Math Questions

Make sure to justify your answer. A normal distribution has a mean of 75 and a standard deviation of 15. Determine the z- score for the data value of 85.

A sample of 200 sodas filled on a new machine showed that 22 were over-filled. The factory will get rid of the new machine if the data indicates that the proportion of over-filled sodas is significantly more than 7%. At a significance level of 10% does the factory get rid of the machine or not? Yes, the factory gets rid of the machine. There is evidence the machine is over-filling the bottles. No, the factory does not get rid of the machine. There is not evidence the machine is over-filling the bottles. Yes, the factory gets rid of the machine. There is not evidence the machine is over-filling the bottles. No, the factory does not get rid of the machine. There is evidence the machine is over-filling the bottles.

Two pyramids are similar with a ratio of surface areas of 25:64. Find the volume of the second pyramid given that the first has a volume of 250 m³. A 61.0 m³ B 640 m³ C 1024 m³ D 97.7 m³ E 4194 m³

Rosurvastatin/Crestor is a medicine used to decrease bad cholesterol and increase good cholesterol in the body. The half-life of Rosurvastatin is 1 day, which means that at the end of 1 day, half as much of the medication is left in your system. 1. If you take 60 mg of Rosurvastatin, how long do you think will it stay in your system?

Consider the following system of equations. x+y+z=1 2x + 2y = 6 3x + 4y -z = 13 a) Write the system as an augmented matrix. buse row operations to write the augmented matrix from part (a) in row echelon form. Show your work, clearly label each row operation used. c) Using your final matrix from part (b), solve for the values of x, y, and z for the solution to the system of equations. Write your solution. If the system has no solution, write "inconsistent'".

A taxi driver charges for a trip, with a base fare, using the function = 3k + 2, where t is the total cost ($) for the trip and k is the number of kilometers traveled in the trip. Find the rate of change (cost per kilometer traveled). $1 $3 $1.5

Bentley invested $26,000 in an account paying an interest rate of 6.8% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?

Taylor is on one side of a river that is 50 meters wide and wants to reach a point 200 meters downstream on the opposite side as quickly as possible by swimming in a diagonal line across the river and then running the rest of the way. Where should Taylor exit the water if she can swim at 1.5 meters per second and run at 4 meters per second.

A queen-sized mattress is 20 inches longer than it is wide. A king-sized mattress is 16 inches wider than the queen-sized mattress but has the same length. The area of the king-sized mattress is 1,280 square inches more than that of the queen- sized mattress. An equation that can be used to solve for the dimensions of the king size mattress is The dimensions of the king size mattress are

When hired at a new job selling jewelry, you are given two pay options: ption A: Base salary of $12,000 a year, with a commission of 11% of your sales Option B: Base salary of $20,000 a year, with a commission of 4% of your sales In order for option A to produce a larger income, you would need sell at least $ of jewelry each year.

Brenda bought 10 dresses for 100 dollars. Find the rate of change and the cost of 15 dresses. $30 and $450 $10 and $150 $20 and $300

Use the following triangle to find the value of the indicated trigonometric function. Rationalize any denominators that you encounter in the answer.

1,889,550. In 1995 the population was 1,885,550. Compute the slope of the population growth (or decline) and choose the most accurate statement from the following: A city's population in the year x = 1979 was y The population is decreasing at a rate of 300 people per year. The population is decreasing at a rate of 250 people per year. The population is increasing at a rate of 300 people per year. The population is increasing at a rate of 250 people per year. The population is increasing at a rate of 450 people per year. The population is decreasing at a rate of 450 people per year.

A television network, Network A, is scheduling its fall lineup of shows. For the Tuesday night 8 p.m. slot, Network A has selected its top show. If its rival network, Network B, schedules its top show during the same time slot, Network A estimates that it will get 1.1 million viewers. However, if Network B schedules a different show during that time slot, Network A estimates that it will get 1.5 million viewers. Network A believes that the probability that Network B will air their top show is 0.3 and the probability that Network B will air another show is 0.7. Determine the expected number of viewers for Network A's top show.

