Answer:
The maximum volume of the open box is 24.26 cm³
Step-by-step explanation:
The volume of the box is given as 
, where 
and 
.
Expand the function to obtain:
Differentiate wrt x to obtain:
To find the point where the maximum value occurs, we solve
Discard x=3.54 because it is not within the given domain.
Apply the second derivative test to confirm the maximum critical point.
, 
This means the maximum volume occurs at 
.
Substitute into to get the maximum volume.
The maximum volume of the open box is 24.26 cm³
See attachment for graph.
23x =14 this will be the answer
Answer:
The 95% confidence interval for the true population mean dog weight is between 62.46 ounces and 71.54 ounces.
Step-by-step explanation:
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of 
.
So it is z with a pvalue of 
, so 
Now, find M as such
In which 
is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 67 - 4.54 = 62.46 ounches.
The upper end of the interval is the sample mean added to M. So it is 67 + 4.54 = 71.54 ounces.
The 95% confidence interval for the true population mean dog weight is between 62.46 ounces and 71.54 ounces.
Answer:
6 mm and 9 mm are the dimensions of the piece of plastic.
Step-by-step explanation:
Keep in mind the formulas for the area and perimeter of a rectangle:
A = lw
P = 2 (l + w)
List the factors of 54:
1, 2, 3, 6, 9, 18, 27, 54
POSSIBLE DIMENSIONS of the piece of plastic:
1 mm and 54 mm:
Area - 54 mm^2
Perimeter - 110 mm
2 mm and 27 mm
Area - 54 mm^2
Perimeter - 58 mm
3 mm and 18 mm
Area - 54 mm^2
Perimeter - 42 mm
6 mm and 9 mm
Area - 54 mm^2
Perimeter - 30 mm
The rectangular piece of plastic with the dimensions 6mm and 9 mm corresponds with the area and perimeter of the piece of plastic mentioned. So these are the correct dimensions.
Hope this helps!
