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# Basic Algebra

### Find the Vertex and Intercepts of a Function

See attached file 1. Write the polynomial in descending order and find the degree: x2 - x5 + 2x4 - 1 2. Subtract 3x -5 + 2x3 from 3x3 - 1 3. Multiply: (9x - 2) (x + 4) 4. Multiply (5x - 6y) (5x + 6y) 5. Simplify 6. Divide:

Questions (also attached): Graph each equation and state its domain and range. 27) g(x)= x 2 + 2 28) f(x)= x 2 - 4 32) y= 2x 2 + 3 Graph each square root and state its domain and range. __ 34) g(x) = &#8730; x - 1 _____ 36) f(x) = &#8730;x + 1

### Linear inequalities and conditions

Compare the amount of information conveyed to a collaborator when you inform her that an object is located: At a point (1,3) On a line y=x+1 Below this line, so that its coordinates satisfy y < x+1 When are you being the most specific, and when are you being the most vague? What happens as you increase the number o

### Word Problem : How much will each party pay?

The Gooch family, the McCoy family, a bachelor and a couple without children have decided to buy a summer home together. They will divide the purchase price according to the size of each family. The house costs \$264,000. The smaller of the two families- the McCoys - have 2 children and will carry one third of the cost. The large

### Heat Equation and Boundary Value Problems : Steady-State Solution, Neumann Boundary Conditions

Please see the attached file for the fully formatted problems.

### Types of asymptotes considered for rational functions

One of the archeologists you interviewed for your article is graphing asymptotes to illustrate the data generated through carbon dating the half-life of fossil specimens. Help him with his work by solving these problems: Explain and contrast the types of asymptotes considered for rational functions. Browse through some news

### 1. If gcd(m,n) = 1, then &#966;(m,n) = &#966;(m)&#966;(n). Use this to give a proof that &#966;(n) = n &#928;(1 - 1/p) p/n 2. Prove that d(n) is odd iff n is a perfect square. 3. Prove that &#963;(n) &#8801; d(m)(mod 2) where m is the largest odd factor of n. 3.(2nd Part) If &#963;(n) = 2n, n is a perfect number. Prove that if n is a perfect number , then &#8721;1/d = 2. d/n 4.Evaluate &#963;(210), &#966;(100) and &#963;(999). 5.Evaluate d(47), d(63) and d(150).

Arithmetic Functions Combinatorial Study of &#966;(n) 1. If gcd(m,n) = 1, then &#966;(m,n) = &#966;(m)&#966;(n). Use this to give a proof that &#966;(n) = n &#928;(1 - 1/p

### Cost Function : Maximum Profit

If a chain store manager has been told by the main office that daily profit, "P", is related to the number of clerks working that day, x, according to the equation P = -25x^2 + 300x. What number of clerks will maximize the profit and what is the maximum possible profit?

### Equation or expression? Please simplfy.

10x^2y^4 + 4x^4y^2 - 16x^6y^3/-2x^2y^2

A person's revenue "R" (in dollars) on the sale of "X" fruitcakes is determined by the formula R = 50x - x squared. Her cost "C" in dollars for producing "X" fruitcakes is given by the formula C = 2x + 40. For what value of "X" is the person's profit positive? (Profit = revenue - cost).

### Set Operations : Commutativity, Unity, Zero Divisors and Multiplicative Inverses

Consider the set R={0,2,4,6,8} C Z10. a) Construct addition and multiplication tables for R, using the operations in Z10. b) Is R a commutative ring? Does it have unity and, if so, which element is unity? c) Does R have zero divisors? d) Which elements of R have multiplicative inverses? Please see the attached fi

### Does the operation a*b = ab in Q give a group structure?

Modern Algebra Group theory Determine whether the following binary operation give

### Convergence of series

Please help with the following problem. This problem is from Advanced Calculus II class. It is also an introduction to real analysis. Consider the series n = 1 to infinity 1/( 1 + n^2 x) (a) For what values of x in R does the series converge absolutely? (b) On what intervals of R does it converge uniformly? (c) On wh

### Finite Extension Field and Isomorphism

Argue that every finite extenstion field of R is either R itself or is isomorphic to C. Note: R is set of all real numbers C is set of all complex numbers

### Exponential & Logarithmic Models : Continuously Compounding Interest

An initial deposit of \$3000 is made in a savings account for which the interest is compounded continuously. The balance will double in seven years. What is the annual interest rate for this account? Please show all work and logic in getting the answer.

