Answer:
(a) The Venn diagram is attached below.
(b) The probability that neither university admits Ramon is 0.20.
(c) The probability that Ramon gets into Stanford but not Harvard 0.30.
Step-by-step explanation:
Let's denote the events as follows:
<em>H</em> = Ramon gets admitted to Harvard
<em>S</em> = Ramon gets admitted to Stanford.
The information provided is:
P (H) = 0.50
P (S) = 0.50
P (H ∩ S) = 0.20
(a)
The Venn diagram is attached below.
(b)
Compute the probability that Ramon gets admitted in neither Harvard nor Stanford as follows:
![P(H^{c}\cup S^{c})=1-P(H\cup S) \\= 1 - [P(H)+P(S)-P(H\cap S)]\\=1-[0.50+0.50-0.20]\\=1-0.80\\=0.20](https://tex.z-dn.net/?f=P%28H%5E%7Bc%7D%5Ccup%20S%5E%7Bc%7D%29%3D1-P%28H%5Ccup%20S%29%20%5C%5C%3D%201%20-%20%5BP%28H%29%2BP%28S%29-P%28H%5Ccap%20S%29%5D%5C%5C%3D1-%5B0.50%2B0.50-0.20%5D%5C%5C%3D1-0.80%5C%5C%3D0.20)
Thus, the probability that neither university admits Ramon is 0.20.
(c)
Compute the probability that Ramon gets admitted in Stanford but not in Harvard as follows:
Thus, the probability that Ramon gets into Stanford but not Harvard 0.30.
Answer:
7.2 units
Step-by-step explanation:
Distance² = (Change in y)² + (Change in x)²
Distance² = (4 - -5)² + (-3 - -7)²
Distance² = 36 + 16
Distance² = 52
Distance = 7.211102551
Rounding off the answer to nearest tenth gives 7.2 units
Answer:
48-12y
Step-by-step explanation:
6(7-3y) + 6(y+1)
distribute the 6 on both parentheses
42-18y+6y+6
combine like terms
42-12y+6
combine like terms again
48-12y
MO = 12 and PR = 3
Solution:
Given 
.
Perimeter of ΔMNO = 48
Perimeter of ΔPQR = 12
MO = 12x and PR = x + 2
<em>If two triangles are similar, then the ratio of corresponding sides is equal to the ratio of perimeter of the triangles.</em>
Do cross multiplication.
Subtract 48x from both sides.
Divide by 96 on both sides, we get
⇒ 1 = x
⇒ x = 1
Substitute x = 1 in MO an PR.
MO = 12(1) = 12
PR = 1 + 2 = 3
Therefore MO = 12 and PR = 3.
The answer to life, the universe and everything is 42.
