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Graphs and Functions

Automobile Production: Table, Graph and Modeling

The table shows the retail market share of passenger cars from Ford Motor Company as a percent of the US market. Year Market share 1980 17.2% 1885 18.8% 1990 20.0% 1995 20.7% 2000 20.2% 2005 17.4% A mathematical model for this data is given by f(x) = -0.0206x^2

Determining the Nearest Integer

Use the following graph of a function f to determine x or y to the nearest integer as indicated. Some problems may have more than one answer... Here is the information on the graph: Where Y would be is f(x) Y=f(x) if you have your box and have 10 sets on each line, I will start on the 5th set on the lower left side. T

Solution graphs of linear systems

Consider the linear system x' = Ax, where A is a n x n real matrix. If x = x(t) is a solution of the linear system, we define: G(x) = {x(t) : t E R), which is the set of points on the solution curves x=x(t) in R^n. The set G(t) is called the graph of x = x(t) . Show that if x(1) = x(1)(t) and x(2) = x(2)(t) are any two

Making Proper Graphs

Read the article "How to Display Data Badly," by Howard Wainer. It was published in the American Statistician in 1984, volume 38, pages 137-147. You can find it here: Next, scour the Internet (or if you are feeling particularly plucky, look through your company's annual report!) to find an

Determining Inverse Functions and Relations

I've attached a problem set which contains the following questions related to inverse functions. Can you help explain the concepts to me? Given point P of the function f(x), state the corresponding point P' in the inverse of the function. Determine if the inverse of each relation graphed below is a function. Find the inver

Steps/Examples to graphing functions

Please help with the following problems. 1. Express each function graphed in terms of a base function. 2. Sketch the graph of a function based on a given base function. For example: Given f(x), sketch: f(x+3).

A rental company charges $40.00 a day plus $0.34 per mile to rent a moving truck. The total cost, y, for a day's rental if x miles are driven is described by y = 0.34x + 40. A second company charges $32.00 a day plus $0.44 per mile, so the daily cost, y, if x miles are driven is described by y = 0.44x + 32. The graphs of the two equations are shown in the same rectangular coordinate system. a. Determine from the graph the x-coordinate of the intersection point of the two graphs. Describe what this x-coordinate means in practical terms. Choose the correct answer below. A. Both companies charge the same for 80 miles driven. B. Both companies charge the $80 for the same number of miles driven. C. The maximum amount of miles that can be driven is 80. D. The maximum amount that both companies charge is $80. b. Substitute the x-coordinate of the intersection point from part a into one of the two equations. Find the corresponding value for y. y = ? Describe what this value represents in practical terms. Choose the correct answer below. A. Both companies charge $67.20 for 80 miles driven. B. Both companies always charge more than $67.20. C. Both companies alyways charge less than $67.20. D. Both companies charge $67.20 for 67 miles driven.

A rental company charges $40.00 a day plus $0.34 per mile to rent a moving truck. The total cost, y, for a day's rental if x miles are driven is described by y = 0.34x + 40. A second company charges $32.00 a day plus $0.44 per mile, so the daily cost, y, if x miles are driven is described by y = 0.44x + 32. The graphs of the two

Function Definition and Examples

1. In your own words, define the word "function." 2. Give your own example of a function using a set of at least 4 ordered pairs. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and 5. Your example should not be the same as those of other students or the textbook. There a

Rational Functions

I need some help instructing me how to complete the following questions: Part 1: From a 220 feet high lighthouse in the Bahamas island of Nassau, a person sees a ship on the horizon. Due to the curvature of earth, how far is the ship from the lighthouse? Use the formula: d = sqrt[3h/2], where d is the distance in nautical

Graphing a utility function with exponents and calculating Marginal Utility

a) With a utility function of U(S,A)= S^0.4*A^0.6, derive a set of data points for U=1 and then plot a graph to show this indifference curve. Hint: use maximum values of 9 apples (A) and 27 sandwiches (S). b) When U=1, and using a maximum value of 27 sandwiches (S) and 9 apples (A), calculate the marginal utility of S and A.

Evaluate and graph the given functions.

1. Evaluate the function f(x) = 9x - 6 for x=0. 2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost? 3. Find the slope of the line through the poin

Application of Bolzano-Weierstrass Theorem

Recall that a point z0 is an accumulation point of a set S if each deleted neighborhood of z0 contains at least one point in S. ------------------------------------------------------------------------------------- One form of the Bolzano-Weierstrass theorem can be stated as follows: An infinite set of points lying in

Linear Programming Graphically

Solve the following linear programming problems graphically: Maximize profit = 4X + 6Y Subject to: X + 2Y ? 8 5X + 4Y ? 20 X,Y ? 0 Minimize cost = 24X + 15Y Subject to: 7X + 11Y ? 77 16X + 4Y ? 80

Statistical Concepts

Plotting the Binomial Probabilities using MINITAB 1.) Create plots for the three binomial distributions above. Select Graph > Scatter Plot and Simple then for graph 1 set Y equal to 'one fourth' and X to 'success' by clicking on the variable name and using the "select" button below the list of variables. Do this two more ti

Find an example online of a graph used in real life

Find an example online of a graph used in real life. Please provide the link to the web page by using the link button in the editor. Describe at least one mathematical feature of the graph (e.g. shape, slope, coordinates, axes, quadrants, etc.) and how the feature/graph can help us to analyze the real-life situation.

