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A combination lock requires three selections of numbers, each from 1 through 39. Suppose the lock is constructed in such a way that no number can be used twice in a row but the same number may occur both first and third. For example, 20 13 20 would be acceptable, but 20 20 13 would not. How many different combinations are possible?
Let A and B be arbitrary n x n matrices whose entries are real numbers. Use basic matrix laws only to expand (A + B)². Explain all steps. Hint: Use the distributive laws.
Find the rate of change of the volume of a cylinder when its radius is 6 ft if its height is always (3/2) times its radius and its radius is increasing at the rate of 2 feet per minute
How many keys do we need to have probability at least two thirds that some slot has at least two keys hash to it?
Where should Steve cut the wire so that the total area of the circle and square combined is as small as possible? What is this minimal area? What should Steve do if he wants the combined area to be as large as possible?
The angles of a triangle sail measure 90°,30°,60°. it's sides measure approximately 2 feet, 3.5 feet , and4 feet. Classify the triangular shape of the sail in two different ways
Suppose a rectangular plot runs along a building, so that you only need to fence three sides. What dimensions will now yield a maximum area with 100 meters of fencing?
Find the intervals on which the function f(x) = x2/3(10 - x) is increasing and decreasing.
Find the expression for dV/dx.
Provide a plot of temperature versus distance east. Based on its appearance, is it a good linear model for predicting temperature as a function of distance?
The Sky Ski team has five entrants in a women's slalom event. The coach would like the first, second and third places to go to SS members. In how many ways can the five team entrants achieve the coach's goal?
Find the empirical probability that an iris bulb of this type will bloom. Give answer as a fraction in lowest terms.
if the length of the hypotenuse of the right triangle is 10, find the lengths of the other sides when the area is maximum.
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