Answer:
E(M) = 23/3
Var(M) = 53/9.
Step-by-step explanation:
There are three possible values for M: 4, 6, and 10.
.
That's six unique combinations in total. If the balls are drawn randomly, the probability for getting each combination shall be equal. That is:
.
Consider the formula for the expected value of a discrete random variable:
.
Formula for the variance of a discrete random variable (note that this formula can take many other forms):
.
1.
Lines a and b are parallel lines.
Line t is a transversal.
Corresponding angles are congruent.
Angle 1 is a corresponding angle to the 107-deg angle, so m<1 = 107.
Angles 1 and 2 are supplementary angles since they are a linear pair.
m<1 + m<2 = 180
m<2 = 180 - 107
m<2 = 73
2.
Lines a and b are parallel lines.
Line t is a transversal.
Corresponding angles are congruent.
Angle 3 is a corresponding angle to the 95-deg angle, so m<3 = 95.
Angles 3 and 4 are supplementary angles since they are a linear pair.
m<3 + m<4 = 180
95 + m<4 = 180
m<4 = 180 - 95
m<4 = 85
3.
Lines a and b are parallel lines.
Line t is a transversal.
Corresponding angles are congruent.
Angle 5 is a corresponding angle to the 49-deg angle, so m<5 = 49.
Angles 5 and 6 are supplementary angles since they are a linear pair.
m<5 + m<6 = 180
49 + m<6 = 180
m<6 = 180 - 49
m<6 = 131
We know that
if <span>the probability of hitting the blue circle is the same as the probability of hitting the green region
then
the area of the blue circle is equal to the area of the green region
Let
x----> diameter of the blue circle
area of the blue circle=pi*(x/2)</span>²----> (pi/4)*x² m²-----> equation 1
area of the green region=area of the larger circle-area of the blue circle
area of the green region=pi*(1/2)²-(pi/4)*x²
=(pi/4)-(pi/4)*x² m²----> equation 2
equate equation 1 and equation 2
(pi/4)*x²=(pi/4)-(pi/4)*x² -----> divide by (pi/4)---> x²=1-x²
2x²=1-----> x²=1/2----> x=1/√2-----> x=√2/2 m
the diameter of the blue circle is √2/2 m