Math Questions

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

What is the center of the shape formed by the equation (x-3)²/49 - (y+5)²/25 = 1? (0,0) (-3,5) (3,-5) (9,25) (-9, -25) (x-3)²

Julio must invest a total of $6300 in two accounts, one paying 10% simple annual interest and the other paying 7% annual interest. If he wants to earn $534.00 annual interest, how much should be invested at each rate?

The length of a path going diagonally across a rectangular field is 100 yards, the width of the rectangular field is 50 yards. What is the measure of the angle these two lines form? (Round your measure to the nearest whole degree).

Consider the function f(x) = 25x² - 64. a) Determine the zeros of the function: Writing values as simplified fractions if necessary. If there are multiple values, separate the solutions with a comma. If there are no values, input "DNE". b) Determine the x-intercept(s) of the graph of the function: Write ordered pairs, writing any values as simplified fractions if necessary. If there are multiple x-intercepts, separate them with a comma. If there are no x-intercepts, input "DNE". c) Determine the y-intercept(s) of the graph of the function: Write ordered pairs, writing any values as simplified fractions if necessary. If there are multiple y-intercepts, separate them with a comma. If there are no y-intercepts, input "DNE".

The polynomial of degree 4, P(x), has a root of multiplicity 2 at x = 1 and roots of multiplicity 1 at x = 0 and x - 1. It goes through the point (5, 96). Find a formula for P(x). P(x) =

A sample of size 7-50 is drawn from a normal population whose standard deviation is a-7.1. The sample mean is x=48.52. (a) Construct a 99.9% confidence interval for H. Round the answer to at least two decimal places. A 99.9% confidence interval for the mean is 0<μ< (b) If the population were not approximately normal, would the confidence interval constructed in part (a) be valid? Explain. The confidence Interval constructed in part (a) (Choose one) be valid since the sample size (Choose one) ▼ large.

The two points (-3, 6) and (6, 0) are plotted on the grid below. (a) Find an equation, in y=mx+b) form, for the line passing through these two points. Use of the grid is optional. b) Does the point (30, -16) lie on this line? Justify.

A car was valued at $40,000 in the year 1995. The value depreciated to $14,000 by the year 2007. A) What was the annual rate of change between 1995 and 2007? T= Round the rate of decrease to 4 decimal places. B) What is the correct answer to part A written in percentage form? T = C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2012? value = $ Round to the nearest 50 dollars.

Given a function f (x) = 2x² + 3, what is the average rate of change of f on the interval [2, 2 + h]? 11 2h +8 2h² + 8h 2h² + 8h + 11

Find a 95% confidence interval for the mean of the length of fishes in a pond based on the sample below. The measurements are in inches. 5, 6, 6, 7, 9, 9, 10, 11, 11, 12, 12, 12, 13, 14, 19 (8.62, 12.18) (8.63, 12.17) (8.69, 12.11) 8.56, 12.20)

Consider the equation below. f(x) = 2x³ + 3x² = 120x (a) Find the interval(s) of increase and decrease. (b) Find the local minimum and maximum values of f. (c) Find the inflection point and the intervals on which fis concave up and concave down. (a) Find the interval(s) of increase and decrease. For f(x) = 2x³ + 3x2 - 120x, we have the following f'(x) = This factors into(__)(x+__)(x-4).

Write the following as the sum and/or difference of logarithms. Assume all variables are positive. log (10z/4)= __ The answer format in lowercase characters is: log(number) Spaces in the answer are optional.