Find the conjugacy classes in S₃AND write down the class equation for S₃

We know that S₃ ={ e , f , f² , g , fg , f²g , }

please explain step by step and show centers and centerlizers please.

Find the conjugacy classes in D4, and write down the class equation for D4•

We know that D4 ={ e , f , f^2 , f^3 , g , fg , f^2g , f^3g }

please explain step by step.

7.7.3. Consider a vibrating quarter-circular membrane, 0 < r < a,0 < θ < π/2, with u =0 on the entire boundary. [Hint: You may assume without derivation that λ>0 and that product solutions
u(r,θ,t)=φ(r,θ)h(t)=f(r)g(θ)h(t)
satisfy
∇2φ+λφ =0 dh dt =−λkh d2g dθ2 =−μg
r
d drrdf dr+(λr2 −μ)f =0 .]

*(a) Determine an expression for the frequencies of vibration.

(b) Solve the initial value problem if u(r,θ,0) = g(r,θ), ∂u ∂t (r,θ,0) = 0.

(c) Solve the wave equation inside a quarter-circle, subject to the conditions
∂u ∂r
(a,θ,t)=0,u (r,0,t)=0 ur, π 2,t=0,u (r,θ,0) = 0 ∂u ∂t (r,θ,0) = β(r,θ)

Let n ≥ 3. Show that if G is a graph with the same chromatic polynomial as Cn, then G is isomorphic to Cn. (Hint: Use induction. What kind of graph must G − e be for any edge e? Why?)

Basic properties of growth rates. Use the fact that the growth rate of a variable equals the time derivative of its log to show:

(a) The growth rate of the product of two variables equals the sum of their growth rates. That is, if Z(t) = X(t)Y(t), then Ż(t)/Z(t) = [Ẋ(t)/X(t)] + [Ẏ(t)/Y(t)].

(b) The growth rate of the ratio of two variables equals the difference of their growth rates. That is, if Z(t) = X(t)/Y(t), then Ż(t)/Z(t) = [Ẋ(t)/X(t)]−[Ẏ(t)/Y(t)].

(c) If Z(t) = aX(t)α, then Ż(t)/Z(t) = αẊ(t)/X(t).

Students in a college are allowed to chose their own passwords consisting of three (3) lower-case letters, in that order. How many different passwords are possible if

a. repetitions allowed?

b. repetitions are not allowed?

c. The first character cannot be 0, with no repetitions are not allowed?

Melanoma treatment. An experiment evaluated the use of genetically engineered white blood cells in the treatment of patients with melanoma.^y Patients were divided into three cohorts. Patient cohort 1 received genetically engineered lymphocytes that were cultured ex vivo for 19 days. Cohort 2 received cells that were cultured for between 6 and 9 days. Cohort 3 received cells that were generated by a second rapid expansion performing after 8 to 9 days. Cell doubling times were as follows.

Cohort 1               8.7          11.9        10.0

Cohort 2               11.4        1.0          1.3          1.0          2.0          0.6          0.8          0.7          0.9          1.9

Cohort 3               0.9          3.3          1.2          1.1

Either create a file with these data or download the file MORGAN2006.* from the companion website. Most statistical programs require you to enter that data into two columns: one column for the explanatory variable (COHORT) and the other for the response variable (DOUBLING). Your final data table should have 2 columns and 18 rows.

If you do not have access to a statistical program, consider using BrightStat. com.^z Use of BrightStat.com is free. However, you must register as a user in order to access its ANOVA features.

(a)   Calculate the means, standard deviations, and sample sizes of each group. Use the “double the standard deviation” benchmark to assess whether group variances are significantly different. Is there evidence of heteroscedasticity?

(b)   Conduct Levene’s test for unequal variance. Show all hypothesis testing steps. What do you conclude?

A team of size m has to be chosen from a group of n people (m < n) and a captain chosen for the team.

(a) How many ways can the captained team be chosen if the captain is chosen first then the remainder of the team chosen.

(b) How many ways can the captained team be chosen if the team is chosen first then the captain chosen from the team? This should give the same number as a) but a different formula.

give a justification of answers pls (set notation, bijection principal, addition or multiplication theorem, cartesian product etc...)

(c) If n = 4 and m = 3 draw the selection tree for each of (a) and (b). Be sure to carefully label the nodes of the tree with the corresponding subsets and the branches of the tree with the corresponding choices.

(d) For the selection tree you draw in (c) write down the element of [4] × [3] that each path in the selection tree maps to using the bijection discussed in lectures. That is, write the 2-tuple at the end of each of the selection paths of the selection tree.