### Economy's Lorenz Curve

Author's explanation of a Lorenz curve: Economists use a cumulative distribution called a Lorenz curve to describe the distribution of income between households in a given country. Typically, a Lorenz curve is defined on [0,1] with endpoints (0,0) and (1,1) and is continuous, increasing, and concave upward. The points on this cu

### Newton-Cotes formula

Derive all the weights for closed Newton-Cotes formula. Please see attached for full question.

### Statistics

What is the difference between a sample and a sampling?

### Ratios, LCD and Simplification

1.)The ratio of strawberry ice cream lovers to vanilla is 9 to 5. If there are 144 more strawberry ice cream lovers than vanilla, how many of each are there? 2.) Find the LCD and convert each rational expression into an equivalent rational expression with the LCD as the denominator: 4/15xy^2, 3x/6y 3.) Simplify and writ

### How to solve for the variable "X"

How to solve for the variable "X" The following problems have tripped me up. I can't seem to figure out how to solve them. I've tried, several times, and had my algebra teacher explain them, but I still can't get the answers. 3x - 11 = 6 2x - 7 = 3 + x 3 + 3x = 9 + 2x 3x - 3

### Jointly Distributed Random Variables : Expressions for Density Functions

Suppose X and Y are continuous random variable, X and Y are independent and that x>0 and y>0. The pdf of X is Fx(X) and the pdf of Y is Fy(Y). Find the expressions for the density function of Z in terms of fx and fy, if... a) Z=X/Y b) Z=XY

### Factorization

Factorize: 10a^2 - 27ab + 5ab^2

1. Consider approximating integrals of the form I ( f ) = &#8747; &#8730;x f(x)dx in which f(x) has several continuous derivatives on [0, 1] a. Find a formula &#8747; &#8730;x f(x)dx &#8776; w1 f(x1) &#8801; I1( f ) which is exact if f(x) is any linear polynomial. b. To find a formula

### Parabola and Quadratic Equations: Maximum and Minimum Values

From this we can see that we have function that whose graph is a parabola and we want the values of w that make the function positive. The parabola opens downward, the vertex is at Let me show you an actual example of inequalities. Several years ago I was the chairman of the banquet committee for our ski club. Since one of our m

### Physics and Algebra Traveling Speed

1. Jeff rode his bike 45 miles to get to the park, and his co-worker Chris rode his bike 70 miles to meet Jeff at the park. Chris averaged 5 mph more than Jeff, and his trip took one-half hour longer than Jeff. How fast was each traveling? 2. Mike found a good deal on some golf clubs at an online auction site. The clubs were

See attached

### Mathematical Induction

Prove that 2(2^n-1) = (n+1)/1 + ... + (n+1)/n for every natural number n.

### Solving Algebraic Equations for a Given Variable

1. Solve the following formula for R: I = E / R + r 2. Sqrt of 5x - 9 = 4 3. One bag of grass seed will cover an area of 300 square feet. If the width of the area is 5 ft less than the length, determine the dimensions.

### Functions and Graphs : Heart Disease, Cancer and AIDS - Trends and Real World Implications

Can you please verify (numerically) the numbers listed on the document, I had to come up with total number of deaths in the US for the following years and diseases. The numbers I came up with are on the document along with a graph for each. Please add the numbers for 2005. 1985, 1990, 1995 and 2000 Heart Disease Cancer