Automotive Design. The angle formed by a car's windshield and dashboard is such that tane = √3. If the vertical distance y between the top of the windshield and the horizontal plane of the dashboard is 5 feet, what is the length of the windshield?

Which function has a positive rate of change? 27x-45y = 1 3x + 5y = 9 3x+8y = 12

Find z when x=87, m=65, and s= 11 using the formula z = x-m

Let R be the region bounded by the graphs of f(x) and g(x) as shown in the figure above. Use these graphs o answer the questions in this activity. Instructions are below: 1. sketch and label the graphs 2. Find the points of intersection using your graphing calculator and label them 3. Draw your representative rectangle on the graph to help with the questions below

Determine a polynomial equation for a graph that passes through the point (6, -196) and has three x- intercepts at (-8, 0), (-1, 0), and (5, 0). Show all your work. Points are awarded for setting up the correct equation, solving correctly and showing steps, and providing a correct answer.

Find the volume generated by rotating the area bounded by the graph of the following set of equations around the y-axis.

A particle is moving with acceleration given by a(t) = 6t-12 and an initial velocity of 9 m/s. (a) Find the velocity of the particle at time t. (b) Find the velocity of the particle after 3 seconds. (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) Find the total displacement of the particle during the first 8 seconds. (f) Find the total distance travelled by the particle during the first 8 seconds.

Determine the equation of the line, in y = mx+b form, perpendicular to 4x - 3y = 0 containing the point (-1, 2).

Four million tickets are sold for a lottery. a) If you purchase a ticket, find your odds against winning. b) If you purchase 50 tickets, find your odds against winning a) If you purchase a ticket, find your odds against winning. b) If you purchase 50 tickets, find your odds against winning.

Anesthesia. When a person has a cavity filled, the dentist typically gives a local anesthetic. After leaving the dentist's office, one's mouth often is numb for several more hours. If 70 ml of anesthesia is injected into the local tissue at the time of the procedure (t = 0), and the amount of anesthesia still in the local tissue / hours after the initial injection is given by A 70e-05, how much is in the local tissue 4 hours later?

Use the objective function z = 10x + 12y to determine the maximum profit subject to the constraints {x20 2x + 3y≤6 5x + 7y≤35 6x + 4y224 y21 Graph the feasible region, determine the corner points, and compute the maximum profit.

The function D(p) gives the number of items that will be demanded when the price is p. The production cost, C'(x) is the cost of producing x items. To determine the cost of production when the price is $10, you would: Evaluate D(C(10)) Solve D(C(x)) = 10 Evaluate C(D(10)) Solve C(D(p)) = 10

A researcher is interested in determining whether there is a relationship between price and quantity demanded for her firm.

For the given functions f(x) = 5x + 3 and g(x)=x-2, find (a) (fog)(2). (b) (gof)(-2), (c) (fof)(3), (d) (gog)(-3). (a) (fog)(2)=

The initial bacterium count in a culture is 1200. A biologist later makes a sample count of bacteria in the culture and finds that the relative rate of growth is 15% per hour. a. Find a function that models the number of bacteria after t hours. [ n(t)=n_e"] b. What is the estimated count after 12 hours? c. After how many hours will the bacteria count reach 500,000?

Luke purchased a warehouse on a plot of land for his business. The figure represents a plan of the land showing the location of the warehouse and parking area. The coordinates represent points on a rectangular grid with units in feet. In the future, Luke has plans to construct a circular storage bin centered at coordinates (50,40) on the plan. Which of the listed measurements could be the diameter of a bin that will fit on the plot and be at least 2 feet away from the warehouse? Select all that apply.

Choose all of the statistical questions. How many texts a day do most high school students send? How many texts did you send today? On average, how old are college graduates? When is your birthday?

Suppose a paint that is 15% gloss is mixed with a paint that is 30% gloss to make 5 gallons of a paint that is 20% gloss. How many gallons of each paint were used in the mixture? One must set a system of equations and use substitution or elimination to solve.

