Basic Math Questions and Answers

The demand for a particular commodity is given by D(x) = -35x + 150; that is, x units will be sold (demanded) at a price of p= D(x) dollars per unit. Consumer expenditure E(x) is the total amount of money consumers pay to buy x units. Use calculus to find the instantaneous rate of change of expenditure with respect to x when x = 6. Is expenditure increasing or decreasing when x = 6?

In this problem we will give a graph sketch of f(x) = (3-x)(x + 2)²(x - 1). (a) Factor f(x), find the roots. (b) For each root from part (a), give the degree. (c) Determine the sign decomposition for f(x). (d) Graph f(x):

Health and Fitness Jorge measured his heart rate after jogging. He counted 11 beats during a 6-second interval. What was the unit rate for Jorge's heart rate in beats per minute? 3. Chen bikes 2 miles in hour. What is Chen's unit rate in miles per hour? Amal can run mile in 13 minutes. A. If he can maintain that pace, how long will it take him to run 1 mile?

In Washington DC, the tax on a property assessed at $490,000 is $6,860. If tax rates are proportional in this city, how much would the tax be on a property assessed at $390,000? Choose the proportion you would use to solve the problem.

Which of the following lines is PARALLEL to the graph of 5x + 2y = 8? y = x - 19 y = 2x - 5 y = − 2x + 7 y = 2x/5

Anut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per pound. But at the end of the month the peanuts had not sold well, so, in order to sell 70 pounds of peanuts, the manager decided to mix the 70 pounds of peanuts with some cashews and sell the mixture for $3.50 per pound How many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue? The manager should mix pounds of cashews with the peanuts.

A shark is at -80 feet. It swims up and jumps out of the water to a height of 15 feet. Write a subtraction expression for the travels.

The total stopping distance T of a vehicle is shown below, where T is in feet and x is the speed in miles per hour. Approximate the change and percent change in total stopping distance as speed changes from x = 17 to x As speed changes from x = 17 to x = 19 miles per hour, an approximation of the change in x is To approximate the change in total stopping distance, differentiate T = 2.5x + 0.5x² with respect to x and solve for the differential dT. Substitute 17 for x and 2 for dx, to conclude that the approximate change in total stopping distance is as follows.

What is your probability of winning given this situation: You are trying to win a stuffed animal. You have to hit a target two times in a row to win. The probability of you hitting the target in one try is 63%. 23.3% 63% 39.6% 106%

The volume of a rectangular prism is 2x³ +17x² +38x + 15 and one side has a length of x + 5. Find the length of one of the other sides. x-3 x+5 2x + 1 2x-1

A town has a merchant, a baker, and a farmer. To produce $1 worth of output, the merchant requires $0.20 worth of baked goods and $0.45 worth of the farmer's products. To produce $1 worth of output, the baker requires $0.4 worth of the merchant's goods, $0.20 worth of his own goods, and $0.35 worth of the farmer's goods. To produce $1 worth of output, the farmer requires $0.30 worth of the merchant's goods, $0.25 worth of baked goods, and $0.35 worth of his own products. How much should the merchant, baker, and farmer produce to meet a demand for $25,000 worth of output from the merchant, $14,000 worth of output from the baker, and $12,000 worth of output from the farmer? The merchant should produce $, the baker should produce $, and the farmer should produce $[ (Round the final answer to the nearest dollar as needed. Round all intermediate values to two decimal places as needed.)

Use transformations of the graph of f(x)=x² to determine the graph of the given function. g(x)=(x-6)² ***** Select all the transformations that are needed to graph the given function using f(x)=x² A. Shift the graph 6 units to the left. B. Reflect the graph about the x-axis. C. Shift the graph 6 units to the right. D. Reflect the graph about the y-axis. E. Stretch the graph vertically by a factor of 6. F. Shift the graph 6 units up. G. Shift the graph 6 units down. H. Shrink the graph vertically by a factor of 6. I. Shrink the graph horizontally by a factor of 6. J. Stretch the graph horizontally by a factor of 6.

