(11) Prove that a union of two countable sets is countable. (Hint: the same idea used to show that Z is countable might be useful.) (Don’t forget that countable sets can be finite.)

(12) We saw in class that N × N ∼ N is countable. Prove that A × B is is countable for any countable sets A, B. (Hint: If you can prove that A × B ∼ N × N then you can use what has already proved...) (Don’t forget that countable sets can be finite.)

According to U.S census estimates there were about 20 million children between 8 and 12 years old( referred to as tweens) in the united states in 2009. A recent survey of 1, 223 8- to 12 -year-old children ( S. Jayson , it's cooler than ever to be a tween.''USA today February 4, 2009 pp, 1A, 2A) reported the following results, Suppose that the survey was based on 600 boys and 623 girls.

What tween did in the past week Boys girls

Played a game on a video 498 243

Game system

Read a book for fun 276 324

Gave product advice to parents 186 181

Shopped a mall 144 262

For each type of activity, determine whether there is a difference between boys and girls at the 0.05 level of significance.

A car loan is taken for $13,000 to be paid back in 5 years, with monthly payments of $495. What nominal annual interest rate is being charged in this loan?

1) 27.42%

2) 42.26%

3) 39.00%

4) 2.29%

A square membrane of side lengths L, which is initially at rest on the xy-plane has its edges fixed on the xy-plane. A periodic force per unit area, given by A⋅cos⁡(ω⋅t) for t > 0,and A=constant, acts at every point in the membrane. Apply appropriate finite Fourier transforms to show that the displacements in the membrane.

In 2001, Windsor, Ontario received its maximum amount of sunlight,
15.28 hrs, on June 21, and its least amount of sunlight, 9.08 hrs, on
December 21. (10)

1. Due to the earth's revolution about the sun, the hours of daylight function is periodic. Determine an equation that can model the hours of daylight function for Windsor, Ontario.
2. On what day(s) can Windsor expect 13.5 hours of sunlight?

Show that f(x) = x^4+x^3+3x^2+7x−8 is irreducible over Z.

i need to do piano in matlab . its keys number should ve 88 and i need a source . Can u help ne ?

The​ parlor's second month results show that it made six sales at

​$25​, one at ​$48​, one at ​$64, three at ​$76, three at ​$107, and two at ​$121.

Calculate the standard deviation for this data set.

Does your answer for the standard deviation indicate that this is a normal​ distribution? If​ not, what are the​ implications?

A.

Yes

More than​ 68% of the values are within one standard deviation from the mean. This means that future sales will not vary greatly.

B.

No Less than​ 68% of the values are within one standard deviation from the mean. This means that future sales may vary greatly.Your answer is correct.

C.

No More than​ 68% of the values are within one standard deviation from the mean. This means that future sales may vary greatly.

D.

Yes Less than​ 68% of the values are within one standard deviation from the mean. This means that future sales will not vary greatly.

Prove that a full m-ary tree of height h has at least h(m − 1) leaves.

Theory: A vector with nonnegative entries is called a probability vector if the sum of its entries is 1. A square matrix is called right stochastic matrix if its rows are probability vectors; a square matrix is called a left stochastic matrix if its columns are probability vectors; and a square matrix is called a doubly stochastic matrix if both the rows and the columns are probability vectors.

**Write a MATLAB function

function [S1,S2,P]=stochastic(A)

which accepts a square matrix A with nonnegative entries as an input. An output P will be a stochastic matrix, when it can be created according to the instructions given below. You will also calculate and output the row vectors S1=sum(A,1) and S2=transpose(sum(A,2)) in your code, where the entries of the vectors sum(A,1) and sum(A,2) are the sums of the entries of A down each column and across each row, respectively You may also employ the conditional “if” statements and logical function all.

**First, the function has to check whether a matrix A contains both a zero column and a zero row. If yes, the output has to be a message “A is not stochastic and cannot be scaled to stochastic”. (Meaning: it is neither right- nor left-stochastic and cannot be scaled to either of them.) The output P in this case will be an empty matrix, P= [ ].

**Then, the function checks whether a matrix A is: (1) doubly stochastic, (2) only left stochastic, (3) only right stochastic, or (4) neither left nor right stochastic but can be scaled to stochastic.

In the cases (1)-(3), output the corresponding messages that comment on the types of the matrices and assign to the output P the matrix A itself.

**When you are working with the case (4), output a message “neither left nor right stochastic but can be scaled to stochastic”. If the vector S1 does not have any zero entry, use this vector to modify A into a left-stochastic matrix P by scaling each of its columns by the reciprocal of the corresponding entry of S1, and output a message that you are scaling A to a left-stochastic matrix P. If S1 has a zero entry, use the vector S2 to modify matrix A into a right-stochastic matrix P by scaling each of its rows by the reciprocal of the corresponding entry of S2, and output a message that you are scaling A to a right-stochastic matrix P. Output the matrix P.

**Type the function stochastic in your Live Script.

**Run the function [S1,S2,P]=stochastic(A) on each of the matrices below (display the matrices in your Live Script file):

(a)A=[0.5, 0, 0.5; 0, 0, 1; 0.5, 0, 0.5]

(b)A = transpose(A)

(c)A=[0.5, 0, 0.5; 0, 0, 1; 0, 0, 0.5]

(d)A=transpose(A)

(e)A=[0.5, 0, 0.5; 0, 0.5, 0.5; 0.5, 0.5, 0]

(f)A=magic(3)

(g)A=diag([1,2,3])

(h)A=[0, 0, 0; 0, 0.5, 0.5; 0, 0.5, 0.5]

(k)A=randi(10,5,5);A(:,1)=0;A(1,:)=0

NOTE: Make sure that you will verify that your outputs and the messages match the corresponding definitions of stochastic matrices. If they don’t, make corrections in your code!

Compare and contrast John Taylor's and Howling Wolf's Treaty Signing at Medicine Lodge Creek. In your discussion, incorporate the following terms: ethnocentric, aesthetic, form, content, representational, abstract, and iconography. Make sure your answer demonstrates your working knowledge of the terms and your understanding of the reading.

Suppose the system AX = B is consistent and A is a 6x3 matrix. Suppose the maximum number of linearly independent rows in A is 3. Discuss: Is the solution of the system unique?

• Read the following problem.
• Use your knowledge about the Inclusion-Exclusion Principle to support your criteria.

Telephone numbering is an application of the inclusion-exclusion principle. Discuss with your peers a way in which the current telephone numbering plan can be extended to accommodate the rapid demand for more telephone numbers. (See if you can find some of the proposals coming from the telecommunications industry). For each new numbering plan you discuss show how to find the number of different telephone numbers it support.

Find the values of p for which the series is convergent

(a) Σ(n=2 to ∞) 1/n(ln n)^p

(b) Σ(n=2 to ∞) n(1+n^2)^p

HINT: Use the integral test to investigate both