test is a (Choose one) test.

The area of a right triangle is 210 square inches. The height of the right triangle is 35 inches. What is the length of the hypotenuse of the right triangle? Enter your answer in the box.

1. A block of clay contains twenty 4-ounce portions of clay. A ceramics teacher wants to use the block to make as many spheres of clay as possible, each weighing 2/5 pound. How many spheres can she make?

Consider these functions: f(x) = 5x² +2 g(x)=x²-1 What is the value of g(f(-1))? A. 2 B. 8 C.22 D.48

Answer the following. (a) The total surface area of Africa is approximately 11,700,000 square miles. Write this number in scientific notation. (b) The signal from a certain satellite takes approximately 1.3 × 10-3 seconds to reach Earth. Write this number in standard notation.

A waterfall has a height of 700 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 16 feet per second. The height of the pebble h in feet after t seconds is given by the equation h= - 16t² + 16t+ 700. How long after the pebble is thrown will it hit the ground? The time it takes for the pebble to hit the ground is about

(1 point) Find the length of the arc on the unit cicle that is defined by the given angle. (a) π/4 radians (b) 2 radians (c) 1.6 radians (d) 46°

Given that the polynomial f(x) has 7 x-intercepts, which of the following most accurately describes the degree of f(x)? Select the correct answer below: The degree of f(x) is at least 6. The degree of f(x) is at least 8. The degree of f(x) is at most 7. The degree of f(x) is at most 8. The degree of f(x) is at least 7. The degree of f(x) is at most 6.

A psychologist would like to estimate the proportion of Americans that say "the future of the nation is a significant source of stress for me." To help form an estimate, the psychologist randomly selected 922 Americans and found that 59.6% of the sample agreed with the statement "the future of the nation is a significant source of stress for me." Using a 96% confidence level, determine the margin of error, E, and a confidence interval for the true proportion of all Americans that say the "the future of the nation is a significant source of stress for me." Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary. The margin of error is given by E = A 96% confidence interval is given by

A sample of 650 grams of radioactive substance decays according to the function A(t)= 650e ^028t, where t is the time in years. How much of the substance will be left in the sample after 10 years? Round your answer to the nearest whole gram.

Use the properties of exponents to simplify the following as much as positive. (X^5/6) / (x^3/5)=

A pharmacy produces a certain medication in a daytime variety and a nighttime variety. A bottle of the daytime variety contains 2 ounces of the active ingredient and 6 ounces of flavored syrup. A bottle of the nighttime variety contains 3 ounces of the active ingredient and 5 ounces of flavored syrup. The pharmacy currently has no more than 385 ounces of the active ingredient and no more than 850 ounces of flavored syrup available. If at least 65 bottles of the daytime variety must be filled, what is the maximum number of bottles of the nighttime variety that can be filled? A) 78 B) 85 C) 92 D) 106

Complete the sentence below. If 9^x = 9^6, then x = If 9^3x = 9^6, then x =

Given: cos (4π/9) cos(2π/9) — sin (4π/9) sin(2π/9) 1. Identify the Trig identity that corresponds with the expression above. 2. Simplify and find the exact value. Show all work. Answers without justification will

The correlation coefficient of a set of data is 0.91. Select all of the statements that are true. The positive correlation coefficient tells us that there is an outlier. The two variables involved have a very strong positive correlation. The correlation coefficient implies that as the independent variable increases, the dependent variable increases. Because the correlation coefficient is positive, there is no causation. The correlation coefficient implies causation.

Use the sets to find Fn(DUE). Let D=(16,19,21), E = (16,18,19,20), and F= (15,17,18,19,21). Fn(DUE)= (Use a comma to separate answers as needed.)

The palm tree on the left is 10 years old. The palm tree on the right is 8 years old. The trees grow at the same rate. b. a. Estimate the height y (in feet) of each tree. Plot the two points (x, y), where x is the age of each tree and y is the height of each tree. c. What is the rate of growth of the trees? d. Write an equation that represents the height of a palm tree in terms of its age.

b) At age 35, Alberto stops making monthly payments into his annuity, but he takes the money he accumulated in his annuity and invests it into a savings account with an interest rate of 8% compounded monthly. Using the compounded interest formula A = p(1 + )" determine the amount Alberto has in n.t his savings account 30 years later when he retires at age 65,

Make a conjecture. Choose the correct answer below. A. cos 4x - sin 4x = (cos x)² B. cos x - sin^x= cos x C. cosx- sin^x= cos 2x D. cos 4x - sin4x = (cos 2x)² cos 4x - sin 4x = (cos²x- sin2x) (cos²x+ sin²x)

Which of the following is the first step of the four essential steps in designing an observational study or experiment in statistics? Formulate a question that can be answered with data that is collected. Interpret the results to draw a conclusion. Ensure that all treatments are randomly assigned to the subjects. Make a design on how the data will be collected.

