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# Basic Algebra

### Economic investment options

An investor is consider 4 different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below. Economic Condition Poor Average Good Excellent Inves

### Factor Completely Polynomial Functions

11. Factor completely. If the polynomial is prime, state this. 3x3 + 6x2 - 189x 12. Factor completely. If the polynomial is prime, state this. x2 - 1.1x + 0.28 13. Factor completely. If the polynomial is prime, state this. 2x2 - 8x + xy - 4y 14. Solve by factoring and using the principle of zero products.

### Finding the power function of hypothesis test

Let X ~ B(1,theta) (f(x) = (theta^x)*(1-theta)^(1-x) x = 0,1). To test H_0 : theta=0.25 vs H_a : theta < 0.25, we take a random sample of size 10 and reject the H_0 if and only if Sigma(x_i)<1 (i.e. the sum of all x sub i with i ranging from 1 to 10 is less than 1). Find the power function pi(theta), 0 < theta <= 0.25, of this t

### Contraction Mapping Principle and Metric Spaces

Show that none of the following mappings f:X→X have a fixed point and explain why the Contraction Mapping Principle is not contradicted: X=(0,1)⊆R and f(x)=x/2 "for " x" in" X X=R and f(x)=x+1 "for " x" in" X X={(x,y) "in" R^2│x^2+y^2=1}"and" f(x,y)=(-y,x) "for " (x,y) "in" X

### Abstract algebra proof, modulo m, rings and fields

Prove that the equivalence relation modulo m where m is an integer, forms a ring. Also, does this same equivalence relation form a field and why? For this proof, you are given that [a]m (m is a subscript) represents an equivalence class modulo m, where m is an integer. We also know that for any two integers, a and b, that

### Abstract Algebra Proof and Equivalence Class

Suppose [a]m (m is a subscript) represents an equivalence class modulo m, where m is an integer. Prove that for any two integers a and b that, under multiplication, [a]m[b]m = [ab]m. Again, m is written as a subscript.

### Elementary & Intermediate Algebra

Chapter 2 of Elementary and Intermediate Algebra. I do not understand the questions below: 1.What is the difference between an equation and an expression? How does knowing how to simplify an expression help with solving an equation? 2.When is it all right to cross-multiply when solving an inequality, and what are the rul

### Difference between a polynomial and exponential function

Here are the questions: 1. What is "e"? Where does it come from and how is it used in mathematics? Give an example. 2. What is the fundamental difference between a polynomial function and an exponential function? Be sure to include a description of the graph of each type of function.

### MAT101 - College Mathematics (Exponential & Logarithmic Functions)

1. Convert the following equations into logarithmic form: a. 2 = 6x b. 7 = 6y c. 9 = 3y d. X = 8y 2. Convert the following equations into exponential form: a. X = log54 b. 7 = log6Y c. X= log8Y d. 90 = log4Z 3. Simplify the following expressions: a. X

### Algebraic Expressions and Integers Evaluation

1.Classify each number below as an integer or not. 10/3 -68.44 -56/8 -956.29 -69 2. Classify each number below as a rational number or an irrational number. 12.34_ 16 -5~ 17.56 21 3. Evaluate the expressions below. Write each response as an integer or as a fraction (-2)5 (4/3)3 Evaluate the following. 8/2+6+4x

### Functions and Models: Create a linear equation from your own life

Think of a mathematical function that represents something from your own life. For example, suppose the number of beers you drink depends on the number of football games you watch. If you drink five beers during every football game, the function would be: Number of Beers (B) = 5 times Number of Football Games (F), or B = 5F

### Functions, Models, and Linear Equations

1. What is a function? 2. What is a linear function? 3. What form does a linear function take? (I.e., What is the standard mathematical notation of a linear function?) 4. What is the formula for determining the slope of a line? 5. Which of the following are functions? The last two problems, i.e., b & c, are mul

### Elementary and Intermediate Algebra

1) What are some examples of real-life situations where the addition of fractions, multiplication of fractions, or division of fractions might be required? Select one, and discuss your methodology for solving problems in this situation. 2) In this chapter, you are working a lot on evaluating expressions using some of the pr

### Homework Problem

A marketing group developing online ad space is offering two payment options: Option 1: \$210 set up fee plus \$10/inch of the ad Option 2: No set up fee but \$25/inch of the ad. Let x = inches of the proposed ad, for example, x = 2 for a column ad that is 2" long. a) Write a mathematical model representing the total ad cos

### quotient of any nonzero quantity and its negative

1. The quotient of any nonzero quantity and its negative is . 2. Simplify the following expression. 3. Simplify the following expression. 4. Simplify the following expression. 5. Perform the operations and simplify. ÷ 6. Perform the operations and simplify. 7. Perform the operations and simplify.

