Math Questions

Super fine 40-gauge copper wire has a diameter of only 0.080 mm and weighs only 44.5 g/km. Suppose a spool of 40-gauge wire weighs 245. g less after some wire is pulled off to wind a magnet. How could you calculate how much wire was used? Set the math up. But don't do any of it. Just leave your answer as a math expression. Also, be sure your answer includes all the correct unit symbols. length of wire =

Suppose that f(x) is a continuous function with f(1) = -6 and f(5)= 6. Determine which choice best describes the following statement. "f(3) = 0 Always true Sometimes true and sometimes false Always false

Find the average rate of change of g (x)=2x² +8 from x=2 to x = 4.

Consider the line y=-8x+7. Find the equation of the line that is parallel to this line and passes through the point (-6, -2). Find the equation of the line that is perpendicular to this line and passes through the point (-6, -2). Note that the ALEKS graphing calculator may be helpful in checking your answer.

A biologist has a 691-gram sample of a radioactive substance. Find the mass of the sample after two hours if it decreases according to a continuous exponential decay model, at a relative rate of 14% per hour.

Fill in the blank. To complete the square of x²-8x, add To complete the square of x²-8x, add (Type an integer or a simplified fraction.)

P (n), given below, is the price P in dollars for n grams of vitamins. P(n)=0.8n+5.2 Complete the following statements. Let P-¹ be the inverse function of P. Take x to be an output of the function P. That is, x= P (n) and n = P-¹(x). (a) Which statement best describes P-¹(x)? The amount of vitamins (in grams) for a price of x dollars. The price (in dollars) for x grams of vitamins. The ratio of the price (in dollars) to the number of grams, x. The reciprocal of the price (in dollars) for x grams of vitamins. (b) p-¹(x) = (c) P-¹(10.4) =

If using the method of completing the square to solve the quadratic equation x² + 8x + 37 = 0, which number would have to be added to "complete the square"?

Suppose that the functions & and t are defined for all real numbers x as follows. s(x)=4x-3 t(x)=x-2

Use the Factor Theorem to determine whether x-3 is a factor of P(x) = -x4+x3+5x²-4. Specifically, evaluate P at the proper value, and then determine whether x-3 is a factor.

Use the ALEKS graphing calculator to find the vertex and x-intercept(s) for the quadratic function. f(x)=-3.38x²-5.2x-2

A vector u has initial point (5, 4) and terminal point (4, -2). Write u in the form u = ai + bj.

Find the unit vector in the direction of (15, 8).

Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum = 8, maximum = 78, 6 classes The class width is. Choose the correct lower class limits below. A. 8, 19, 32, 43, 55, 68 B. 8, 20, 32, 44, 56, 68 C. 19, 31, 44, 55, 67, 79 D. 20, 31, 44, 56, 68, 79 Choose the correct upper class limits below. A. 20, 32, 44, 56, 68, 79 B. 19, 31, 44, 56, 67, 79 C. 19, 31, 43, 55, 67, 79 D. 20, 32, 43, 55, 68, 79

How long will it take for a $4000 investment to grow to $7148 at an annual rate of 9.4%, compounded quarterly? Assume that no withdrawals are made.

13. Diego wants to purchase a used car that sells for $6,399. The dealer has offered him $299 on his trade-in car. The total cost of the car Diego wants to buy will be a. $4,543 b. $6,100 c. $6,399 d. $6,698

Given vectors a = (4, -5) and b=(3, 6), find 5a-3b.

Identify and graph the polar equation. r=7-7 sin θ What shape does the polar equation form when graphed? A. Limacon without an inner loop. C. Limacon with an inner loop. B.Cardioid that is symmetric to line θ =π/2 D. Cardioid that is symmetric to the polar axis.

A building 160 feet tall casts a 90 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.) 61° 56° 29° 34°

12. Harrison loaned his friend Mattson $100 for one year at a simple interest rate of 5%. The total amount of money that Mattson will pay back at the end of the year is a. $5.00 b. $100.00 c. $105.00 d. $120.00

A chemistry student needs 20.0 g of diethylamine for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers that the density of diethylamine is 0.706 g/cm^3 . Calculate the volume of diethylamine the student should pour out.

The functions f and g are defined as follows. f(x)=x²+9x+5 and g(x)= 3/ x²-2 Find f(x-3) and g(-/x)

Andrea simplified a polynomial expression. The solution was 4x²-7x + 5. Which of the following could have been the original expressions? SELECT ALL THAT APPLY. (3x²-9x+8)+(x²+2x-3) (2x² - 4x-5)-(-2x² + 3x - 10) (5x²-2)-(x²+7x+3) (4x² + 3x) -(10x + 5)

If θ=210°, find the exact value of each expression below. (a) 2 sin θ = (b) sin (-θ) = (c) sin 2θ =

Which situation is an example of exponential decay? The amount of a radioactive element is decreasing at a rate of 35% per year. The weekly earnings of a part-time job that pays $8 per hour is increased by a weekly bonus of $25. The amount deducted for taxes decreases an annual salary by about 22%. The number of ants in an ant farm is increasing at a rate of 108% per week.

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.