down voteaccepted
P(X=1) = 0.09
P(X < 5) = 0.09 + 0.36
P(X >= 2) = .36 + .23 + .09 + .23
P(2 <= X <= 7) = .36 + .23
If angles are complementary, they add up to 90 whereas when they are supplementary, the add up to 180. So now let's focus on this problem. It says angle 1 and 2 are complementary. Therefore;
angle 1 + angle 2 =90
x+(3x+30)=90
x+3x+30=90
4x+30=90
-30 -30
4x=60
4/4x=60/4
x=15
Therefore, the value of x is 15
Answer:
Overall rectangle: 100 ft × 8 16/23 ft ≈ 100 ft × 8.696 ft
Individual pen: 8 16/23 ft × 4 6/11 ft ≈ 8.696 ft × 4.545 ft
Step-by-step explanation:
Half the fence will be used in each of the orthogonal directions to make the pen. That is, the long side of the overall rectangle will be (400 ft/2)/2 = 100 ft. The short side of the overall rectangle will be (400 ft/2)/23 = 8 16/23 ft. (There are 21 partitions between the 22 pens, and 2 end fences, for a total of 23 fence segments of the short length.)
The long (100 ft) side of the overall rectangle is divided into 22 parts by the internal partitions, so each pen will have a short dimension of 100 ft/22 = 4 6/11 ft.
_____
We know half the fence will be used in each direction because we know the total area is a quadratic function of the side length. If the long side of the overall pen is x, then the short side is (400 ft -2x)/23, and the overall area is ...
... A = x(400 ft -2x)/23
The vertex of this quadratic function is halfway between the zeros, at x = 100 ft. That is, the two long sides of the pen total 200 ft, or half the overall length of fence.
Answer:
A, B are correct
Step-by-step explanation:
