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Prove that if the function, phi, G to G' (G and G' are groups) is a homonorphism then the kernel of phi is a normal subgroup of g.
Now let phi be the function from R to GL(2,R) where phi(x) is:Cos(x) -sin(x)Sin(x) Cos(x)
Prove that this is a homonorphism, what is the kernel of phi? And what is phi(R)?
Describe the history of the Chinese Remainder Theorem. Describe some of the relevant problems posed in Chinese and Hindu writings and how the Chinese Remainder Theorem applies to them.
A copier that originally cost $300 was sold on the installment plan as $28 per month for 12 months. Find the installment price if no down payment was made. Find the finance charge.
Determine the expected payoff of the game
Probability and Statistical Methods. A manufacturing intraocular lens is in a process of verifying a polishing machine. The polisher will be accepted only if the percentage of polished lenses containing surface defects does not exceed 1.5%
Write a method to calculate the area of a circle. Return the area and write a method to calculate the circumference of a circle.
A union strike vote is scheduled for tomorrow, and it looks close. You expect 100 people to vote, and the probability that a typical individual will vote to strike is estimated to be 0.4. Suppose that the voters make their decisions independent from ..
G is a finite group with elements a and b. Let the conjugacy classes of these elements be A and B respectively and suppose |A|^2, |B|^2
How many different triple-scoop cones can be made if the flavors can be duplicated?
Consider an annuity-immediate with monthly payments for twenty years. The payments are level in the course of each year, then increase by 2% for the next year. Find the present value of this annuity if the initial payment is $1, 000 and i = 4%.
Jose borrowed $12,000 for 140 days at 10 1/2% to add a hot tub and enclosure to his home. Find the interest and the maturity level.
How could you interpret infinity in the y values for costs, a negative x value for time, or a horizontal asymptote in y values for profits?
what is the probability of drawing an orange marble? Give solutions exactly in reduced fraction form.
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