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    Basic Algebra

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    Answer study guide

    (See attached file for full problem description) --- 1. Which property of the real numbers is illustrated by the following statement? 9 ? (7 + 11) = 9 ? 7 + 9 ? 11 A) Commutative property of multiplication B) Associative property of addition C) Associative property of multiplication D) Distributive property 2.

    Polynomial, Rational, Exponential, and Logarithmic Functions

    1) An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. Please Place Answer Here:

    Logarithms : Change of Base Formula

    Most calculators have 2 different logs on them: log which is based 10, and in which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers availabe to the computer, 0 and 1. When a computer scientist needs a logarithm, he/she needs a log to base 2

    Fixed Rate and Logarithm Change of Base Formula

    For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, A=P(1+r)^nt, let r= n 10%, P=1 and n=1 and give the coordinates(t,A) for the points wher

    Logarithms

    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)

    Voting

    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