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Given any two sets C and D, under what condition on them will C×D and D×C have the same number of elements? Give reason for your answer
If A and B are the set of even integers and set of odd integers, respectively, find( A union B) and (A union B) ^c
Obtain the resolvent cubics by Descartes method and by Ferrari method of equation x^4+4x^3+8=0 are the cubics the same? Further, use either method to obtain the roots of this equation
Is there a solution for AX=B matrix equation with zero diagonal constraint, such that: X_ii=0 ?
where, A, B, X are n×n matrices.

Is it right to solve the equation as follows?

X=inv(A)*B
X_ii=0
I went through a number of university websites (and videos) and all of them have solved Chi square test of homogeneity problems in the line of test of independence which appears very semantic to me. However this is inconsistent with a book I have, which solves homogeneity problems in a different way. A link to a sample problem from it: http://pasteboard.co/4dc2r3GZo.png
I was wondering if the process mentioned in my book is wrong. I couldn't understand what was the need to subtract the usual X2 from the X2 obtained by adding the data points of the respective categories (here yellow and green seeds) of all the samples.
A price-taking profit-maximising business, which operates at its optimal plant
size, has a TC curve give by TC = q³ − 2q² + 2q + 0.576 where TC
is measured in 1000s of £ per week and q is the rate of output measured in
1000s of units per week.
a) If the market price of output is £1.00 show that the firm will produce 1000
units per week and make a loss. Explain why the business is, at this price,
indifferent between producing and closing down. Draw a diagram to show
this.
b) If the market price of output is £3.28 what will each firm produce and what
profit is made?
c) Assuming that all firms in the industry have identical cost structures and that
there is freedom of entry, show that the long-run weekly rate of output will fall
to 1200 units.
d) What is the price of output when the industry is in equilibrium?
$100 of savings 5%ps. over 3 years with a $1 monthly fee
Solve 0.306a^2 - 10a + 0.306 = 7
Find a
Find sup A, inf A, B sup, inf B and justify your answer. Determines whether the borders are rational and decide how the borders for A and B lies respectively for A and B.
You are going to test the claim at least 60% of women

do the income taxes for their household.

If you use a significance level of 0.05,

what will the critical number be for your rejection region?

See Table A-2 for your answer
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