Bill earned $10.00 per hour. He worked 40 hours at regular rate, 2 hours at time and a half
2 answers:
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Answer:
Step-by-step explanation:
The probability mass function P(X = x) is the probability that X happens x times.
When n trials happen, for each , the probability mass function is given by:
In which p is the probability that the event happens.
is the permutation of n elements with x repetitions(when there are multiple events happening(like one passes and two not passing)). It can be calculated by the following formula:
The sum of all P(X=x) must be 1.
In this problem
We have 3 trials, so
The probability that a wafer pass a test is 0.7, so
Determine the probability mass function of the number of wafers from a lot that pass the test.
Answer:
The largest possible volume of the box is 2000000 cubic meters.
Step-by-step explanation:
The volume (), in cubic centimeters, and surface area (
), in square centimeters, of the box with a square base are described below:
(1)
(2)
Where:
- Side length of the base, in centimeters.
- Height of the box, in centimeters.
By (2), we clear within the formula:
And we apply in (1) and simplify the resulting expression:
(3)
Then, we find the first and second derivatives of this expression:
(4)
(5)
If and
, then we find the critical value of the side length of the base is:
Then, we evaluate this result in the expression of the second derivative:
By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:
The largest possible volume of the box is 2000000 cubic meters.