Answer:
12 units²
Step-by-step explanation:
The two are congruent, so C'D' is still 6units long. L*W = 6 * 2 = 12 units^2
You can roll a total of 6 by rolling (1, 5), (2, 4), (3, 3), (4, 2), or (5, 1). There are 36 total possible rolls that can be obtained, so you roll a total of 6 with probability 5/36.
You can roll a total of 11 by rolling (5, 6) or (6, 5), hence with probability 2/36 = 1/18.
Any of the other remaining 29 outcomes occurs with probability 29/36.
The expected value of your winnings is
$18*5/36 + $72*1/18 - $9*29/36 = -$0.75
so the answer is E.
Answer:
15 15 goes into 45 5 times and 60 5 times. highest number that goes into both numbers evenly
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be

.
You're minimizing

subject to the constraint

. Note that

and

attain their extrema at the same values of

, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
The Lagrangian is

Take your partial derivatives and set them equal to 0:

Adding the first three equations together yields

and plugging this into the first three equations, you find a critical point at

.
The squared distance is then

, which means the shortest distance must be

.
Answer:
40 minutes
Step-by-step explanation:
Given 1 mile = 8 minutes
5 miles = (5 × 8) minutes
5 miles = 40 minutes
It would take 40 minutes to run 5 miles