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# Consumer Mathematics

### 5 Consumer Mathematics Problems: WACC, Repurchase of stock, Treasury bond, Stock price, Price of bonds

1) Acetate, Inc., has equity with a market value of \$20 million and debt with a market value of \$10 million. The cost of the debt is 14 percent per annum. Treasury bills that mature in one year yield 8 percent per annum, and the expected return on the market portfolio over the next year is 18 percent. The beta of Acetate's equit

### Energy stored in springs

What is the energy stored in the two springs? (See attached file for full problem description)

### Ratio and Proportion Application Word Problem

Girth is distance around. If volume is 35 cubic feet, when height is 20 feet and the girth is 5 feet. What is the heigth when the volume is 85.75 feet and the girth is 7 feet?

### Ratio and Proportion Application Word Problem - Volume of wood in a tree varies jointly as the height and the square of the girth.

The volume of wood in a tree varies jointly as the height and the square of the girth. Girth is the distance around. If the volume is 35 cubic feet, when the height is 20 feet and the girth is 5 feet, what is the height when the volume is 85.75 cubic feet and the girth is 7 feet?

### Extreme-Means Property and Ratio and Proportion

Using Extreme-Means property, Solve each proportion (Four Problems) 45. Voting. If 220 out of 500 voters surveyed said that they would vote for the incumbent, then how many votes could the incumbent expect out of the 400,000 voters in the state? 60. Bear Population. To estimate the size of the bear population on the Ke

### Solving Expressions with Fraction Exponents

I can get the answers usually by calculator but I need to show my work. (5^2/3)^7/2 (3^1/2)(12^1/2) 5^200 / 5^-201 (5^1/2)(11^1/2) (21^1/2)(21^1/2) also writing a decimal as a fraction in simplest form ___ .0204 = 68/333 by calculator but how would I show my work without using a calulator.

### Important information about Ratio and proportion Application

I have started this problem but I cannot figure out what im doing wrong or if I am even go about the problem the right way. Could somebody please help? 1. Arianne casts a shadow of 6m. If she measures 160cm, how tall is a tree that casts a shadow of 10m. show all calculations. 6/10 = x/1.6 10x = 6 x 1.6 10x = 9.

### Word Problem : Complete a table and write a rational expression involving rate.

Kent can Paint a certain house by himself in x days. His helper Keith can paint the same house by himself in x + 3 days. Suppose that they work together on the job for 2 days. To complete the table, use the fact that the work completed is the product of the rate and the time. Write a Rational expression for the fraction of th

### Ratio and Proportion Word Problem

If 300 of 560 voters surveyed said they would vote for the incumbent, how many votes could the incumbent expect out of 843,000 votes?

### Details of a Fraction Word Problem

Students with a class size of under 30,have finished their tests. One third of the class received a "B," one quarter a "B-",and one sixth a "C". One eighth of the class Failed. How many students in class received an A?

### Subtraction of polynomial fractions

Perform the indicated subtraction x/x^2-2x-3 - 3x/x^2-9

### Ratio and Proportion : Elk and Fuel Efficiency

1. Park rangers catch, tag, and then release 140 elk back into a national park. One month later, they select a sample of 130 elk, 91 of which are tagged. Assuming the ratio of tagged elk in the sample holds for all elk in the park, approximately how many elk are in the park? 2. The formula M = 0.0075x2 - 0.2676x + 14.8 mode

### Word Problems : System of Equations and Ratio and Proportion

An investor bought 2000 shares of stock. An initial purchase was for \$12 per share and a second purchase was for \$18 per share. If \$27,000 worth of stock was purchased, how many shares were purchased at each price? A saltwater solution is formed by mixing 3 lbs of salt with 15 gal of water. At this rate how many additiona

### Fraction Application Problem

The amount of the ingredients needed to make 3 and 5 servings of rice are: to make rice and water salt butter _________________________________________ 3 servings 1 cup 3/8 tsp 1 1/2 tsp 5 servings 1 2/3 cup 5/8 tsp 2 1/2 tsp Find the amount of each ingredient

