The two angles (6x+4) and 32 degrees are complementary angles. They add to 90 degrees. The two angles are adjacent and form a right angle. The right angle marker is the square marker. Two adjacent right angles form a straight angle (180 degrees)
Add up the angles and set the sum equal to 90. Then solve for x
(6x+4) + (32) = 90
6x+4 + 32 = 90
6x+36 = 90
6x+36-36 = 90-36 .... subtract 36 from both sides
6x = 54
6x/6 = 54/6 ... divide both sides by 6
x = 9
Since x = 9, this means that
6x+4 = 6*9+4 = 54+4 = 58
So the missing angle is 58 degrees (note how 58+32 = 90)
Opposite angles in a parallelogram have to be equal so
3y=66
y=22
Answer:
a. P(E) = 1033/ 2851=0.3623
P(R) = 854/2851=0.2995
P(D) = 964/2851=0.3381
P(E ∩ D) = P(E) +P(D)= 0.3623 +0.3381= 0.7004
(d) 0.423 158
Step-by-step explanation:
a. P(E) = 1033/ 2851=0.3623
P(R) = 854/2851=0.2995
P(D) = 964/2851=0.3381
(b) Are events E and D mutually exclusive?
Yes these events are mutually exclusive. If students are deferred they may be admitted later but not early. Mutually Exclusive or disjoint events do not occur at the same time.
P(E ∩ D) = P(E) +P(D)= 0.3623 +0.3381= 0.7004
(c) For the 2,375 students who were admitted, the probability that a randomly selected student was accepted during early admission is
P(E) = 1033/ 2851=0.3623
P(E) + P(D for later admission) =0.3623 + 18%*0.3381
=0.3623 + 0.0609 = 0.423 158
