Answer:

Step-by-step explanation:
Given



Required
Determine the volume
Volume is calculated as:

Substitute values for Length, Width and Height


<em>Hence, the volume of the box is </em>
<em></em>
Answer:
And the 96% confidence is given by (110.06; 117.34)
Step-by-step explanation:
Information given
represent the sample mean
population mean (variable of interest)
s=9.1 represent the sample standard deviation
n=29 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
(1)
The degrees of freedom are given by:
The Confidence is 0.96 or 96%, the significance is
and
, and the critical value would be
Replacing the info we got:
And the 96% confidence is given by (110.06; 117.34)
The derivative of
in the direction of a vector
is

With
, we get

and
,

Then
