Answer:
length=53 in
width= 23 in
Step-by-step explanation:
First, we know that each corner has now a square of 6 in long, so the heigth of the box will be of this size (as you can see in the picture attached). Then, the length and the width of the box would be the same as the piece, but with 12 in less. Therefore the equations to solve the problem are:
We factorize the 6 and we get:
Finally we solve for x, and we get the initial dimensions of the piece of metal:
Answer:
There is a 98.26% probability that it is overloaded.
This elevator does not appear to be safe.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
In this problem, we have that:
Assume that weights of males are normally distributed with a mean of 170 lb, so
They have a standard deviation of standard deviation of 29 lb, so .
We have a sample of 8 adults, so we have to find the standard deviation of the sample to use in the place of in the Z score formula.
Find the probability that it is overloaded because they have a mean weight greater than 162 lb, so
has a pvalue 0.0174.
So, there is a 1-0.0174 = 0.9826 = 98.26% probability that it is overloaded.
Any probability that is above 95% is considerer unusually high. So, this elevator does not appear to be safe, since there is a 98.26% probability that it is overloaded.