Question

Prove that there is no integral domain with exactly 6 elements. Can your argument be adapted to show that there is no integral domain with exactly 4 elements? What about 15 elements? Use these observations to guess a general result about the number of elements in a finite integral domain.

Answer #1

Conducting a Simulation
For example, say we want to simulate the probability of getting
“heads” exactly 4 times in 10 flips of a fair coin.
One way to generate a flip of the coin is to create a vector in
R with all of the possible outcomes and then randomly select one of
those outcomes. The sample function takes a vector of elements (in
this case heads or tails) and chooses a random sample of size
elements.
coin <- c("heads","tails")...

4. When the second derivative test (SDT) is used for a critical
point the result can be local maximum, local minimum, saddle point
or test inconclusive. Consider the function f(x, y) = y^2 − 2y
cos(x) with domain restricted to {(x, y) | −1 ≤ x ≤ 4 and − 2 ≤ y ≤
4} and the three points P = ( π/2 , 0) Q = (0, 1) and R = (π,
−1).
(a) Find all the critical points...

4. When the second derivative test (SDT) is used for a critical
point the result can be local maximum, local minimum, saddle point
or test inconclusive. Consider the function f(x, y) = y 2 − 2y
cos(x) with domain restricted to {(x, y) | −1 ≤ x ≤ 4 and − 2 ≤ y ≤
4} and the three points P = ( π 2 , 0) Q = (0, 1) and R = (π,
−1).
(a) Find all the...

1.Utopian economics characterizes speculation as stabilizing yet
reality economics said that speculation could be de-stabilizing.
Explain these two views.
2.Let’s assume that market is inefficient. They why don’t more
people beat the market?
3.Show how efficient markets is the child of free-market
thought.
4.Explain what is meant by rational irrationality and explain an
example that is not directly related to finance.
5.Why does an efficient market imply a normal distribution in
stock returns?
6. Let’s play the following game: Guess...

) In the Extra Problem on PS 2 we defined a map φ:M2,2(Z) →
M2,2(Z2) by the formula φ a b c d = a mod (2) b mod (2) c mod (2) d
mod (2)
On PS 2 you showed that φ is a ring homomorphism and that ker(φ)
= 2a 2b 2c 2d a, b, c, d ∈ Z We know the kernel of any ring
homomorphism is an ideal. Let I = ker(φ).
(a) (6 points) The...

Lab 6: Taxonomy
INSTRUCTIONS:
· On your own and without
assistance, complete this Lab 6 Answer Sheetelectronically and
submit it via the Assignments Folderby the date listed in the
Course Schedule(under Syllabus).
· To conduct your laboratory
exercises, use the Laboratory Manual located under Course Content.
Read the introduction and the directions for each
exercise/experiment carefully before completing the
exercises/experiments and answering the questions.
· Save your Lab 6 Answer
Sheetin the following format: LastName_Lab6 (e.g.,
Smith_Lab6).
· You should submit your document
as a...

The number of new businesses established in the US since 1990
can be modeled by the function
N(x)=110.8x^3-5305.5x^2+76,701x+332,892 where x = 0 represents 1990
and the domain is [0, 25].
1. According to the model, about how many new businesses were
established in 2011? Don’t forget to label and interpret the
answer.
2. What was the average rate of change in the number of new
businesses established between 2000 and 2010? Don’t forget to label
and interpret the answers.
3....

Expert Session 6 Quiz Expert: Duane Forrester Title: Learn the
Basics of Search Engine Optimization External Link --
https://www.youtube.com/watch?v=Dm2KXhBPZDg -- End External
LinkPlease review this expert session and answer each of the
following questions by placing an * beside the relevant answer(s)
and saving your response. If you would like to defend a particular
response, you may do so by entering your comments in the FREE
RESPONSE BLOCK in this file. Next, complete the actual quiz
provided in Canvas so...

Research is an integral part of all professional fields.
Designing a research study can be a complicated task that can be
simplified if the appropriate techniques can be identified. This
assignment will give you the opportunity to design an experiment,
including finding relevant prior research, determining the
appropriate sample, data analysis techniques, and discuss the
results you hope to see. Working from the topic chosen earlier in
the topic selection, you will be designing your own statistical
study. In a...

1. The data below show the historical
relationship between production levels and overhead costs at your
company.
a) Construct a scatterplot of y versus x.
b) Find the least-squares regression line
(i.e., calculate the coefficients and show the equation) relating
overhead costs to production.
c) Graph the regression line on the plot.
It is recommended that you use Excel to create the scatterplot,
but do not use the Excel functions to calculate the slope and
intercept of the regression line....

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