Math Questions

A function of x contains the five ordered pairs of the form (x, y). Four of these points are given below. (-2, 7), (0, 3), (1, -4), (5,-2) Which ordered pair could represent the fifth point? A. (1,9) B. (5,7) C. (3,-4) D. (0, -8)

You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 3x-2y=7 Equation 1 3x+4y=17 Equation 2 A. Multiply equation 1 by 2. Then add the new equation to equation 2. B. Subtract the left side of equation 2 from the left side of equation C. Subtract equation 2 from equation 1.

A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12). Find P(7). 1/12 1/2 5/12 7/12

When we throw a tennis ball into a lake for my dog she knows that if she swims straight for it she'll take longer to get to the ball. Instead, she runs along the beach for a short distance and then turns and swims for the ball. Let's say we throw the ball so that it lands 15 meters out into the water and 5 meters to the right of where we're standing. Draw a picture of this scenario. Finally, let's say that the dog runs at a rate of 2.5 meters per second and swims at a rate of 1 meters per second. (A) If the dog were to swim directly for the ball how long will it take? Recall that distance is equal to rate multiplied by time. Direct Swim Time = seconds. (B) If the dog were to run down the beach and make a 90 degree turn and then swim directly for the ball how long would it take to get to the ball? Time for longest run and 90 degree turn to swim = seconds. (C) My dog is smarter than either of the answers in parts (A) or (B). She knows that there is a better solution. Let be the amount of running that she does down the beach (clearly r is less than 5 and greater than 0). The trip has now been broken into two parts: a running leg of length x meters and a swimming leg at some angle to the beach. What is the length of the swimming leg as a function of r? Length of swimming leg = (D) Write a function T(r) that expresses the total time to get to the ball in terms of how far she runs down the beach. T(r):

At a point on the ground 80 ft from the base of a tree, the distance to the top of the tree is 11 ft more than 2 times the height of the tree. Find the height of the tree.

The side of a square floor tile is measured to be 16 inches, with a possible error of 1/32 inch. Use differentials to approximate the possible error and the relative error in computing the area of the square. Step 1 Recall that the formula for the area of a square is A = x2 where x is the side of the square. We are given that the side of the square floor tile is x = 16 inches and the possible error Δx = dx = ±1/32 Step 2 To approximate the possible propagated error in computing the area of the square, differentiate A =x² with respect to x. dA /dx= dA= Step 3 Substitute the given values of x and dx into the equation. dA = 2x dx Step 4 Assuming that ΔA=dA, we can conclude that the approximate possible propagated error in computing the area of the square is in².

Complete the missing measurement for each diagram. Then create an exponent equation and a square root equation that relate to the diagram Diagram Exponent Equation Square Root Equation Area = Area = 144

Solve the 3 by 3 system of equations by using the matrix capabilities of your calculator to solve the system. For full credit you must write the augmented matrix you entered in your calculator, the matrix resulting from using the calculator function, and the solution as an ordered triple. 2x -y + 5z = -2 x+3y-z=6 4x + y + 3z = -2

A robot's body is made up of a rectangular prism with side lengths 4 feet by 2 feet by 3 feet. The head is made up of a cylinder with a height of 2 feet and a radius of 6 inches. What is the volume of the robots head and body in cubic feet? 25.57 ft^3 250.08 ft^3 37.68 ft^3 51.15 ft^3

4. Choose the appropriate answer for each of these questions: A. The derivative of a function measures: a. How steep its graph is b. What value it takes for a given x c.Where its graph crosses the x-axis B. The derivative of a function at a given point is a: a.An equation b.A number c.A function C. The derivative of a function is closely related to the a. Set of solutions of an equation b. Slope of a line c. Zero of a function

The pH scale was designed to make it convenient to express hydrogen ion concentrations that are small in aqueous solutions. The definiton of pH is in terms of base 10 logarithms. pH = -log[H+] where [H+] is the hydrogen ion concentration. a. If the hydrogen ion concentration in a solution is 7.60 × 10–5 mol/L, the pH is b. If the pH of a solution is 3.165, the hydrogen ion concentration is mol/L.

Paul Curcio earns $7.45 per hour for regular time up to 40 hours, time-and-a-half for overtime, and double time for working on holidays. Find his gross pay (in $) if he worked 6 holiday hours for a total of 58 hours Monday through Saturday.

