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The velocity of a wave of length L in deep water is v = K square root of (L/C + C/L)
where K and C are known positive constants. What is the length of the wave that gives the minimum velocity?
What is the probability that the mean of a random sample of size n = 4 of tire lifetimes will be less than 20,000 miles?
Work out what constraints in a maximum entropy problem will give rise to the true inverse Gaussian distribution.
If the solution to an equation is imaginary or irrational, it takes a bit more effort to check. Replace x by each given number to verify the following statement.
A jazz concert brought in $166,500 on the sale of 8,100 tickets. If the tickets sold for $15 and $25 each, how many of each type were sold?
Determine whether the mean value Theorem applies to the following functions on the given interval [a,b] and if, so find or approximate the point(s) that are guaranteed to exist by the mean value theorem.
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).
Derive an expression using the given data - Show that this reduces to the integration-by-parts formula if u and v are continuous across x = c. It is not necessary for du/dx and dv/dx to be continuous at x = c.
Probability : Counting Principle, A social security number has 9 digits. How many different S.S numbers are possible if:
Draw conclusions involving the uncertainty from the results of the simulation.
the number of coins that Josh spots when walking to work is a poisson rv with mean 6. Each coin is equally to be a penny, a nickel, a dime, or a quarter. Josh ignores the pennies but picks up the other coins.
Using the second derivative or otherwise, distinquish the maximum and minimu points of the curve.
Quadratic equations may be solved by graphing, using quadratic formula,completing the square, and factoring. What are the pros and cons of each of these methods? When might each method be most appropriate? Which method do you prefer? Explain why?
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