Math Questions

Verizon offers to sell cellular phones listing for $100.24 with a chain discount of 15/10/5. Cellular Company offers to sell its cellular phones that list at $103.49 with a chain discount of 25/5. If Irene is to buy six phones, how much could she save if she buys from the lower-priced company? (Do not round intermediate calculations. Round all dollar amounts to the nearest hundredth. Round your final answer to the nearest cent.)

How did advances in physics and chemistry dramatically change manufacturing? made large multinational companies possible forced companies to share control of the production process employed fewer workers created research and development divisions

In 2004, the highest spaceplane flight was made in SpaceShipOne. A flight with this altitude can be modeled by the function below, where h is the altitude in meters and t is flight time in seconds. Approximately how long did the flight last? h(t) = -0.17t² + 187t +61,000 t≈1101.3 seconds t≈1363 seconds t≈261.7 seconds t≈1596 seconds

X' is a normally distributed random variable with a mean of 7.0 and a standard deviation of 3.00. Find the value x such that P(X<x) is equal to 0.86. (Note: the diagram is not necessarily to scale.)

Consider the given function f(x) = -3(x+1)² +12. (a) Determine whether the graph of the parabola opens upward or downward. (b) Identify the vertex. (c) Determine the x-intercept(s). (d) Determine the y-intercept(s). (e) Sketch the function. (f) Determine the axis of symmetry. (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in interval notation. Write your answers in exact form.

Victoria invests $300 into an account with a 2.5% interest rate that is compounded semiannually. How much money will she have in this account if she keeps it for 5 years? Round your answer to the nearest dollar.

The ratio of the number of mystery books to the number of science fiction books is 4:3. The ratio of the number of science fiction books to the number of biographies is 4: 5. If there are 48 science fiction books, find the total number of books.

Two cities have nearly the same north-south line of 97° W. The latitude of the first city is 27° N, and the latitude of the second city is 37° N. Approximate the distance between the cities if the average radius of Earth is 6400 km. The cities are approximately (Round to the nearest integer as needed.) kilometers apart.

An astronaut is returning to Earth in a spacecraft. If the spacecraft is descending at a rate of 13.81 kilometers per minute, what will be its change in height after 51/2 minutes? Round your answer to the nearest kilometer. 76 km -76 km 760 km -760 km

According to a goverment statistics department, 19.8% of women in a country aged 25 years or older have a Bachelor's Degree, 15.8% of women in the country aged 25 years or older have never married; among women in the country aged 25 years or older who have never married, 23.8% have a Bachelor's Degree; and among women in the country aged 25 years or older who have a Bachelor's Degree, 19.0% have never married. Complete parts (a) and (b) below.

The function fis defined as follows. f(x) = -x² +6 If the graph of fis translated vertically downward by 3 units, it becomes the graph of a function g. Find the expression for g (x).

Consider the system of equations. x+2y=8 -3x-2y=12 How do you solve the system of equations with Cramer's rule? Drag a value or determinant expression into each box to correctly solve the system using Cramer's rule.

Angle is in standard position and (-6, -4) is a point on the terminal side of θ What is the exact value of secθ in simplest form with a rational denominator?

Solve the equation for x. x² - 12x +32 = 0

Assuming the population has a bell-shaped distribution, if a sample size n = 19 has a sample mean x̄ = 33 with a sample standard deviation s = 7, find the margin of error at a 95% confidence level. Round the answer to two decimal places.

Carmen is choosing between two exercise routines. In Routine #1, she burns 44 calories walking. She then runs at a rate that burns 16.3 calories per minute. In Routine #2, she burns 22 calories walking. She then runs at a rate that burns 18.5 calories per minute. For what amounts of time spent running will Routine #1 burn at most as many calories as Routine #2? Use t for the number of minutes spent running, and solve your inequality for t

Using the verbal description below, write the original function and it's inverse. Explain your solution strategy. 1. Starting with a number x, subtract 5 2. Take the square of that quantity 3. Divide by 3

The number of bats in a colony is growing exponentially. After 2 years, there were 207 bats. After 4 years, there were 1863 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 11 years? Do not include units in your answer.

