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The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.
A linear transformation L:V->V is said to be idempotent if L dot L = L. If L is idempotent, show that there exists a basis S={a1,a2,...,an} for V such that L(ai)=ai for i= 1,2,...,r
The mean of the sales is 141.1 with a standard deviation of 13.62. What is the probability that he will not be able to sell 160 or more widgets in the next year?
Mary is taking courses in both Reading and English. She estimates her probability of passing Reading of 0.4 and English at 0.6 and she estimates her probability of passing at least one of them at 0.8.
The number of workers in the U. S. increased from 41.3 million to 44.4 million. What is the percent increase? Employees working from home increased from 23.5 million to 24.1 million. What is the percent increase.
If I have a 10,000 death benefit at work that is left on deposit for 7 years at an annual interest rate of 5%. The balance after 7 years is what? and then is going to be paid out in 120 equal payments.
Use the point-slope form of the linear equation to find an equation of the line with the given slope and passing through the given point. Then write the equation in standard form.
The theoretical probability of undesirable side effects resulting from taking Grebex is 1 in 12. If 600 people take Grebex to lower their blood pressure, how many will encounter undesirable side effects?
A rectangular package can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume. Assume cross section is square.
The probability that federal income tax returns will have 0,1, or 2 errors is 0.53,0.15, and 0.32. if 10 randomly selected returns are audited
The probability that both defective lights will be found, A box contains two defective Christmas tree lights that have been inadvertently mixed with eight non-defective lights. If the lights are selected one at a time without replacement
Complex problems
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.
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