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Basic Algebra


Logarithms: a) Using a calculator, find log 10000 where log means log to the base of 10. b) Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available t

Logarithmic functions explained in this solution

The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by A is the amount of returned. P is the principal amount initially deposited. r is the annual interest rate (expressed as a decimal). n is the compound period. t is the number

Graphing, Domain and Range

# 18, 38, 44 18, Function; Domain: The union of (-infinity, 16) and (16, infinity); Range: The union of (-infinity, 0) and (0, infinity) 38. y = -7/(x-16) 44. g(10)


After their star pitcher moved to another town, the eight remaining members of the company baseball team needed to select a new pitcher. They used approval voting on the four prospects, and the results are listed below. An "X" indicates an approval vote. Which pitcher is chosen if just one is to be selected? (see attached

The possibilities of voting

(See attached files for full problem description) --- 1. Four members are running for president of the Local Math Club - Alicia (a), Brice (b), Charlie (c), and Destiny (d). The voter profile is summarized in the table. Use the Hare method to determine the winner. Number of voters Ranking 17 c > d > a > b 11

Bol-ful and Ful-bol Numbers; Unit Conversions

7. An integer is a ful-bol number if it is divisible evenly by the square of an integer that is greater than on. For example, 343 is a ful-bol number because it is divisible by 49 which is the square of 7. A bol-ful number is a ful-bol number which, when the digits are reversed, it is still a ful-bol number. Note: 343 is a

Finding Width of the Swimming Pool

1. A swimming pool is twice as long as it is wide. It took 1,224 square feet of material to cover a 6-foot wide deck around the pool. How wide is the pool? 2. The height reached by a ball thrown vertically upward is directly proportional to the square of its initial velocity. If a ball reaches a height of 46m when it is thr

Examples of Integers

1. Which of the following numbers are examples of integers? -7, -9/3, -1.0, -3/8, 0, 2.2, 5, 6.66666 2. Multiply and simplify your answer as much as possible: (4f - 3)(7f + 1) [to express (f)(f) use f^2] 3. If n is a negative number, what is the absolute value of n? 4. Factor: 25p^2 -

Uncountable Basis

It can be shown that R (the set of all real numbers) is an infinite-dimensional vector space over Q (field of rationals). Is it true that any basis (by basis I mean algebraic basis or Hamel basis) of R over Q has to be uncountable ?

Z-Modules and Modules Associated with Representations

1)I understand what a standard R-module (ring-module) is, but I have heard talk of modules associated with representations. Could someone please give me some idea of what these are? 2) I am trying to find all modules over Z-the Integers; so far, I have only come up with additive groups. How can I find all others?

What is the advantage of using exponents rather than radicals?

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. What is an example of an equation easier to solve as a rational exponent rather than as a radical sign.

Polynomial Functions : Positive Degree

The questions are asking for solving h(x) of positive degree. --- 1A) Let F be a field and let e(x), f(x), g(x) and h(x) be polynomials in F[x] with h(x) of positive degree. Prove that if e(x) = gcd(g(x),h(x)) and e(x) divides f(x), then there is a polynomial j(x)  F[x] such that g(x)j(x)  f(x) (mod h(x)).

Finding the Discriminant in a Quadratic Equation

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. What I need to do is figure out how to create three unique equations where the discriminant is positive, zero, or negative. For each case, please explain what t

Solve the Given Quadratic Equation

For the equation , perform the following: a) Solve for all values of x that satisfies the equation. Answer: Show work: b) Graph the functions and on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs. Graph: c) How does the graph relate to part a? Answer

Exponential and Logarithmic Functions and Examples

1. Give an example of an exponential function. Convert this exponential function to a logarithmic function, then plot the graph of both functions. 2. Given the following values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, x, and y, form: A linear equation in one variable A linear equation in two variables A quadratic equation A polynom

Common and Natural Logarithms

For the exponential function e^x and logarithmic function log x, graphically show the effect if x is doubled. My response needs to include the reasons for graphically representing the effect in a particular way. I also need to scan the plotted graph and post it along with my response. I need to correctly calculate the values

Exponential and Logarithmic Function Graphs

Referring to the graph below (which is attached), identify the graph that represents the corresponding function. I need to justify my answer. y = 2^x y = log2x (where the 2 is lower case below log, not above)then; x Also, I need to plot the graphs of the following functions and show them. f(x)=6^x f(x)=3^x - 2 f(x)

Creation of Quadratic Equations

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c

See problem below ...

It is approximately 300 miles from Chicago, Illinois, to St. Louis, Missouri. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour. a)Write a linear function that expresses the distance traveled, d, as a function of time, t. Answer: b)How far have you traveled after 3 hour

Proof of density function

In the game of odd man wins, three people toss coins. The game continues until someone has an outcome different from the other two. The individual with the different outcome wins. Let X equal the number of games needed before a decision is reached. Prove by induction that the density function of X is (see attached).

Literal equations processes

I am having a hard time solving literal equations. I know the process is the same as you would solve any linear equation, but I still am having trouble grasping the whole concept. Is there any way of making this easier to learn?

Algebra Basics, Equations, and Mathematical Models

Need comparison. 1. When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imagina

Graphing the System Inequalities

(See attached file for full problem description). 1. Graph the system x^2 + y^2≤16 y≤4-x^2 2. Graph the solution { y<1/4x Bracket covers both entries but I don't know how to make it bigger. y ≥ -2x+3 3. Show the graph of the systems of inequalities? 16x^2+64y^2 ≥1024