Given a set of samples which belong to two classes C1 and C2, assume C1 and C2 are linearly separable, please prove that perceptron learning algorithm applied to the samples will terminate after a finite number of iterations.

How many ways can you arrange 2,3,4 letters of the title "the endless summer"?

       - Assume that your given 2 spaces , 3 spaces , 4 spaces where you are able to use all the letters (must include the repeated letters)

       - Finding the total number of ways to order them in these certain spaces and finding the sum of all 3

          -

Look online to find an interest rates for each of the following:

a) Credit Card

What is the rate charged for overdue monthly balances? Clearly state your answer.

b) Car Company (for financing a new car)

Include your sources (links) AND a screencapture of where on the page you found the information.

Numerical Analysis: Perform the steps of the secant method to approximate the first three positive roots of the transcendent equation x = sin (πx).

Suppose we use the ElGamal signature scheme with p = 65539, ? = 2, ? = 33384. We send signed messages (m, r, s): (809, 18357, 1042) = hi and (22505, 18357, 26272) = bye. (a). Show that the same value of k was used for each signature. (b). Use this fact to find this value of k and to find the value of “a” such that ? ≡ ?? (??? ?).

You have been hired as a consultant to advise Sandbaggers, Inc., a company that purchases silica sand, cleans it, and then sells the silicon dioxide to manufacturers of computer chips. Sandbaggers, Inc., operates two cleaning plants: Plant A and Plant B.

They obtain their supply of silica sand from three independent suppliers (Sand Solutions, Dirt Dudes, and Terra Firma) who are willing to supply the sand in the following amounts and at the following prices:

Shipping costs in dollars per ton from each supplier to each of the plants are as follows:

Labor costs at each of the plants are as follows:

Plant capacities are as follows:

The cleaned and processed silicon dioxide is sold at $50 per ton to the chip manufacturers. Sandbaggers, Inc., can sell all they can produce.

Determine how Sandbaggers, Inc. should plan its operation at the two plants to maximize its profit. The executives of Sandbaggers, Inc. would also like to know whether or not both plants are able to operate at maximum capacity and whether they should look for additional suppliers based on your analysis. Prepare a report for the Sandbaggers, Inc. executives detailing your plan and addressing their questions regarding plant capacity and suppliers.

1-An explanation of how you set up the problem and arrived at your answers. This should include:

• A list of your decision variables and what they represent
• Your objective function, what it represents, all math used to obtain it, and a brief explanation of your math
• All constraints, what they represent, and a brief explanation of how you determined the constraints

2-CAN I HAVE THE SOLUTION DONE WITH SIMPLEX METHOD ???

in Research related to
MATHEMATICAL/ANALYTICAL Perspective of Inquiry

• What are the economical issues involved?
• Which economic theories or approaches best explain the issue?
• What are the statistical facts related to the issue?
• Which statistical processes used to study the issue provide for the best explanation or understanding of the issue?

Create a table that computes the money in an account for three years under the following investment scheme: the account starts at $500, each month 0.75% is added in interest and then $100 is added in new principal. Compute the total principal invested, the total amount in the account, and the total interest after three years of investing.

Solve the initial value problem:

y''' - 12y'' + 48y' - 72y = 0 ; y(0) = 1, y'(0) = 0, y''(0) = 0

Solve two different first order differential equations (one linear and one non-linear) both analytically and numerically and compare the results in tabular and graphical forms. Include at least two different numerical solution techniques for each differential equation analyzed.

a) In a collection of 900 coins, one is counterfeit and weighs either more or less than the genuine coins. Find a good lower bound on the number of balance scale weighings needed to identify the fake coin and determine whether it is too heavy or too light. Assume the balance scale has three states: tilted left, tilted right, or balanced.

b)In a collection of 10 coins, 2 coins are counterfeit and weigh less than the genuine coins. Find a good lower bound on the number of balance scale weighings needed to identify all the fake coins. (Assume the balance scale has three states: tilted left, tilted right, or balanced. )

c)Consider the problem of identifying a counterfeit coin with a balance scale. Suppose, as we did in Example 5.18, that 1 coin out of a set of 10 is fake, but this time suppose that the fake coin could be eithertoo heavy or too light, and it must be determined which is the case. What does Theorem 5.1 say about the minimum number of weighings in this case?

d)Suppose that one coin in a set of fourteen coins is fake, and that the fake coin is lighter than the other coins.

Use Theorem 5.1 to find a lower bound on the number of balance-scale weighings needed to identify the fake.

Discuss the application of Fibonacci numbers in music.

Need some detailed explanation in like 200 words.Thank you.

Exercise 3 A test for the variance can be done based on the following rejection rules: Case (a) Case (b) Case (c) H0 : σ 2 ≤ σ 2 0 (or σ 2 = σ 2 0 ) H0 : σ 2 ≥ σ 2 0 (or σ 2 = σ 2 0 ) H0 : σ 2 = σ 2 0 H1 : σ 2 > σ2 0 H1 : σ 2 < σ2 0 H1 : σ 2 6= σ 2 0 Reject if (n − 1)S 2 σ 2 0 > χ2 n−1,α (n − 1)S 2 σ 2 0 < χ2 n−1,1−α (n − 1)S 2 σ 2 0 < χ2 n−1,1−α/2 or (n − 1)S 2 σ 2 0 > χ2 n−1,α/2 Use this test to solve the following problem: A pharmaceutical company is concerned about the variability of the content of the active ingredient in a new allergy medication they plan to submit for approval to the FDA. Even though certain level of variability is not a problem, if there is evidence that the standard deviation of the content exceeds 0.1mg, the FDA would not approve the new medication. The pharmaceutical company’s managers want to make sure that the new medication will get the approval before submitting it because, otherwise, the reputation of the company would be seriously damaged and, therefore, conduct a test at the 1% significance level to try to prove that, at this level of significance, they can prove that the variability is below the standards required by the FDA. (a) Propose a null and an alternative hypothesis to test the safety of the medication (note that the test is written for the variance and not for the standard deviation!). (b) The company takes a sample of 100 pills and measures the content of the active ingredient in all of them, obtaining a standard deviation of 0.085mg. Is this enough evidence at the 1% significance level to say that the variability is below the FDA requirements? (c) Find and interpret the p-value of this test. Should the company submit the medication?

A good starting point is to explore the life of Pythagoras and his contribution to the world of mathematics, and one part of his life or his discoveries. supported with a detailed example.

Is it possible to have one region whose volume can be described in BOTH cylindrical and spherical coordinates using triple integrals that have only constant bounds (i.e., no variables in any of the bounds)? If yes, provide an example of such a region. If no, explain why not.