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A 450-gallon water storage tank is filled by a single inlet pipe, and two identical outlet pipes can be used to supply water to the surrounding fields (see the figure). It takes 9 hours to fill an empty tank when both outlet pipes are open. When one outlet pipe is closed, it takes 5 hours to fill the tank. Find the flow rates (in gallons per hours) in and out of the pipes.
In a local election, there are eight candidates for five positions as judges on the Supreme Bench. The number of possible outcomes of the election is:
150 members indicated that they plan to attend the next Summer Olympic Games, and 90 indicated that they plan to attend the next Winter Olympic Games. How many members of the club plan to attend.
Let V be a finite-dimensional real (i.e. F = R) vector space. Let T be an element of L(V)(set of operators on V), and assume that T^2 = 0.
Suppose that a county ordinance requires a 2 1/5% 'fall' for a sewage pipe from the house to the main pipe at the street. How much vertical drop to nearest foot must there be for a horizontal distance of 55 feet.?
Probability : Drawing Cards and Sampling Without Replacement, 3 cards are drawn in succession from a regular straight deck of 52 playing cards. Find the probability that
Show that these topologies are the same and What is the resulting space and identify the familiar quotient space given by this relation and then show precisely that the quotient topology on this space is the same as the usual one.
Prove that there cannot be a nilpotent group N generated by two elements with the property that every nilpotent group generated by two elements is a homomorphic image of N
Hamilton Quaternions : Kernels and Images, Show that the map phi: H->M_2(C) defined by phi(a+bi+cj+dk)=(a+b(sqrt -1),c+d(sqrt-1);-c+d(sqrt-1),a-b(sqrt-1)) is a ring homomorphism
the man is 5 feet tall. The pole casts a shadow that is 36 feet and the man casts a shadow of 8 feet. How tall is the telephone pole?
Failures per day for a computer network follow the Poisson distribution with mean 0.3. What is the probability that two or more failures occur in
Could you clarify what constitutes a spanning set and a basis? Also how does one test to see if a set of vectors is a spanning set and if it is a basis?
A computer processes jobs on a first-come first-serve basis in a time-sharing environment. The jobs have Poisson arrival rates with an average of six minutes between arrivals.
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