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# Basic Algebra

### Exponential & Logarithmic Functions

The problems below follow closely the examples shown in the background materials. Complete these problems showing your work and turn them in by the end of the Module. 1. Convert the following equations into logarithmic form: a. 2 = 6x b. 7 = 6y c. 9 = 3y d. X = 8y 2. Convert the followi

### Find an expression for E(X^k), where k is a positive integer.

Please give step-by-step instructions for solving these. Let X ~ Exp(Beta). (a) Find E(X^(-1/2)). (b) Find an expression for E(X^k), where k is a positive integer. (c) Use part (b) to show that V(X) = 1 / (Beta^2). Where X = Exponential Distribution E(X) = Expected Value V(X) = Variance

### Emphasize Functions Convergence

1. Show that if (f_n), (g_n) converges uniformly on the set A to f and g respectively,then (f_n+g_n) converges on A to f+g. 2.Show that if f_n(x) :=x+1/n and f(x) := x for x in the reals, then (f_n) converges uniformly on the reals to f, but the sequence ((f_n)^2) does not converge uniformly on the reals (thus the product of un

### variables for this problem

Please explain how to go about solving this problem. An author has received an advance against royalties of \$10,000. The royalty rate is \$1.00 for every book sold in the United States, and \$1.35 for every book sold outside the United States. Define variables for this problem and write an expression that could be used to calcu

### System of equations: algebraic and graphical method

Explain the difference between solving a system of equations by the algebraic method and the graphical method to a sixth grader? This student also wants to know why there are different methods for solving the same problem-what would you tell him?

### Order of Operations in evaluating a mathematical expression

The order that we use to assemble a cake or build a house is important. The same holds true for evaluating any expression in math. We call this the Order of Operations. In your own words, explain the Order of Operations. Give an example of an expression to fit this situation in math and an example in real life. Please sh

### Road Trip: A Story Problem on Duration, Speed, and Distance

Harry and Irene decided to take a road trip. The first 45 miles of the drive is pretty easy, while the last 76 miles of the drive is filled with curves. The drove at an average of 7 miles per hour faster for the first 45 miles of the trip. The entire trip took 4 hours. How fast were Harry and Irene driving for the first 45 miles

### Algebra - Function Composition

If f(x) = 5x + 3 and g(x) = (x-3)/5, find 1. f o g(x), 2. g o f(x), and 3. f o g(4). 4. What are the y-intercept and the x-intercept of the line y = 2 ? 5. What are the y-intercept and the x-intercept of the line x = 2 ?

### Growth of nails

1) In a study it was found that the average rate of a toe nail growth was 1.6 mm per month. Using this result work out how many meters a toe nail grows in one year to an appropriate number of significant figures. Express answer in scientific notation. 2) In the same study it was found that on average the fingernail grew about

### Usual Formula Solves the Quadratic Equation

When the coefficients a,b, and c are complex numbers. Specifically, by completing the square on the left-hand side, derive the quadratic formula z=(-b+(b^2-4*a*c)^1/2)/2*a where both square roots are to be considered when b^2-4*a*c cannot equal zero Use the result to find the roots in the equation z^2 + 2*z+(1-i)=0.

### Celsius temperature

96. World grain demand. Freeport McMoRan projects that in 2010 would grain supply will be l.8 trillion metric tones and the supplly will be only 3/4 of world grain demand. What will world grain demand be in 2010? 94. Fahrenheit temperature. Water boils at 212 F. a. Use the accompanying graph to determine the Celsius t

### Algebra and Geometry

Task: A. Complete the following graphs: 1. Graph the following values on a number line. • 1 • 0 • -6 • 3/4 • -1.7 2. Graph the following points on a coordinate plane. Make sure to include labels for each quadrant. • (3, -2) • (0, 0) • (-1, 7) • (3, 5) • (-4, -5) 3. Graph t

For Project 1, complete all 6 steps (a-f) as shown in the example. For Project 2, please select at least 5 numbers; 0 (zero), 2 even and 2 odd. Make sure you organize your paper into separate projects. Project 1: An interesting method for solving quadric equations came from India. The steps are A. move the constant

### Algebra: Factorzation & Principle of Zero Products

128. Factor completely Remember to look first for a common factor. Check by multiplying. If a polynomial is prime, state this. − x3 + x2 + 42x 28. Factor completely. Remember to look first for a common factor and to check by multiplying. If a polynomial is prime, state this. 25x2 + 10x + 1 8. Solve using the principle of z

### Simplifying Expressions

How does the knowledge of simplifying an expression help you, personally, to solve an equation efficiently? Give an example from your life in how knowing the reason why helped you with the process of solving a difficult situation or problem.

