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1. Let l_1 and l_2 be lines through the origin in R^2 that intersect in an angle pi/n, and let r_i be the reflection about l_i. Prove that r_1 and r_2 generate a dihedral group Dn.
2. The symmetric group S_3 operates on two sets U and V of order 3. Decompose the product set U x V into orbits for the "diagonal action" g(u, v) = (gu, gv), when
A) the operations on U and V are transitive
B) the operation on U is transitive, the orbits for the operation on V are {v_1} and {v_2, v_3}
3. Let G be the group of symmetries of a cube, including the orientation-reversing symmetries. Describe the elements of G geometrically.
Dotties Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 13 percent of the re..
What is the probability of drawing three queens in a row from a deck of cards when the drawn card is returned each time?
Explain why a decision maker might feel uncomfortable with the expected value approach, and decide to use a non-probabilistic approach even when probabilities are available.
Suppose I had a lemonade stand. When I charge $1, I sold 50 cups, when I raised the price to $2, I only sold 25 cups. Write an equation for the number of cups I sold as a function of the price i charged.
Suppose V is a complex inner product space and T: V --> V a linear operator. Use the results from parts (a) and (b) to show V = im(T) + ker (T*) = im(T*) + ker(T).
If a department has 10 men and 15 women, how many ways are there to form a committee with 6 members if it must have more women than men?
Your company plans to transport 20 horses to a racetrack in Denver. It takes 12 hours to drive from Phoenix to Denver. You have to stop and feed the horses every 2 hours.
Find an equation for the sphere, in the form of a level surface
The solution to Queuing Analysis. The Bay City Police Department has eight patrol cars that are on constant call 24 hours a day. A patrol car requires repairs every 20 days, on average, according to an exponential distribution
Let f be the function whose graph goes through point (3,6) and whose derivative is given by f'(x) = (1+e^(x))/(x^2). Write the equation of the line tangent to the graph of f at x=3 and use it to approximate f(3.1)
Compute the integral of xdz (|z|=r) for the positive sense of the circle in two ways first by using parametrization and second by observing that x=(1/2)(z+z conjugate)=(1/2)(z+r^2/z) on the circle.
If interest is compounded annually, it grows as follows. Suppose P0 is the initial amount and INT is the interest rate per year. If P1 and P2 represent the balance at the end of the first and second year
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