To create an open-top box out of a sheet of cardboard that is 25 inches long and 13 inches wide, you make a square flap of side length x inches in each corner by
13 in.
cutting along one of the flap's sides and folding along the other. (In the diagram,
a solid line segment in the interior of the rectangle indicates a cut, while a
dashed line segment indicates a fold.) Once you fold up the four sides of the
box, you glue each flap to the side it overlaps. To the nearest tenth, find the value of x that maximizes the
volume of the box.

Step-by-step explanation:

length of the box is a = 25 -2x

width of the box is b =13 -2x

height of the box is x

and x < 6,5

so the volume of the box V=f(x) = x.(25-2x)(13-2x)= 4x^3 -76x^2 +325x

f'(x) = 12x^2 - 152x + 325

to maximize the volume of the box ( f(x) max ) then f'(x) = 0 --> x ≈ 2,72 and x ≈ 9,94

so x = 2,72 inches

length of the box is a = 25 -2x

width of the box is b =13 -2x

height of the box is x

and x < 6,5

so the volume of the box V=f(x) = x.(25-2x)(13-2x)= 4x^3 -76x^2 +325x

f'(x) = 12x^2 - 152x + 325

to maximize the volume of the box ( f(x) max ) then f'(x) = 0 --> x ≈ 2,72 and x ≈ 9,94

so x = 2,72 inches

Step-by-step explanation:

8

Step-by-step explanation:

In order to find the range you need to subtract maximum card number from the minimum card number. We know that the range is 5 and that the minimum card is 6 so we can set up the equation like this to find the maximum shown as x.

Add 6 to both sides

Now we know all the the numbers of the three cards Anthony has since we were given the minimum = 6, 7, and solved for the last card which was the maximum = 11. In order to find the mean we have to add all of the numbers then divide by how many numbers there are (in this case it will be 3):

Add 6+7+11

Divide by 3