A die is rolled 3 times. What is the probability of showing a (n) 2 on every roll?

The total amount of sodium in 2 hot dogs and 3 cups of cottage cheese is 4,720 mg. The total amount of sodium in 5 hot dogs and 2 cups of cottage cheese is 6,300 mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese?

Liz does screen-printing. When she screen-prints a batch of T-shirts, there is an initial set-up time of 15 minutes. After that, it takes 3 minutes to print each shirt. How long does it take to screen-print a batch of 14 shirts?

A coach bought 3 jerseys and 2 pairs of shorts for each of the 14 players on her soccer team. The jerseys cost $15 each, and the shorts cost $12 each. The coach used a $100 coupon to hel pay for the uniforms. Rewrite the numerical expression with parentheses to model the total cost, $866. 14 x 3 x 15 +2 x 12 + 100

A contractor is in charge of hiring people for a construction project. The number of days it would take to complete the project with a full time workers can be found using the function f(x) = 234. Assume once workers are assigned to the project, no workers may be added or taken off the project until it is finished. Find and interpret the given function values and determine an appropriate domain for the function. f(-1) = meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. of the problem. f(2)= meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. f(6.5) = meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. Based on the observations above, it is clear that an appropriate domain for the function is

Given g(x)=x²-4x, find the equation of the secant line passing through (-4, g (-4)) and (2, g (2)). Write your answer in the form y=mx+b.

In Fall 2020, 10.5 million undergraduate students attended a 4-year institution full- time. Of those, 9,240,000 were under age 25, 945,000 were ages 25-34, and 315,000 were age 35 and older. Answer the questions below. Label your answers with a, b, c. a. What percent of the students were under age 25? b. What percent of the students were ages 25-34? c. What percent of the students were age 35 and older?

Express 9.603603603... as a rational number, in the form p/q where p and q have no common factors.

A circle has the equation x2 + y² + 6x-4y-23=0. (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any, of the graph. (a) The center of the circle is (Type an ordered pair, using integers or decimals.) The radius of the circle is (Type an integer or a decimal.) (b) Use the graphing tool to graph the circle. (c) What are the intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed. Type exact answers for each coordinate, using radicals as needed. Simplify your answer.) B. There is no intercept.

A point on the unit circle in the third quadrant has an x-value of -1/4, and makes an angle of a with the positive x-axis. (a) Draw the unit circle and plot the point. Indicate a.

A cell phone company charges $40 per month for unlimited calling, and $0.20 per text message sent. If t represents the number of text messages Roxy sent last month, which expression represents the cost of her bill last month before any taxes or additional fees?

Which of the following expressions is incorrect? |-12| = 12 |12| = 12 -|-12| = -12 -|12| = 12

If you were to solve the following system of equations by elimination, what number should you multiply the top equation by? 7x + 2y = 29 3x + 4y = 25 a.) 4 b.) -2 c.) 2 d.) 2 e.) 8

The Thomas Jefferson Memorial is on 18.36 acres of land and the Franklin Delano Roosevelt Memorial is on 7.5 acres of land. How many more acres is the Jefferson Memorial than the Roosevelt Memorial? 9.86 acres 10.86 acres 11.31 acres 17.61 acres

A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $7.80 and then an additional 7 cents per minute of use. In Plan B, there is no monthly fee, but the customer pays 9 cents per minute of use. For what amounts of monthly phone use will Plan A cost at least as much as Plan B? Use m for the number of minutes of phone use in a month, and solve your inequality for m.

The amount of water an electric dishwasher uses to wash dishes varies directly with the number of loads of dishes. The dishwasher uses 32 gallons of water to wash 4 loads of dishes. How many gallons of water will the dishwasher use to wash 10 loads of dishes? Record your answer. Be sure to use the correct place value.

Assuming the population has a bell-shaped distribution, if a sample size n 12 has a sample mean x= 35 with a sample standard deviation s = 7, find the margin of error at a 95% confidence level. Round the answer to two decimal places.

