A production line is comprised of two machines: Machine A and Machine B such that the output from Machine A is used by machine B to make the finished product. On a typical day, Machine A breaks down with a probability of 30% and Machine B breaks down with the probability of 40%. What is the probability that the production line works properly on a typical day

42%

Step-by-step explanation:

If the probability of the first machine breaking down is 30%, the probability of it operating normally is 100% - 30% = 70%

The probability of the second machine operating normally is 100% - 40% = 60%

So, the probability of both machines operating normally in one day is:

P = 70% * 60% = 0.7 * 0.6 = 0.42 = 42%

false

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1