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Modern Algebra
Group Theory (LXXXIV)
Permutation Groups
The Order of a Permutation
The Order of a Cycle
(a) What is the order of an n-cycle?
(b) What is the order of the product of the disjoint cycles of lengths m1 , m2 , ... , mk ?
(c) How do you find the order of a given permutation?
Find the quotient and leave the result in a +bi form. 15(cos 240° + i sin 240°) / 3(cos 30° +i sin 30°). Find the angle between the given vectors, to the nearest tenth of a degree. u=5i + 6j, v = 3i -2j.
Bill invests in a plan that has an APR of 3%. He invests four times as much in a plan that has an APR of 8%. If the total interest from the investments is $805 after one yaer, how much was invested in each plan?
Does either one of these formulas define a norm? If yes, show that all three axioms of norm hold. If no, demonstrate which axiom fails.
Ron and Kathy are telemarketers. Ron contacts potential home buyers and is paid $30.00 for each buyer he gets to work with a realtor at the company. Kathy contacts potential sellers and is paid $65.00 for each seller she gets to discuss listing a ..
write a quadratic function in standard form having zeros of -9 and
A clear explanation of the relationship between Boolean Algebra and the circuits that you designed.
Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen
1. Discussion Question: Discuss the difference in appearance of a graph of an equation and a graph of an inequality. Include the dashed vs. the solid line in the graph of an inequality.
A COMMITIE OF 12 MEMBERS IS HEADED BY 3 DIRECTORS OF EQUAL RANK WHO ARE VOTED IN. HOW MANY WAYS CAN THE 3 DIRECTORS BE CHOSEN FROM THE 12 MEMBERS?
Find the maximum harvest.
Calculate the future value of the investment. You must use the advertised interest rate, the number of compounding periods per year, and the time the funds will be invested.
During the summer, a group of students builds kayaks in a converted garage. The rental for the garage is $1,500 for the summer, and the materials needed to build a kayak cost $125. The kayaks can be sold for $275 apiece.
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