Math Questions

The polynomial function g is defined by g(x)=-x-5x³-4x² + 4x-1. Use the ALEKS graphing calculator to find all the points (x, g(x)) where there is a local maximum.

Solve the system of equations by graphing. Check your solution. y = -3x+2 3y + 9x =6

Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $125. Two adults and three children must pay $89. Find the price of the adult's ticket and the price of a child's ticket. The price of a child's ticket is $. The price of an adult's ticket is $

The functions f and g are defined as follows. f(x)=4x+3/5x+2 and g(x)=√x^2-8x Write your answers without parentheses and simplify them as much as possible. Find f(1/x) and g(x-2).

Use the power reducing formulas to rewrite cos44x in terms of the first power of cosine. Simplify your answer as much as possible. To indicate your answer, first choose one of the four forms below.

The area A (r) (in square meters) of a circular algae colony with radius r meters is given by A (r) =πr². The radius M (t) (in meters) after t minutes is given by M (t) = 10/3 t. Write a formula for the area Z (t) (in square meters) of the algae colony after t minutes.

Use a half-angle formula to find the exact value of tan 11 π/12

A sports arena can hold 18,500 people, plus or minus 1200 people. A. Write an absolute value equation to represent the number of people that can attend an event. B. Explain the steps to solve the equation.

Match each action with its effect on the set of scores shown. Use each action only once. 90, 85, 35, 70, 67, 76, 90, 79, 94, 100, 87, 61, 56, 80, 67, 65 The greatest change on the mean because it is an outlier The mode of the data changes to 67. The median of the data changes to 79. The range of the data changes to 59. The mean of the data changes to 73.87.

Find the unit vector in the direction of (7,5). Write your answer in component form.

A vector t has initial point (3,-6) and terminal point (4,-2).

Graph the solution of the following system. x-4y ≥-4 2x+y≤≤ 4

Use interval notation to represent all values of x satisfying the given conditions. f(x) = 5x-4, g(x) = 4x-6, and f(x) > g(x) A. (-10,00) B. (-∞0.-2] C. (-2,00) D. [-2.00)

Suppose a point has polar coordinates (6, 2π/3) with the angle measured in radians. Find two additional polar representations of the point. Write each coordinate in simplest form with the angle in [-2π, 2π].

Which of the following regressions represents the strongest linear relationship between x and y? Regression 1 y = ax + b a =-17.8 b = -8.1 r = -0.4682 Regression 2 y = ax + b a = = 4 b = -19.5 r = 1.1369 Regression 3 y = ax + b a = = 4.9 b = -16.8 r = 0.5454 Regression 4 y = ax + b a = 4.1 b=-17.5 r = 0.5836

Alexa is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Alexa will earn $20 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties on 8 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Alexa's songs were played. Define the variables that you use to write the system.

Find the solution to the system by the addition (elimination) method. Check your answers. 10x + 7y = 21 5x +9y = 27 What is the solution to the system? (Type an ordered pair.)

Find the direction angle of the vector v=-3i-8j. That is, find the angle between 0 and 360° that v makes with the positive x-axis (measured counterclockwise), when v is in standard position. Do not round any intermediate computations, and round your answer to the nearest whole number.

At a school, the school population is 2/5 boys. There are 450 students at the school who are boys. A. Write a proportion to represent the number of girls in the school. B. How many girls are in the school?

The base of a 13-foot ladder is 3 feet from a building. If the ladder reaches the flat roof, how tall is the building? The height of the building is

Graph the solution of the following system. x-2y ≥ -6 3x + y ≤ 6

Point T is at (-6, 2). What are the coordinates of T' after R(x-axis) o R(y-axis)? If a figure is translated with the rule T<-6, 3>, what translation moves the image back to the original position?

Solve the quadratic equation using the square root property. (x-5)² = -3

The base of a 10-foot ladder is 2 feet from a building. If the ladder reaches the flat roof, how tall is the building?

Against the wind a small plane flew 280 miles in 1 hour and 10 minutes. The return trip took only 50 minutes. What was the speed of the wind? What was the speed of the plane in still air? The speed of the plane in still air was mph. The speed of the wind was mph.

For the given data set, find the a. mean and b. mode (or state that there is no mode) Ages of teachers in the mathematics department of a certain high school: 26,31,48,37,24,30,26,37,20 a.37 b. 30 a. 31 b. 26,37 a. 26 b. 31.5 a. 30 b. 31

Consider the line - 6x+7y=4. Find the equation of the line that is perpendicular to this line and passes through the point (1, 5). Find the equation of the line that is parallel to this line and passes through the point (1, 5). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line: Equation of parallel line:

Against the wind a small plane flew 210 miles in 1 hour and 10 minutes. The return trip took only 50 minutes. What was the speed of the wind? What was the speed of the plane in still air? The speed of the plane in still air was mph. The speed of the wind was mph.