The specific gravity of a substance is the ratio of its density to the density of water. If the density of a steel alloy is 492 lb/ft³ and that of water is 62.4 lb/ft³, what is the specific gravity of the steel alloy?

Which property justifies rewriting the equation 1.6+ z = 8 as 1+ z = 8 A Additive Identity Property B Multiplicative Identity Property C Multiplicative Inverse Property D Substitution

Q. You are driving to a conference in Cleveland and have already traveled 100 miles. You still have 50 more miles to go. When you arrive in Cleveland, how many miles will you have driven? A. 50 miles B. 150 miles C. 1200 miles D. 1500 miles

Angela took a general aptitude test and scored in the 81st percentile for aptitude in accounting. (a) What percentage of the scores were at or below her score? (b) What percentage were above?

Given the function g(x) y, which of the following statements is true? g(x) is the name of the function, is the dependent variable, and y is the independent variable. g is the name of the function, a is the dependent variable, and y is the independent variable. g(x) is the name of the function, is the input variable, and y is the output variable. g is the name of the function, is the input variable, and y is the output variable.

Write a program that uses a two-dimensional array to store the highest and lowest temperatures for each month of the year. The program should output the average high, average low, and the highest and lowest temperatures for the year. Your program must consist of the following functions: 1. Function getData: This function reads and stores data in the two-dimensional array. 2. Function averageHigh: This function calculates and returns the aver- age high temperature for the year. 3. Function averageLow: This function calculates and returns the average low temperature for the year. 4. Function indexHighTemp: This function returns the index of the highest high temperature in the array. 5. Function indexLowTemp: This function returns the index of the lowest low temperature in the array. These functions must all have the appropriate parameters.

Solve the differential equation, such that the equation passes through the given point (x, y). (Remember to use absolute values where appropriate.) dy/dx = 5/x (1, 2) y = log(x5) +2

Find the area of a triangle whose two sides are 12 inches and 14 inches long, and has a perimeter of 34 inches. A. 23.24 in² B. 24.74 in² C. 47.91 in² D. 79.84 in²

Tonya has a small picture with a length of 4^(4/5) inches. She wants to enlarge the picture by a factor of 7 and frame it. Which of the following is true? O A. The enlarged picture has a length of 28^(4/5) inches. O B. The enlarged picture has a length of 33^(3/5) inches. O C. The enlarged picture has a length of 6^(1/5) inches. O D. The enlarged picture has a length of 18^(1/7) inches.

The mathematics department of a college has 12 male professors, 15 female professors, 9 male teaching assistants, and 10 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female. The probability is (Type an integer or a fraction. Simplify your answer.)

Mika can eat 21 hot dogs in 6 minutes. She wants to know how many minutes (m) it would take her to eat 35 hot dogs if she can keep up the same pace. How many minutes would Mika need to eat 35 hot dogs?

Identify the transformations. Sketch a graph of the following functions as a transformation of the graph of a toolkit function by first graphing the toolkit function, then the progression of transformations (in the correct order). f(x) = -3(-x - 5)² + 4

A car salesman is offered a choice between a weekly salary of $160 and a commission of $140 on each car, or no salary and a commission of $180 on each car. How many cars would he have to sell in one week to make the same money under both plans?

Express the confidence interval (0.065,0.109) in the form of p-E <p<p+E. <p< (Type integers or decimals.)

Write an equation of the line that passes through (-1,1) and is parallel to the line defined by 4x+y=5. Write the answer in slope-intercept form (if possible)band in standard form (Ax+By=C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable. The equation of the line in slope-intercept form:

Identify the equation of the circle that has its center at (9, 12) and passes through the origin. A. (x +9)2 + (y + 12)² = 225 B. (x-9)2 + (- 12)² = 225 c. (x-9)2 + (-12)² = 15 D. (x + 9)2 + (y + 12)² = 15

Use the Monotonicity Theorem to find the intervals where the given function is increasing and where it is decreasing f(x)=9x+9 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The function is increasing on B. The function is not increasing on any interval (Type your answer in interval notation.)

3(x-3)=11-5(3x + 1) Select the correct choice below and, if necessary, fill in the answer box. A. The solution is (Type an integer or a simplified fraction.) B. The solution set is (-∞,∞). C. There is no solution.

