10. All of this was based on data collected regarding the Quantity and Price. Find the Correlation value (r) between the Quantity (x) and Price (y). From the original data set. Record that value here.

11. Summarize your findings from the above problem. Explain what you see in a way that would make sense to someone who does not like math :)

Many thanks for all you help in my last class.

Determine whether each of the following statements is True or False. If True, write a proof. If False, exhibit a counterexample.

1) If m, n are arbitrary positive integers, then any system of form

x ≡ a (mod m)

x ≡ b (mod n)

has a solution.

2) If m, n are arbitrary positive integers and the system

x ≡ a (mod m)

x ≡ b (mod n)

    has a solution, then the solution is unique modulo mn.

Modern Abstract Algebra

Summarize a probability and statistics journal, 1 page long. Any kind please!

What would be a good business case to use one-way table? What about two-way table?

Solve the the congruence 11x 4 (mod 26)

Use the Lucas-Lehmer Test to show that 127 = 2^7-1 is prime.

Use the Lucas-Lehmer Test to show that 2047 = 2^11- 1 is not prime

Use the Lucas-Lehmer Test to show that 8191 = 2^13 - 1 is prime.

Assume Alice uses the following information to develop the public key, N, in an SS Cryptosystem: p = 23 and
q = 41 with N = p2q = 21689. Suppose Bob wants to encrypt the message m = 143 what ciphertext c does he
send Alice? Show this message, c, decrypts into m.

Playing the role of Eve, suppose Alice published the public key, N = 21689, in an SS Cryptosystem and you
intercept the message c = 263 sent from Bob to Alice. What was Bob's original message?

Solve with Laplace transform

1. y''+ 4 t y'− 4y = 0, y(0) = 0, y'(0) = −7

2. (1− t) y''+ t y' − y = 0, y(0) = 3, y'(0) = −1

1. Write an algorithm to convert base 2 number string b_nb_n-1…..b₁.c₁c_2…..c_k(please note the numbers  c_1,c₂…. And c_k are the numbers after the point in the string.) in to decimal.

2. Construct a trace table of the algorithm in question with input 11101.01₂

A car company produces 3 models, model A / B / C. Long-term projections indicate an expected demand of at least 100 model A cars, 80 model B cars and 120 model C cars each day. Because of limitations on production capacity, no more than 200 model A cars and 170 model B cars and 150 model C cars can be made daily. To satisfy a shipping contract, a total of at least 300 cars much be shipped each day. If each model A car sold results in a $1500 loss, but each model B car produces a $3800 profit, each model C car produces a $2500 profit, how many of each type should be made daily to maximize net profits?

5.5 (a) Determine the roots of f (x) = −12 − 21x − 2.75x3 graphically. In addition, determine the first
root of the function with (b) bisection and (c) false position.
For (b) and (c) use initial guesses of xl = −1 and xu = 0
and a stopping criterion of 1%.
5.6 Lo

Find the first four terms in the Taylor series expansion of the solution to

y′′(x) − 2xy′(x) + 2y(x) = 0, y(0) = 1, y′(0) = 0.

Find the first four terms in the Taylor series expansion of the solution to

a. y′(x)=y(x)−x,y(0)=2.
b. y′(x)=2xy(x)−x3,y(0)=1.
c. (1+x)y′(x)=py(x),y(0)=1.
d. y′(x) = ?x2 + y2(x), y(0) = 1.
e. y′′(x)−2xy′(x)+2y(x)=0,y(0)=1,y′(0)=0.

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}.

a) Prove or disprove: A ⊆ X

b) Prove or disprove: X ⊆ A

c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y )

d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )