Answer:
68 feet square
Step-by-step explanation:
The rectangle with the maximum area for a given perimeter is a square. The perimeter of a square is 4 times the side length, so the side length of the square area will be ...
(272 ft)/4 = 68 ft
_____
<em>More formally ...</em>
You can let x represent the length of one side. Then the length of the other side for the given perimeter will be 136 -x, and the area will be the product ...
area = x(136 -x)
The area function is a quadratic with zeros at x=0 and x=136. The vertex (maximum area) will be at the value of x that is on the line of symmetry between these points, at their midpoint: x = (0 +136)/2 = 68. This value of x makes the rectangle a square.
6x² + 11x + 3 = (3x+1)(2x+3)
Hope that helps
Answer:
The expected number of keys she will try before she opens the door is 4.5.
Step-by-step explanation:
A woman has eight keys on a key ring, one of which fits the door she wants to unlock.
Each of them is equally as likely to be the one to work, which means that this situation is represented by an uniform distribution with lower bound
and upper bound
.
Find the expected number of keys she will try before she opens the door.
The expected value of the uniform distribution is given by:

Considering
, as is the case in this exercise:

The expected number of keys she will try before she opens the door is 4.5.