Use the frequency histogram to complete the following parts. (a) Determine the number of classes. (b) Estimate the greatest and least frequencies. (c) Determine the class width. (d) Describe any patterns with the data. classes. (a) There are (Type a whole number.) (b) The least frequency is about (Round to the nearest whole number as needed.) The greatest frequency is about (Round to the nearest whole number as needed.) (c) The class width is (Type an integer or a decimal. Do not round.) (d) What pattern does the histogram show?

A building is 60 feet high. At a distance away from the building, an observer notices that the angle of elevation to the top of the building is 41°. How far is the observer from the base of the building? 79.5 ft 69.0 ft 52.2 ft 91.5 ft

The population density of an area can be computed by dividing the total population by the total land area. The population density of Rhode Island is 870.5 people/square mile and the population is 1,055,046. What is the area of Rhode Island?

Make a box-and-whisker plot that represents the data. Describe the plot, in the area provided, by giving Q1,Q2,Q3, and Q4. If there are any outliers be sure to identify them. Newly planted tree heights (in inches): 16, 10, 10, 18, 18, 6, 24, 16

Find the unit vector in the direction of (-8,-6). Write your answer in component form. Do not approximate any numbers in your answer.

A technical machinist is asked to build a cubical steel tank that will hold 540 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.01 m.

Which of the following is a true statement? a. A horizontal translation changes the x-coordinate of the endpoints of a figure but the y-coordinate remains the same. b. A vertical translation changes the x- coordinate of the endpoints of a figure but the y-coordinate remains the same. c. A horizontal translation changes the y-coordinate of the endpoints of a figure but the x-coordinate remains the same. d. A vertical translation changes both coordinates of the endpoints of a figure.

A space plane skims the edge of space at 4000 miles per hour. Neglecting altitude, if the circumference of the planet is approximately 20,000 miles, how long will it take for the plane to travel around the planet? How long will it take for the plane to travel around the planet? It will take__for a plane to travel around the planet. (Type an integer or a decimal.)

Brandon is on one side of a river that is 80 m wide and wants to reach a point 250 m downstream on the opposite side as quickly as possible by swimming diagonally across the river and then running the rest of the way. Find the minimum amount of time if Brandon can swim at 2 m/s and run at 4 m/s. (Use decimal notation. Give your answer to two decimal places.)

Ivan takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit hour, and at Pinewood, class fees are $115 per credit hour. Ivan is taking a combined total of 19 credit hours at the two schools. Suppose that he is taking w credit hours at Westside. Write an expression for the combined total dollar amount he paid for his class fees.

Divide and express the result in standard form. 2i/6-8i

Express the following interval in set-builder notation and graph the interval on a number line. [0, 8) What is the interval in set-builder notation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. B. All real numbers. C. There is no solution.

Suppose H (x)= (5x-2)6. Find two functions and g such that (fog)(x) = H (x). Neither function can be the identity function. (There may be more than one correct answer.) ƒ(x) = g(x)=

A plane flying a straight course observes a mountain at a bearing of 30.2° to the right of its course. At that time the plane is 9 kilometers from the mountain. A short time later, the bearing to the mountain becomes 40.2°. How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a km)? 7 km 13.1 km 4.7 km 11.5 km

Chris has a job selling newspapers every morning. He receives a base pay of $10 per day and also gets 15 cents for every paper he sells. One morning he made $16.45. How many papers did he sell? A 39 B 43 C 52 D 64

How is a sample related to a population? Choose the correct answer below. A. A sample is a numerical measure that describes a sample characteristic. B. A sample is a subset of a population. C. A sample is the collection of all outcomes, responses, measurements, or counts.

You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly more than 0.18. Thus you are performing a right-tailed test. Your sample data produce the test statistic z 1.92. Find the p-value accurate to 4 decimal places.

Brent Pickett borrowed $4000 from his brother Dave. He agreed to repay the money at the end of 2 years, giving Dave the same amount of interest that he would have received if the money had been invested at 3.25% compounded quarterly. How much money did Brent repay his brother? Brent repaid his brother $ (Round to the nearest cent as needed.)

Read the sentence. Toni's father taught at two schools, Concordia College and University of Wisconsin-Madison. How does the underlined phrase function in the sentence? as an adverb prepositional phrase as an appositive with essential information as an appositive with nonessential information as an adjective prepositional phrase

A man uses a loan program for small businesses to obtain a loan to help expand his vending machine business. The man borrows $29,000 for 4 years with a simple interest rate of 1.3%. Determine the amount of money the man must repay after 4 years. The man must repay $

Veronica wants to cut a sheet of paper into squares with an area of 12 square inches. For the best approximation, the length of inches. If each side were exactly this length, the each side of the square pieces of paper must be approximately equal to area of each square would be square inches.

A scuba diver is taking samples for research. The depths (in feet) from which samples were taken are listed below. 24.2, 11.1, 8.2, 17.5, 28.4, 8.2, 9.7, 41.2, 13.4, 12.1, 26.8, 8.2 a. Find the mean, median, and the mode of the depths. Be sure to show your work. b. Which measure of center best represents the data? Explain.