An airline finds that if it prices a cross-country ticket at $500, it will sell 300 tickets per day. It estimates that each $10 price reduction will result in 30 more tickets sold per day. Find the ticket price (and the number of tickets sold) that will maximize the airline's revenue. ticket price number of tickets

In a laboratory, it was observed that a colony of bacteria increases at the rate of 30% per hour. If the original number of bacteria is 10 000 how many will there be, (a). after 15 minutes? (b). in 30 minutes? (c). in 5 hours?

What is the area of a sector with a central angle of 4π/5 radians and a radius of 11 cm? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.

The point (a, b) is on the terminal side of angle C in the coordinate plane. If a is a positive integer and b is a negative integer, which of the following statements is correct? Select all that apply. A.Angle C is in Quadrant II B.tan C < 0 C.sin C <0 D.cos C <0

IMPROVING QUALITY - THE WRITE RIGHT COMPANY MANUFACTURERS BALLPOINT PENS AND HAS BEEN EXPERIENCING A 6% RATE OF DEFECTIVE PENS. MODIFICATIONS ARE MADE TO THE MANUFACTURING PROCESS IN AN ATTEMPT TO IMPROVE QUALITY. THE MANAGER CLAIMS THAT THE MODIFIED PROCEDURE IS BETTER BECAUSE A TEST OF 60 PENS SHOWS THAT ONLY ONE IS DEFECTIVE. A) ASSUMING THAT THE 6% RATE OF DEFECTS HAS NOT CHANGED, FIND THE PROBABILITY THAT AMONG 60 PENS, EXACTLY ONE IS DEFECTIVE.

The population of a parish is growing with an annual percentage rate compounded continuously. The population reaches 1.1 times its previous size in 2 years. Find the annual percentage rate according to the exponential growth function.Write your answer in exact form, using In (do not round). Note: When entering natural log in your answer, enter lowercase LN as "In". There is no "natural log" button on the Alta keyboard. Provide your answer below:

Cosider the quadratic function y =x² - 4x - 3. The vertex is the point_____ The equation of the line of symmetry is_____ The vertical intercept is the point_____ The horizontal intercept(s) is/are the point(s)___

Suppose a ball is thrown upward to a height of h0 meters. Each time the ball bounces, it rebounds to a fraction r of its previous height. Let hn be the height after the nth bounce. Consider the following values of h0 and r. Complete parts (a) and (b) below. h0=45, r=0.5 a. Find the first four terms of the sequence of heights {hn}.

Makayla has a bag that contains orange chews, cherry chews, and watermelon chews. She performs an experiment. Makayla randomly removes a chew from the bag, records the result, and returns the chew to the bag. Makayla performs the experiment 50 times. The results are shown below: A orange chew was selected 14 times. A cherry chew was selected 12 times. A watermelon chew was selected 24 times. Based on these results, express the probability that the next chew Makayla removes from the bag will be orange or cherry as a fraction in simplest form.

While attending a major league baseball game, you think you can guess the attendance within 10% of the actual value. If the announced attendance is 35,000, within what number of people would your guess have to be in order for you to support your claim?

Solve the following equation for x and assume a, b, c > 0. |x-a| = |bx - cl. b) Solve the following inequality for x and assume a, b > 0. |x - a| <b/|x + al c) The relationship between Celsius and Fahrenheit temperature scale is given by C = (F - 32) where C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit. What is the interval in Celsius scale that corresponds to the temperature range 59 ≤ F≤ 86?

Polly and Olivia just had business cards made. Polly's printing company charged a one-time setup fee of $10 and then $7 per box of cards. Olivia, meanwhile, ordered hers online. They cost $8 per box. There was no setup fee, but she had to pay $5 to have her order shipped to her house. By coincidence, Polly and Olivia ended up spending the same amount on their business cards. How many boxes of business cards did each buy? Write a system of equations, graph them, and type the solution.

