## A certain component is critical to the operation of an electrical system and must be replaced immediately upon failure. If the mean lifetime of this type of component is 100 hours and its standard deviation is 30 hours, how many of the components must be in stock so that the probability that the system is in continual operation for the next 2000 hours is at least .95?

October 14, 2019// Blog//

If the following are the correct equations:

then you can change the last one by dividing through by 2 to look like:

These two lines have the same slope, which means they are parallel, leaving you with two possibilities, either they different lines and there are no solutions or they are the same exact line, where there would be infinitely many solutions. Since the two lines have the same slope, but different y-intercepts they have to be different lines, and they are parallel, hence there are no solutions. One way to check this analytically is to set the two equations equal to each other (by solving each of them for y or x):

you can see that the (5/2)x terms cancel, leaving you with 4 = 2, which is obviously false. This means that there are no values of x such that these two lines are equal, hence they are parallel and there are no solutions. On the other hand you might get something like 2 = 2, this means that every value of x is a solution, this means that the lines are the same and there are infinitely many solutions.