It would be letter D - 3648.
The probability of winning is 0.76 and the probability of losing is 0.24.
In each simulation the probability of winning exactly one match is: P(win one match) = 2C1 x 0.76 x 0.24 = 0.3648
Multiply the result by 10,000 simulations to get the expected number of times that exactly one match is won.
10,000 x 0.3648 = 3648 times.
(2x+10)(2x+10) use FOIL to solve (First, Outer, Inner, Last)
4x^2+20x+20x+100
Combine like terms
4x^2+40x+100
Find the intercepts for both planes.
Plane 1, <em>x</em> + <em>y</em> + 2<em>z</em> = 2:



Plane 2, 4<em>x</em> + 4<em>y</em> + <em>z</em> = 8:



Both planes share the same <em>x</em>- and <em>y</em>-intercepts, but the second plane's <em>z</em>-intercept is higher, so Plane 2 acts as the roof of the bounded region.
Meanwhile, in the (<em>x</em>, <em>y</em>)-plane where <em>z</em> = 0, we see the bounded region projects down to the triangle in the first quadrant with legs <em>x</em> = 0, <em>y</em> = 0, and <em>x</em> + <em>y</em> = 2, or <em>y</em> = 2 - <em>x</em>.
So the volume of the region is