The vertices of an ellipse are located at (1,4) and (9,4) and its co-vertices are located at (5, 7) and (5, 1). a. Find the center of the ellipse.

If you solve a system of equations, and your final step ends with the following answer: 12= 12....how many solutions are there to the system of equations? infinite solutions no solution one solution

Suppose that in a large population of students, the mean amount of sleep the previous night was μ = 6.9 hours and the standard deviation was σ = 1.55 hours. Consider randomly selected samples of n = 220 students. (a) What is the value of the mean of the sampling distribution of possible sample means? Mean = 6.9 (b) Calculate the standard deviation, s.d., of the sampling distribution of possible sample means. (Round your answer to three decimal places.) s.d.(x) = 105 (c) Use the Empirical Rule to find values that fill in the blanks at the end of the following sentence. (Round your answers to three decimal places.) For 68% of all randomly selected samples of n = 220 students, the mean amount of sleep the previous night will be between 219.895 and 220.105 hours. (d) Use the Empirical Rule to fill in the blanks at the end of the following sentence. (Round your answers to three decimal places.) For 95% of all randomly selected samples of n = 220 students, the mean amount of sleep will be between 219.790 and 220.210 hours.

Find the function that is finally graphed after the following transformations are applied to the graph of y=√x in the order listed. (1) Vertical stretch by a factor of 2 (2) Shift down 3 units (3) Shift right 1 unit

What does the graph of y=x+- 1/(x+2)²-3 look like? Graph the equation on your calculator. Use the trace and/or zoom buttons to find the r- and y-intercepts. What is the domain of this function? What is the range?

Match the amplitude, midline, period, and frequency for the cosine equation. f(x) = 5 cos(2x) + 3 1.5 2. π 3. 2 4. y = 3 a. Amplitude b. Frequency c. Midline d. Period

Given g(x)=x²-5x, find the equation of the secant line passing through (-3, g (-3)) and (4, g (4)). Write your answer in the form y=mx+b.

Find the exact value of the following expression. Do not use a calculator to enter a decimal approximation. sinπ/4

According to a recent Pew Research poll, 68% of Americans say that the U.S. economic system unfairly favors the powerful. In a recent sample of 830 Americans, 111 agreed that the U.S. economic system unfairly favors the powerful. Determine the values of p and p. Round solutions to two decimal places, if necessary. p= p^=

An elliptical whispering gallery is 10 m long. Anna and Francis find that if they each stand 4 m away from the ends of the gallery at its foci, they can hear each other perfectly. What is the width of the gallery?

Write the equation that results in the desired transformation. The cube root function, vertically shrunk by a factor of 0.5, and reflected across the x-axis. y = (Type an expression using x as the variable.)

The mean weight of all Goliath grouper caught on the Treasure coast is 438 pounds, with a standard deviation of 49 pounds. Suppose a random sample of 92 Goliath Grouper from the Treasure Coast are aught and weighed. Determine the probability that the average weight of the sample of 92 Goliath Grouper is within 8 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast. Round the solution to four decimal places, if necessary. P( within 8 pounds of μ)

Suppose there are eight salespeople. If seven of the salespeople earned $2,400, $2,500, $2,800, $2,800, $3,400, $3,400, and $3,800, how much would the eighth person would need to earn for the median to be $3,000? $3,200 $3,000 $2,800 $3,100

Two groups of students on a fieldtrip is getting food in a fast food restaurant. The first group bought 8 burgers and 4 soft drinks for $34.08. The second group bought 5 burgers and 5 soft drinks for $25.25. How much does one burger cost? $1.58 per burger $2.97 per burger $3.47 per burger $2.08 per burger

A landscaping company placed two orders with a local nursery. The first order was for 13 bushes and 4 trees and totaled $487. The second order was for 6 bushes and 2 trees and totaled $232. What was the cost of each bush and each tree? Bushes $31, Trees $64 Bushes $47, Trees $23 Bushes $23, Trees $47 Bushes $23, Trees $52