Store normally sells cashews for $4.00 per pound and peanuts for $1.50 per pound, But at the end of the month the peanuts had not sold well, so, in order to sell 70 pounds of peanuts, the manager decided to mix the 70 pounds of peanuts with some cashews and sell the mixture for $3 50 per pound. How many pounds of cashews should mixed with the peanuts to ensure no change in the revenue?

Farmer Ed has 150 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed? The width, labeled x in the figure, is

A rocket is fired upward with an initial velocity v of 676 feet per second. The function S(t)= - 16t² +676t can be used to find the height S of the rocket, in feet, at any time t in seconds. Find the height of the rocket 2 seconds after it takes off.

At a local car dealer, the ideal selling price of a car is $22,000. The dealer allows this price to vary $1200. Create an absolute value inequality that models the range of the price the dealer can sell the car. (Hint: Test your inequality to make sure the price is $1200 below and above the selling price works.)

Determine which of the equations, y = 2x+8 or y=0.5x+8, is the better fit for the data points. (0,8), (1,9), (2,9), (3,10) Which equation is a better fit for the data points? A. y=0.5x+8 B. y=2x+8

Solve the equation by factoring. 2x(x - 2) = 6x² - 5x Rewrite the equation in factored form. =0 (Factor completely.) The solution set is

Dave will drive 42.3 miles from home to his doctor's office. Then he plans to drive 24.4 miles from the doctor's office to a department store. Finally, he will drive 48.5 miles from the department store to home. If Dave's car gets 22 miles per gallon of gasoline, then the total amount of gasoline his car will use during these three trips is a. Between 3 and 4 gallons b. Between 4 and 5 gallons c. Between 5 and 6 gallons d. Between 6 and 7 gallons e. Between 7 and 8 gallons

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of degree Celsius. II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. III. A temperature increase of degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. A) I only B) II only C) III only D) I and II only

A driver averaged 42 miles per hour and took 7 hours to travel between two cities. What is the distance between the two cities? The distance between the two cities is

A shark can take in 600 cubic meters of water in a day when it is feeding. If a shark has taken in 3 x 10 cubic meters of water, how many days has it been feeding? Write your answer in standard notation.

Sketch the graph of y = 2(x - 2)² + 4. Then identify the vertex

The function below has at least one rational zero. Use this fact to find all zeros of the function. g(x)=7x + 29x²³ + 24x² - x - 3 If there is more than one zero, separate them with commas. Write exact values, not decimal approximations.

The sales tax on an item is 5%. Express the total cost, C, in terms of the price of the item, P. Be sure to use the correct case of the variable when entering your expression.

Classify the polynomial by degree and number of terms: f(x) = 4x² - 2x¹ +1 Quadratic trinomial Quartic trinomial Quadratic polynomial Quartic polynomial

Perform the following sequence of transformations on ADEF. D(0, 4), E(2, 0), and F(-1, -3). Translate ADEF 5 units left and 1 unit down Reflect the image AD'E'F' across 3x + 3y = 6 b. Write the algebraic description for the translation. From preimage to image 1. c. Are triangles congruent? How do you know?

Solve the equation. X+5/3= X+2/4 = 5 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is B. There is no solution. (Simplify your answer.)

Which of the following is a false statement? A horizontal cross section of a cylinder and a cross section of a sphere are the same shape. The diagonal cross section of a pyramid is a rectangle. The cross section of a sphere is the same no matter where the cross section is cut. A perpendicular cross section of a cylinder and a horizontal cross section of a rectangular pyramid are the same shape.

A freight train starts from Los Angeles and heads for Chicago at 40 mph. Two hours later a passenger train leaves the same station for Chicago traveling 60 mph. How long before the passenger train overtakes the freight train?

Which function has real zeros at x = -10 and x = -6? f(x) = x² + 16x + 60 f(x)=x²-16x + 60 f(x) = x² + 4x + 60 f(x) = x² - 4x + 60

Profit A cellular telephone company esti- mates that, if it has x thousand subscribers, its monthly profit is P(x) thousand dollars, where P(x) = 12x - 200. a. How many subscribers are needed for a monthly profit of 160 thousand dollars? b. How many new subscribers would be needed to raise the monthly profit from 160 to 166 thousand dollars?

