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A swimming pool currently contains 500 gallons of water. Water is drained from the pool at a constant rate of 4 gallons per minute. Write the linear function that models the amount of water in the pool in terms of the time since the drain was opened. What is the domain of this function? How much water will be left in the pool after 14 minutes? How long will it take for the amountof water in the pool to be reduced to 392 gallons?
Computing probability, mean and standard deviation for the given information and evaluate the mean number of sales expected.
a bag of marbles can be shared equally among 3,4,5 students with none left over. What is the least amount of marbles that can be in the bag?
How many ways are there to deal hands of seven cards to each of five players from a standard deck of 52 cards? A bagel show has onion, poppy seed, egg, salty, pumpernickel, sesame seed, raisin, and plain bagels. How many ways are there to choose:
A box with a square base has length plus girth of 106 in. (Girth is the distance "around" the box.) What are the two possible lengths of the box, if its volume is 2200 in3?
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.
Find (partial z)/(partial u)( and ) (partial z)/(partial v) using the chain rule. Assume the variables are restricted to domains on which the functions are defined. Your answers should be in terms of u and v.
Let gamma be a closed rectifiable curve in C (Complex plane) and a is not an element of {gamma}. Show that for n>= 2 integral over gamma of (z-a)^-n dz = 0.
Find the point on the line y = 3x + 9 that is closest to the origin. (Give your answers correct to three decimal places.)
Six people are going to travel to Mexico City by car. There are six seats available in the car. In how many different ways can the six people be seated in the car if only three of them can drive?
If you were to let A be a 6 x 14 matrix where the dimension of the row space is 3 (dim(R(A) = 3), what would the dimension of the null space of matrix A (dim(N(A)) be and what would the dimension of the null space of A^T (dim(N(A^T)) be?
Solve the problem of Critical Path and PERT. A PERT project has 45 activities, 19 of which are on the critical path. The estimated time for the critical path is 120 days. The sum of all activity variances is 64, while the sum of variances along the..
Combine from JPE, Fall 90 and Spring 97) Let A ∈ C^(n X n) be a normal matrix. Prove that A - M is normal for any λ ∈ C. Prove that ||Ax||2 - ||∧*x||2 for all x ∈ C^n
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