Use the following statement to answer parts a) and b). Two hundred raffle tickets are sold for $3 each. One prize of $400 is to be awarded. Winners do not have their ticket costs of $3 refunded to them. Raul purchases one ticket. a) Determine his expected value. b) Determine the fair price of a ticket. a) His expected value is $. (Type an integer or a decimal.) b) The fair price of a ticket is $. (Type an integer or a decimal.)

A house is advertised as having 1500 square feet under roof. What is the area of this house in square meters?

Given the function f(x)=x²-21, x20, complete parts a through c. (a) Find an equation for f¹(x). (b) Graph f and f¹ in the same rectangular coordinate system. (c) Use interval notation to give the domain and the range of f and f¹. (a) Find f¹(x). (Type an exact answer, using radicals as needed.)

Sand falls from a conveyor belt at a rate of 11 m³/min onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. How fast are the height and the radius changing when the pile is 2 m high? The height is changing at a rate of cm/min when the height is 2 m. (Type an integer or decimal. Round to the nearest hundredth.)

Find the quotient and remainder using long division. 25x³ + 45x² + 30x + 8/5x+4 The quotient is The remainder is

The function A = Age-0.00866x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 800 pounds of the material are placed in the vault, how much time will need to pass for only 218 pounds to remain?

Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation).

In the following hypothetical scenarios, classify each of the specified numbers as a parameter or a statistic. There are nine justices currently serving in the United States Supreme Court, and 44% of them were appointed after the year 2000. The 44% here is a In a 2015 Gallup poll of 1025 adults living in the United States, 53% said they trust the judicial branch of the federal government. The 53% here is a A survey of hospital records in 120 hospitals throughout the world shows the mean height of 180 cm for adult males. The mean height of 180 cm is a The 59 players on the roster of a championship football team have a mean weight of 248.6 pounds with a standard deviation of 44.6 pounds. The 44.6 pounds is a

A Food Marketing Institute found that 28% of households spend more than $125 a week on groceries. Assume the population proportion is 0.28 and a simple random sample of 193 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.25? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.25. Round the answer to 4 decimal places.

A professional soccer player kicked a ball across the field. The ball's height, in meters, is modeled by the function graphed below. What's the average rate of change between the point when the ball reached its maximum height and the point where it hit the ground? -1/3 meters per second meters per second 3 meters per second meters per second

A prism of angle 6° made from a crown glass of refractive index 1.5 is placed in contact with another prism, made of flint glass of refractive index 1.6. A ray of light falling normally passes through the two prisms without deviation. The angle of flint glass prism is A 2.0 B 5.0 C 6.6 D 7.2°

TV PURCHASES-AT A CIRCUIT CITY STORE, OF THOSE PURCHASING COLOR TELEVISIONS PURCHASE A LARGE-SCREEN TV. FIND THE PROBABILITY THAT NONE OF THE NEXT FOUR PEOPLE WHO PURCHASE A COLOR TELEVISION AT CIRCUIT CITY PURCHASES A LARGE-SCREEN TV.

Mr. and Mrs. Brown anticipate that they will need $60,000 for their child's education in 18 years. If their savings account earns 4% compounded quarterly, how much would they need to deposit now to reach their goal? (Round to the nearest dollar) $54,000 $34,884 $2327 $29,310

View the video found on page 1 of this journal activity. Using the information provided in the video, answer the questions below. Show your work for all calculations.

Sydney Dukes-Miller deposited $2,430 at 6.75%. She made no other deposits or withdrawals. How much simple interest did she earn in 65 days? What is the final amount in the account? (2 points)

A TV studio has brought in 7 boy kittens and 9 girl kittens for a cat food commercial. The director is going to choose 6 of these kittens at random to be in the commercial. What is the probability that the director chooses 4 boy kittens and 2 girl kittens? Round your answer to three decimal places.

Business Weekly conducted a survey of recent graduates from the top MBA programs. On the basis of the survey, assume that 55% of the recent graduates annual salary exceeds $55000. Suppose you take a simple random sample of 85 recent graduates. Note: round all z scores to 2 decimal places and all other numbers to 4 decimal places. Find the probability that more than 45% of the 85 recent graduates have an annual salary exceeding $55000. 0.0268 Beyond representative sampling, what assumptions are needed to satisfy the requirements for this problem? X binomial and both np and nq at least 5 X~ normal or n ≥ 30 X~ normal and n ≥ 30 X~ binomial and at least 5 successes and failures