Write each expression in radical form. Use "sqrt(x)" fo

To determine whether this possible extrema is a maximum or a minimum, we can use the Second Derivative Test. Again differentiate with respect to s. Therefore, the maximum profit occurs when s = 400 maximum We can therefore conclude that the amount of money the company should spend on advertising in order to yield a maximum profit is $86800

What is the perpendicular cross section from the apex to the base of a pyramid? Circle Square Triangle Rectangle

Tim is choosing between two cell phone plans that offer the same amount of free minutes. Cingular's plan charges $39.99 per month with additional minutes costing $0.45. Verizon's plan costs $44.99 with additional minutes at $0.40. How many additional minutes, a, will it take for the two plans to cost the same?

Graph the following system of equations. x+y = - 4 y=x-8 Use the graphing tool to graph the linear equations.

How much of a(n) 60% orange juice drink must be mixed with 3 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice? The amount of 60% orange juice drink is gallons.

On the first Tuesday of every month, Roth's gives seniors a 15% markdown on everything they purchase including sales merchandise. On the first Tuesday of this month, Jack Graham, a senior, purchased a three-piece suit marked down 40%. If he paid a total of $152.79, including a 7% sales tax, what was the suit's regular selling price?

A pharmacist wishes to mix a solution that is 8% Minoxidil. She has on hand 60 ml of a 3% solution and wishes to add some 10% solution to obtain the desired 8% solution. How much 10% solution should she add?

Select all the expressions that are equivalent (equal) to 2. Show your 8+ (-9) + 3 -4+15-7 -9+8+3 -9-(-12) + (-1) 13-6-3 8- (9+3)

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1800. What was the rate charged per hour by each mechanic if the sum of the two rates was $135 per hour? Note that the ALEKS graphing calculator can be used to make computations easier. First mechanic: $ per hour Second mechanic: $ per hour

Use a graphing utility to complete the table and estimate the limit as x approaches infinity. Then use a graphing utility to graph the function and estimate your answer graphically. (Round your answers to five decimal places.)

Find the real solutions of the equation. 32x4-4x²-1=0 What is the solution set? Select the correct choice below and fill in any answer boxes in your choice. A. B. There are no real solutions.

Suppose two trains leave a station at the same time, traveling in opposite directions. Train B travels 20 mph faster than Train A. In 3.5 hours, the trains are 378 miles apart. Find the speed of each train. The speed of Train A is

In industry, the relationship be- tween wages and the quit ratio of employees is defined to be the percentage of employees that quit within 1 year of employment. The quit ratio of a large restaurant chain that paid its employees the minimum hourly wage ($7.25 per hour) was .2 or 20 employees per 100. When the company raised the hourly wage to $8, the quit ratio dropped to .18, or 18 employees per 100. a. Assuming a linear relationship be- tween the quit ratio Q(x) and the hourly wage x, find an expression for Q(x). b. What should the hourly wage be for the quit ratio to drop to 10 employees per 100?

Use deductive reasoning to arrive at a conclusion based on the assumptions given. (a) ASSUMPTIONS (b) ASSUMPTIONS 1. All Martians have green eyes. 2. Henry is a Martian. 1. The sum of the measures of the angles of a triangle is 180. 2. In a particular triangle, the sum of the measures of two angles is 100. A prime number is any whole number that is divisible only by itself and 1. For example, 7, 11, and 13 are prime numbers. Evaluate the formula n² +n + 17 using all integer values of n from 0 to 9, inclusive. Do you notice a pattern? (a) Using inductive reasoning, draw a conclusion. (b) Is your conclusion true for all values of n? Test n = 16.

Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system. 3x - y = 4 2x + 3y = 21 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. The solution is x= 3 and y = 5. B. There are infinitely many solutions. Using ordered pairs, they can be expressed as {(x,y) | x= C. The system is inconsistent.

Evaluate the following polynomial using synthetic substitution! You need to know how to do this question with this method for future quizzes and tests so please don't solve another way. f(x) = x² + 3x - 20; x = 4

A 15 foot ladder is sliding down a building at a constant rate of 2 feet per minute. How fast is the base of the ladder moving away from the building when the base of the ladder is 9 feet from the building?