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    Basic Algebra

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    Exponential and Logarithmic Functions : Level of Sound

    Determine the level of sound (in decibels) for the given sound intensity. (a) I=10^-3.5 watt per m^2 (jet 4 miles from takeoff) (b) I=10^-3 watt per m^2 (diesel truck at 25 feet) (c) I=10^-1.5 watt per m^2 (auto horn at 3 feet)

    Exponential and Logarithmic Functions

    Endangered Species: A conservation organization releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 1000 animals and that the growth of the herd will follow the logistic curve. p(t)=1000/1+9e^-0.1656t where t is measured in months (a)

    Exponential and Logarithmic Functions: Example Problems

    Sales and Advertising: The sales S (in thousands of units) of a product after x hundred dollars is spent on advertising is: S = 10(1-e^kx). When $500 is spent on advertising, 2500 units are sold. (a) Complete the model by solving for K. (b) Estimate the number of units that will be sold if advertising expenditures are raised

    Exponential and Logarithmic Functions

    Radioactive Decay: Carbon 14 dating assumes that the carbon dioxide on earth today has the same radioactive content as it did centuries ago. If this is true, the amount of carbon 14 absorbed by a tree that grew several centuries ago should be the same as the amount of carbon 14 absorbed by a tree growing today. A peice of anc

    Exponential and Logarithmic Equations : Modeling

    The number of trees per acre N of a certain species is approximated by the model N=68(10^-0.04x), 5 <_ x <_ 40 (<_ = less than or = to) Where x is the average diameter of the trees (in inches) three feet above the ground. Use the model to approximate the average diameter of the trees in a test plot when N=21.

    Describe the Nonabelian Group

    Let G be a finite nonabelian group of order 27 where all the elements have order 3. Prove that there is exactly one such group G and give a complete description.

    Irreducible Polynomial over a Field

    Please see the attached file for the fully formatted problems. 5. Find an irreducible polynomial f(x) over the field Z3 with Z3[x]/(f(x)) = F243. Note that 243 = 3^5 . Please explain your reasoning and solution in as much detail as possible. Thank You.

    Exponential & Logarithmic Functions Word Problem

    NUMBER OF FARMS. The number N of farms in the United States has declined continually since 1950. In 1950 there were 5,647,800 farms, and in 1995 that number had decreased to 2,071,520. Assuming that the number of farms decreased according to the exponential model: A). Find the value of k, and write an exponential function

    Finite Fields : Field Extensions

    Please see the attached file for the fully formatted problem. Show the existence of an extension of Fq of order l for any prime l.

    Quadratic Equations : Discriminants and Solving

    For the equation 24x^2 + 68x + 28 = 0 a) Find the discriminant b) If the discriminant tells you that you can factor, do so. c) Solve the equation by completing the square(HINT: at some point during the process, you will come to a point which looks like (x+(17/12))^2 = (121/144) d) solve the equation by using the quadrati

    Quadratic Equation : Proof by Completing the Square

    1. Prove the Quadratic Formula by completing the square on ax^2+bx+c=0 2. A picture that is 14 in by 20 in is to have an even border. If the area of the picture and the border is 352 in^2, how wide will the border be?

    Simplify the Expression

    Please see the attached file for the fully formatted problems. Simplify the following expression: 1/[1 + 1/(1 + (1/x))]

    Simplify the Expression

    Please see the attached file for the fully formatted problem. (y2 + y - 12)/(y3 +9y2 + 20y)/[(y2-9)/(y2+3y2)]

    Determining Correlation and Distribution

    6) Suppose we have a building with a floor shaped like an isosceles right triangle. The two sides adjacent to the right triangle have length 100 feet. Think of the right angle being at the origin, and other two corners at (100, 0) and (0, 100). The overhead crane is located at the origin and needs to travel to a point (X, Y), w