Suppose another drug is administered intravenously. The concentration c of the drug (in mg/L) in the bloodstream, t hours after it is administered, is modeled by the function c(t) a. Determine when the concentration will be 0.5 mg/L. -The concentration of the drug will fall to a level of 0.5 mg/L with 36 hours after the drug is given. b. Complete the table representing the concentration of the drug in the bloodstream, t hours after administration. Round to two decimal places as needed.

A popular restaurant does not take reservations. As a result, there is usually a waiting time before you can be seated. Assume the waiting time before being seated is normally distributed with a mean of 22 minutes and a standard deviation of 5 minutes. What is the probability that the waiting time will not exceed 20 minutes?

If two opposite sides of a square are increased by 7 meters and the other sides are decreased by 2 meters, the area of the rectangle that is formed is 36 square meters. Find the area of the original square. Must use a quadratic equation to solve the problem for any credit.

A normally distributed data set has a mean of 0 and a standard deviation of 2. Which of the following is closest to the percent of values between -4.0 and 2.0? 2.3% 81.9% 50% 84.1%

For the equation below, eliminate the xy-term and find the standard form of the conic in terms of x' and y'. Sketch the conic on the rotated axes. 41x²-24xy +34y²-25=0

During a game of online hearts, three cards are dealt, one at a time without replacement, from a shuffled, ordinary deck of cards. Find these probabilities rounded to six decimal places: (a) All are red cards. The probability that the three cards dealt are all red cards is (b) All are diamonds. The probability that the three cards dealt are all diamonds is

Using the water tower below, select all the shapes that could be used to model it. Pyramid Hemisphere Cone Prism Cube Cylinder

A set of data has a normal distribution with a mean of 50 and a standard deviation of 10. Draw a normal distribution to model these data and find the percent of data within each interval. A. All values between 50 to 60. B. All values less than 30. C. All values NOT between 40 and 50

A belief based on specific observations that has not been proven or disproven is called a conjecture of Fill in the blank to complete the statement below. A belief based on specific observations that has not been proven or disproven is called a conjecture or

The solution set to a system of dependent equations is given. Write three ordered triples that are solutions to the system. ((5z, 3-z, z) | z is a real number}

The enrollment at a local business school has been decreasing linearly. In 2002, there where 970 students enrolled. By 2007, there were only 710 students enrolled. Determine the average rate of change of the school's enrollment during this time period, and write a sentence explaining its meaning.

If the equation of the line y = 4x - 5 is changed to y = -x - 5, how is the graph affected? A) The line is shifted up. B) The line is closer to vertical. C) The line is closer to horizontal. D) The line is now decreasing from left to right. E) The line is now decreasing from right to left.

Find a formula for the nº partial sum of the series series converges. The formula for the n A. The series converges. The series' sum is B. The series diverges. If the series converges, what is the series' sum? Select the correct choice below and fill in any answer boxes within your choice.

The volume of water in swimming pools in a local neighborhood is normally distributed. What is the percentage of volumes that are within 3 standard deviations of the mean? Write your answer as a percent (use %) rounded to 1 decimal point.

The diagram below shows two spheres, one with diameter 12 cm and one with diameter 9 cm. What is the difference in their surface areas?

There were 24 students running in a race. How many different arrangements of first, second, and third place are possible?

Solve the triangle. Round to the nearest tenth. In AEFD, f = 29, d = 21, e = 13 mZE = 25°, mZF = 131°, mZD = 24° None of the other answers are correct mZE = 30°, m≤F = 110º, m≤D = 40° mZE=24°, mZF = 115°, mZD = 41° mZE=25°, m<F = 111°, mZD=44°

Draw a normal curve representation for the area, then write the numerical value of the area under the normal curve for each of the following. A) All values to the right of z=2.86 B) All values Not between -1.09 and 0.16 standard deviations from the mean. (hint: if you use Desmos, you will need to create two graphs)