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 16.4 years and a standard deviation of 2.1 years. Find the probability that a randomly selected quartz time piece will have a replacement time less than 12.4 years? P(X< 12.4 years) = Enter your answer accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. If the company wants to provide a warranty so that only 2.9% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty? warranty _____ years Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Find the derivative of the function. y = 5(2-x²)4 Step 1 Apply the general power rule which states that if y = [u(x)], where u is a differentiable function of x and n is a rational number, then dy/dx = n[u(x)]n-¹du/dx Let u = 2x² and substitute u for 2x² in the original equation. y = 5(2-x²)4 = 5 4(-2x) (2-x²) ³

For each expression, simplify if possible. If applicable, click on "Cannot be simplified". 4v + 3/3y + 4 v + 6/-v-6

a) Simplify (m8)4 and write your answer without using negative exponents. (b) Simplify (5y9)3 and write your answer without using negative exponents.

Which of the expressions is not equivalent with the rest? a) 79% more than x b) Cost of an item is x with 70% markup and 9% sales tax applied c) 1.79x d)x(1+7. 1/10 + 9. e) They are all equivalent expressions

A circle has a diameter with endpoints at A (-1, -9) and B (-11, 5). The point M (-6, -2) lies on the diameter. Prove or disprove that point M is the center of the circle by answering the following questions. Round answers to the nearest tenth (one decimal place). What is the distance from A to M? What is the distance from B to M? Is M the center of the circle? Yes or no?

Describe how to transform the graph of y = (3)" on to the graph y = 4(3) +2. The graph has a vertical shift down 2 units, a reflection over the y axis and a vertical shrink by a factor of 1/4. The graph has a vertical shift up 2 units, a reflection over the y axis and a vertical stretch by a factor of 4. The graph has a vertical shift up 4 units, a reflection over the x axis and a vertical stretch by a factor of 2. The graph has a vertical shift down 2 units, a reflection over the x axis and a vertical stretch by a factor of 4.

Nadia notices that sales have gradually decreased over the past two years. The sales team has not changed, nor have the products. What should Nadia do next? Read the following possible courses of action and decide which is the BEST way to handle the situation and which is the WORST way to handle the situation. 1. Discontinue all products and offer new products to meet the changing marketplace. 2. Meet with the sales team and brainstorm reasons for declining sales. 3. Ask the sales team to research, evaluate, and test new sales strategies. 4. Conduct a customer survey to find out what customers are saying. Which is the BEST way to handle the situation? Option 1 Option 2 Option 3 Option 4 Which is the WORST way to handle the situation? Option 1 Option 2 Option 3 Option 4

A triangle drawn on a map has sides that measure 15 cm, 8 cm, and 10 cm. The shortest of the real-life distances is 127 km. Find the longest of the real-life distances. corresponding A. 207.7 km B. 217.7 km C. 282.1 km D. 238.1 km

1/2x + 1/3y = 0 1/4x - 1/2y = 8 What is the solution of the system shown? (8,-12) (8,12) (-8, 12)

Solve for x. 8(x - 1) = 4x + 136 A. x=181/12 B. x=36 C. x=11 D. x=12

In the expression below, the x is the 3x + 2 A. Coefficient B. Constant C. Operator D. Variable

It is often necessary to do calculations using scientific notation when working chemistry problems. For practice, perform each of the following calculations. (4.47×10%)(1.00×10)= 1.52x10/3.90×10 (4.47×10 (5.19×10)/(1.00×101.52×10)

Ravi rented a truck for one day. There was a base fee of $18.95, and there was an additional charge of 86 cents for each mile driven. Ravi had to pay $189.23 when he returned the truck. For how many miles did he drive the truck?

For f(x) =x/x+1 and g(x)=2/x find a. (fog)(x); b. the domain of f o g a. (fog)(x) = (Simplify your answer.) b. What is the domain of f o g?

Suppose that the property tax is figured by multiplying the cost of your acreage by 0.293. Change 0.293 to a percent. Write your answer in percent form.

A mineral sample is found to have a density of 3.0 grams per cubic centimeter. It is then broken into two pieces, with one piece twice as large as the other. The smaller of the two pieces will have a density of: A) 6.0 g/cm3 B) 3.0 g/cm3 C) 1.5 g/cm3 D) 1.0 g/cm3

The words below have a similar denotation. Which word has the most. positive connotation as used in this sentence? He was _________ student. A. a good B. an admirable C. an excellent

Simplify by factoring: 16x - 24y 16 (x -8y) 24 (2x - y) Prime 8 (2x - 3y)

Mark is investing his money. He thinks that he should make $10 for every $100 he invests. How much does he expect to make on an investment of $800?