### Finance

1.Samantha's student loans total \$20,000. Part was a personal loan at 12% interest; the other was a Stafford loan at 10%. After one year the loans accumulated \$2160 in interest. What was the amount of each loan? a)Develop an equation to represent the sum of the loans, use 'x' for the personal loan, use 'y' for the Stafford

### Manipulating Expressions and Equations

When we manipulate expressions and equations, we realize that there are basic properties that govern what we can and can't do. One of those properties is the Commutative Property. Let's consider this property in our discussion. Is there a commutative property of subtraction? In other words, does order matter when subtracting? Wh

### Solving Algebra Equations

Please assist me in solving these equations. A. Solve and find solution to X 15x^4 -13x^2 + 2 = 0 1. Solve and find the solution for X w^2 - 6w - 27 = 0 2. Solve and find the solution to X X^2 + 14x - 4 = 0 B. Multiply (r + d) (r^2 - rd + d^2) 1. Multiply (-3n)^2(2n^7)^2 E. Find the solutions. What is/are the soluti

20x^+5x-9=0 What is the value of the discriminant? Which one of the statements below is correct? A. The equation has one real solution. B. The equation has two real solutions. C. The equation has two imaginary solutions.

How do you compute the intercepts of a quadratic function? In case of a quadratic function, why are there two x-intercepts and one y-intercept? Which topic covered in this class was the most challenging for you? Why? How did you overcome this challenge? What is the meaning of "axis" in regards to a quadratic function? Why

### Identify the attitude, values, and ideologies that tend to perpetuate gender inequality

Identify the attitude, values, and ideologies that tend to perpetuate gender inequality

### Boat travel

Debbie traveled by boat 5 miles up stream to fish in her favorite spot. Because of the 4 mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?

### Floor inequality

Please provide a detailed solution. Show that Floor(x) < Floor(y) iff there is an integer in the half-open interval (x,y], or Z Intersection (x,y] != Phi. In particular, note that Z Intersection (Floor(y),y] = Phi. Please refer to the attachment for problem description with appropriate symbols.

### Rational equation, Rational expression, Quadratic equations

1. When solving a rational equation, why it is ok to remove the denominator by multiplying both sides by the LCD (least common denominator)? Why can you not do the same operation when simplifying a rational expression? 2. Why are there usually two solutions in quadratic equations? Under what situation would one or more solution

### Calculate the speed of the current.

Mike's boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current? Please show a complete solution to the problem.

### Seasonal Indexes: Car Dealership Example

1. The following table presents quarterly seasonal indexes for number of new automobiles sold by a car dealership in Halifax, Nova Scotia. Spring Summer Fall Winter 1.15 0.80 1.10 0.95 a) Comment on the seasonal indexes in relation to automobile sales. b) From the original historical data (2002-20

### Graphing and Slope - value depreciation

QUESTIONS LISTED BELOW AND ALSO PROVIDED (WITH GRAPH) AS AN ATTACHMENT. 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 yea

### Fundamental Theorem of Galois Theory

Suppose K is a Galois extension of F of degree p^n for some prime p and some n >= 1. Show that there are Galois extensions of F contained in K of degree p and p^(n-1). Note: It is assumed that you know the following results in order to prove this theorem. You may search for the proofs of these results. 1. G = Aut_F(K)

### Determining Arithmetic and Geometric Sequences

See attachment for more data. 1.) Find the value of a_3 if: a. n = 3 and a_n = 2n - (3/n) b. n = 3 and a_n = 2 (n - 3) 2.) Find the value of: 6!/3! 3.) Find the value of the following expression: 2 Σ3i 1 4.) Find the value of: 3 Σ(3i+1) 1 5.) Find the value of a_n if: n = 2, a_

### change in the number of employees

Compute a simple index for the number of employees for GE. Use 2000 as the base period. What can you conclude about the change in the number of employees over the period? Revenue Employees Year (\$ million) (000) 2000 130,385 90.0 2001 126,416 91.0 2002 132,210 96.0 2003 134,187 87.0 2004 152,363 80.0