### Earned the most money

1)Jack earned twice as much as Mary and Jill earned \$8 more than Mary. Who earned the most money? Explain why. 2)A tire dealer sells 2 tires for as much as he paid for 3 tires. He paid \$240 for a dozen tires. What is the total profit on 12 tires? (See attachment for other two questions)

### Understanding the Basics of Fractions

Explain how you would help students understand that 3/4 is the same as 0.75. Include in your development a translator to 75/100 and from that form to the decimal from using models fo each translation. Also, how would you teach students to compare the fractions 3/7 and 5/8 without using models or cross-multiplying to identify whi

### Financial Problem: Determining the Firm's Economic Order Quantity

Tool Mart sells 1400 electronic water pumps every year. These pumps cost \$54.30 each. If annual inventory carrying costs are 12% and the cost of placing an order is \$90, what is the firm's EOQ? (Q*= Sq root of 2(S)(D)/C)Also: (C = Inventory carrying cost X cost of frames)

### Financial Problem: Determining Interest Savings

Pronet has annual sales of \$724 million from its 600 retail stores. Pronet can reduce its mail float by 2 days through the use of wire transfers. The annual cost of the wire transfers is expected to be \$105,610. If Pronet's cost of short-term funds is 9.75 percent, should the change to wire transfers be made? Assume 365 days per

### Mathematical Modelling; Modelling Cycle

Consider the following situation: {see attachment} Develop a mathematical model which describes the contractors profit from the days work [a very simple model will do]. Then show how, using the modelling cycle, this model might be revised into a sequence of successively more sophisticated mathematical models, which show how the

### Applications of ratios and proportions

The Golden Ratio. The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than the width, then for what dimensions would the length and width have the golden ratio? Let x=

### Partial Fraction Sums

Express f(x) as the sum of partial fractions. f(x)=(3x^2+10x+9)/(2x^3+8x^2+10x+4) This is what I've done so far. f(x)= (3x^2+10x+9)/(2x^3+8x^2+10x+4) = (3x^2+10x+9)/((x+2)(2x+2)(x+1)) = (3x^2+10x+9)= a/(x+2)+b/(2x+2)+c/(x+1) Giving the simultaneous equations: 3=2a+b+2c 10=4a+3b+6c 9=2a+2b+4c

### Reducing polynomial fractions

Reduce each answer to the lowest terms (see attachment)

### Fraction Equation Shown

2m 3m ___ = _____ 3 2

### I need help with these problems, I will give examples for each one,,,,

For O.T.A 103997,,, Example 1,, find the LCD for the given rational expression, and convert into an equivalent rational expression with the LCD as the denominator, X Y 1 - - - 9y5z, 12x3, 6x2y Example 2,, find the LCD for the given rational expression, and convert this rational expression into an

### Lorenz Equations and Equilibrium

Please see the attached file for the fully formatted problems. Show that for , the equilibrium (x*, y*, z*) = (0, 0, 0) is globally (nonlinearly) stable for the Lorenz system. That is, any (x(t), y(t), z(t)) would eventually approach (0, 0, 0) as . Consider the "volume" (a) Show that, using the Lorenz equations

### Using Rectangles for Fraction Addition and Fraction Expression

A. Use a rectangle to explain the process of adding 1/4 and 2/3 - Explain your answer. B. What multiplication problems are represented by each of the following area models? What are the products? (The 1st area model looks like one big rectangle with fifteen little rectangles in it, and 8 of them are shaded) (The 2nd area mo

### Simplifying Fraction Denominators

Simplify attached fractions with polynomial denominators.

### Fractions : Word Problem

All of the primary students at the Sunshine Elementary School were present on the day that one-third of the class went on the science field trip. Two fifths of the remaining primary students went skating at the local rink.If there were 36 primary students remaining at school, how many primary students attend Sunshine Elementary?

### Multiplying fractions

11 /13 X 2/121