### Rational and Irrational Numbers and Expressions

1. Classify each number below as a rational number or an irrational number: a) Square root of 64 b) 9 c) -41.4 d) 46.97 e) -3 sqaure root 2 f) 24+9*(15-13)/6 g) -(1-23/1)2/1-4.5 2. Evaluate the expression when a=-6 and b=4 . a-9b 3. Evaluate the expression for c=-4 c^2 + 7c - 5 4. Write an ineq

### Number of stickers

Michele gave away 21 stickers. She gave half as many to her brother as she gave to her teacher. She gave twice as many to her best friend as she gave to her teacher. How many stickers did Michele give to each person?

### Exponential Function Amounts

1. A laptop computer is purchased for \$1500. Its value each year is about 80% of its value in the preceding year. Its value in dollars after t years is given by the exponential function V(t) = 1500(0.8)^t. A)After what amount of time will the computer's value be \$900? B)After what amount of time will the computer's value be

### Algebra

2-3 paragraphs Suppose that the number of new homes built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of homes built can be modeled by an exponential function, H= p * at , (H = p*a^t) where p is the number of new homes buil

### Dave Bidini has saved 20000 for a down payment on a home and plans to save another 5000

Dave Bidini has saved 20000 for a down payment on a home and plans to save another 5000 at the end of each year for the next 5 yrs. He expects to earn 7.25% compounded annually on his savings. How much will be have in 5 years time? Calculate the FV of an ordinary annuity consisting of quarterly payments of 1200 for 5 yrs if t

### Evaluate the exponential equation for three positive values of x

1. Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Use th

### inequality on a plane Interval notation

1)47-(2x+5)< 3(x+2)+2 = 2)Can this equation be dependent or indepdent ? Is the system consistent or inconsistent? 5x +9y=-27 -5x+9y=27 3) Write interval notation fo rthe set (x|-2 > x>-10) 4)x<2 & y>-2x +4 5)What is the solution of the system? The solution is?in an order pair 7x +4y=2 & 3x-4y=-22 6)x+y<4 gr

### Expotential functions and logarithmic functions

1. Do exponential functions only model phenomena that grow, or can they also model phenomena that decay? Explain what is different in the form of the function in each case. 2. Assume that the number of viruses present in a sample is modeled by the exponential function "f(t) = 10t," where t is the elapsed time in minutes. H

### Valuation

Vonnegut Company and Heller Company are two identical firms that agree to merge. Both have revenues of \$1500, operating margin of 15%, a tax rate of 40%, investment rate of 10%, growth rate of 11%, 5 years of supernormal growth followed by zero growth thereafter, and a 9% cost of capital. a) what are the values of the compani

### Algebra

When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -5t^2 + v*t + k gives the height of the ball at any time, t in seconds, where "v" is the initial velocity (speed) in ft/sec and "k" is the initial height in feet (as if you were on top of a tower or building). Make up a scenario where

### Algebra: MTH133 Unit 1 & 2 Individual Project - A

1) The following graph shows the depreciation for the corporate airplane from 2006 to 2009. The plane was purchased new in 2006; therefore, x = 0 represents the year 2006. X - axis (horizontal) = years starting from 0 = 2006 and increasing by 0.5 years Y - axis (vertical) = price in \$ amounts a) List the coordinates of t

### Example Algebra Problems and Solutions

2-3 paragraphs Part 1: What is the formula for the volume of a rectangular solid? Find an object in your residence that has the shape of a rectangular solid. Measure and record the length, width, and height of your object in either centimeters (to the nearest 10th of a centimeter) or inches (to the nearest quarter of an inch)

### Rational Number to its Lowest Terms

Here are the questions. 1. How do you reduce a rational number to its lowest terms? Explain with examples. 2. What is meant by the term simplified radical expression? Describe the three conditions that characterize a simplified radical expression.

### change-of-base formula

1. Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this and show your work ln x - ln (x - 4) = ln 4 2. Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this and show your work. log x = 1 3. Solve. Where a

### Distance Between Numbers Simplified

1. Express and evaluate the distance between the numbers 84 and -34 using absolute value. 2. -6 (2x-9) -4x+5 3. (x ) -3 4. 5. 2+6 given x = 4 6. ( 8-7w + 2y) 7. 8x+7 given x = -3 8. Simplify 7 completely. 9. 10. 11. 12. 13. Determine whether 15>16 is true or false. 14. 6 + 3 15. Given x = 1 a