Mixed Cost Analysis and the Relevant Range

The Ramon Company is a manufacturer that is interested in developing a cost formula to estimate the fixed and variable components of its monthly manufacturing overhead costs. The company wishes to use machine- hours as its measure of activity and has gathered the data below for this year and last year:

How to Determine If a Relation is a Function

Determine which relation is a function a) {(3,0),(0,3), (5,4),(0,1)} b){ (0,0),(0,3), (0,4),(0,1)} c) {(-1,0),(3,0),(-1,4), (5,2)} d){(3,0),(2,3),(5,4),(6,1)} the relation {(5,0),(1,9),(2,4)} is not a function when ordered pair is added to the set. a)(3,0) b)(9,1) c)(-6,-8) d)(2,7) the table is the projecte

Finding a linear demand function and maximizing profit

You are given two points representing the number of items sold at a particular price. From these two points a linear demand functions is constructed. You are also given information on the cost of each item so that you can construct a cost function. From the demand function you can form a revenue function and finally the profi

Rigid Body - Angular Speed

** Please see the attachment for the complete problem description ** A rigid body is spinning with an angular speed of 60pie radians per second (1800 rpm). The axis of rotation lies in the direction of the vector 2i + 2j -k. A small particle on the spinning body with mass of one kilogram passes through the point P with positi

slope of a line

See the attachment. Is there a relationship between the sign (positive or negative) of the slope of a line and the angle the line makes with the x-axis?

Questions about Cubic Production Function: What are the equations for total product, average product, and marginal product? When does marginal product of labor begin to diminish? What is average variable cost and marginal cost?

In Microsoft Excel please respond to all questions and math problems in the following problem (See Attachment). Please show Microsoft Excel formula(s) and work. ----------------------- Homework Exercise Numbers 1 1. A firm estimates its cubic production function of the following form: Q = AL3 + BL2 and obtains the fo

Expressions, equations, functions, and graphing

What are the differences among expressions, equations, and functions? Provide examples of each. If a line has no y-intercept, what can you say about the line? What if a line has no x-intercept? Think of a real-life situation where a graph would have no x- or y-intercept. Will that always be true for that situation?

Graphing a Population Function

Please help with the following graph and function problem. The population of a city is 50,000 in 2008 and is growing at a continuous yearly rate of 4.5%. Give the population of the city as a function of the number of years since 2008. Sketch a graph of the population against time. The function is 50,000(1.045)^t, but I do

Real-world math - Global Warming graph and questions.

Global warming is an area of great concern for the future of our planet and our society. The graphic below, based on the data from National Aeronautics and Space Administration (NASA), shows the global annual-mean surface air temperature since the year of 1880. It is derived from the analysis of the historical data from the larg

What is the Optimal capital budget for United Medtronics ?

The managers of United Medtronic are evaluating the following four projects for the coming budget period. The firm's corporate cost of capital is 14 percent. Project Cost IRR A $15,000 17% B 15,000 16 C 12,000 15 D 20,000 13 a. What is the f

linear trend

The president of a small manufacturing firm has been concerned about continual growth in manufacturing cost over the past several years. the following is time series of the cost per unit(in dollars) for the firm's leading product over the past eight years Year Cost per Unit ($) 1 20.00 2

Line graphs

1. Graph the equation by plotting points y = -2x 2. Graph the equation by plotting points. y = -3x 3. Graph the equation by plotting points. y = x - 3 4. Graph the equation by plotting points. y = x + 3 5. Use the following equation. Fill in the table. Determine whether the graph has a positive o

Cost structure for a Radiologist group practice

Assume that a radiologist group practice has the following cost structure: Fixed costs $500,000 Variable cost per procedure $25 Charge (revenue) per procedure $100 Assume that the group expects to perform 7,500 procedures in the coming year. a. Construct the group's base case projec

Using the demand function to write cost and revenue functions

A health club has cost and revenue functions given by C = 10,000 + 35q and R = pq, where q is the number of annual club members and p is the prices of a one year membership. The demand function for the club is q = 3000 - 20q. a. Use the demand function to write cost and revenue functions of p. b. Graph cost and revenue as