DO PART C & D ONLY!!! with formulas from part a and b should be 12 ways

I need answers for Chapter 5 Problem 28. Render ISBN # 13: 978-0-13-45316-1. Problem Reads: sales of industrial vacuum cleaners at R. Lowenthal supply Co. over the past 13 months are as follows: sales ($1,000s) Month. First row is 11 sales Month January. Need the following a) using a moving average with three periods, determine the demand for vacuum cleaners for next Feb. also (B), (C), (d) answers? this problem can be found on p. 179. in textbook Quantitative Analysis for Management 13 th. ed. Render. Here is a problem: Sales of industrial vacuum cleaners at R. Lowenthal Supply co. over the past 13 months are as follows. Heading: Monthly Sales are in ($1,000s - Month). January Sales (11) ($1,000s) February Sales (14) March Sales (16) April (10) May (15) June (17) July (11) August (14) September (17) October (12) November (14) December (16) January (11). Question (a). Using a moving average with three periods, determine the demand for vacuum cleaners for next February. (b) Using a weighted moving average with three periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods, respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would have a weight of 2, and January would have a weight of 3. (c) Evaluate the accuracy of each of these methods. (d) What other factors might R. Lowenthal consider in forecasting sales?       

Formulating Financial Statements from Raw Data
Following is selected financial information from General Mills, Inc., for its fiscal year ended May 25, 2003 ($ millions):

Revenue	$10,506
Cash from operating activities	1,631
Cash, beginning year	975
Stockholders' equity	4,475
Noncash assets	17,524
Cash from financing activities	(885)
Cost of goods sold	6,109
Total expenses (other than cost of goods sold)	3,480
Cash, ending year	703
Total liabilities	13,752
Cash from investing activities	(1,018)

Prepare the income statement, the balance sheet, and the statement of cash flows for General Mills for the fiscal year ended May 2003.

Hint: Enter negative numbers only for answers in the statement of cash flows (if applicable).

General Mills, Inc.

Income Statement ($ millions)

For Year Ended May 25, 2003

Revenue	$0
Cash, ending year, total expenses, cost of goods sold, noncash assets	0
Gross Profit	0
Cash, ending year, total expenses, cost of goods sold, noncash assets	0
Net Income	0

General Mills, Inc.

Balance Sheet ($ millions)

May 25, 2003

assets Liabilities

cash	$0	Total Liailities	$0
cash, beginning year, non cash assets, stock holders equity, net income	0	cash, beginning year, non cash assets, stock holders equity, net income	0
Total assets	$0	Total liabilities and equity	$0

General Mills, Inc.

Statement of Cash Flows ($ millions)

For Year Ended May 25, 2003

Cash from operating activities	$0
Non cash assets, net income, cash, beginning year, cash from investing activities	0
Cash from financing activities	0
Net change in cash	0
Non cash assets, net income, cash, beginning year, cash from investing activities	0
Cash, ending year	$0

Does the negative amount for cash from financing activities concern us? Explain. (select)

A negative amount for cash from financing activities implies that the company is unable to pay its debts as they come due and should be interpreted negatively.

A negative amount for cash from financing activities is the result of additional borrowings. Because the additional funds are invested in earnings-generating assets, this should be viewed positively.

A negative amount for cash from financing activities implies that the market value of the company's long-term debt has declined and this change should be viewed negatively.

A negative amount for cash from financing activities reflects the reduction of long-term debt, which is a positive sign of the company’s ability to retire debt obligations.

(c) Using the statements prepared for part a. compute the following ratios (for this part only, use the year-end balance instead of the average for assets and stockholders' equity):

Round answers to two decimal places (example for percentage answers: 0.12345 = 12.35%).

(i) Profit margin
Answer%
(ii) Asset turnover
Answer
(iii) Return on assets
Answer%
(iv) Return on equity
Answer%

Importance and Relevance of Statistics in Your Life

The purpose of this week's discussion topic is to get you thinking about the importance and relevance of statistics in your professional and/or personal life. Please answer the following three questions.

How do you use statistics in your life either at work or for pleasure?

Can statistics be manipulated for those who really understand the subject matter? If so, how? If not, why not?

Has anyone misled you using statistics?

Rolle's Theorem Question

if f(a)=f(b) then it is constant function, so every point c in the interval (a,b) is zero.

I don't understand the terms constant function, is it supposed to be a horizontal line or it can be a parabola curve.

For example, when f(a)=f(b) and they both exist at the endpoint then it can be a parabola curve then it break the assumption that f(a)=f(b) then it is constant function, so every point c in the interval (a,b) is zero.

Please draw the picture to describe and explain

y'' + y' + y = Asin(ωt), y(0) = 0 , y'(0) = 0

License plates in a given state must consist of three letters followed by four digits.  The state's DMV has determined that there are eighteen three-letter words that cannot appear on license plates, and there are five four-digit numbers that cannot appear.   How many license plates are banned? Your answer may be given as an integer, or as a formula.  Either is acceptable.

1) Low-dose aspirin tablets contain 1¼ grains of aspirin in each tablet. How many tablets can be prepared from 1.1 avoirdupois pound of aspirin?

2) If a physician prescribed 3.600 grams of aspirin to be taken by a patient daily, about how many 5-grain tablets should the patient take each day?

3) A physician advises an adult patient to take a children's tablet (81 mg of aspirin per tablet) daily as a precaution against a heart attack. Instead, the patient decides to cut 5-gr aspirin tablets into dosage units. How many full doses (theoretically) could be obtained from each 5-gr tablet?

Question 3 options:

	A) < 2
	B) 3
	C) 4
	D) 5
	E) > 6