Answer:
a) 3/64 = 0.046 (4.6%)
b) 63/64 = 0.9843 (98.43%)
c) 1/64 = 0.015 (1.5%)
d) 1/4 = 0.25 (25%)
Step-by-step explanation:
in order to verify that the f(x) is a probability mass function , then it should comply the requirement that the sum of probabilities over the entire space of x is equal to 1. Then
∑f(x)*Δx = 1
if f(x)=(3/4)(1/4)^x , x = 0, 1, 2, ...
then Δx=1 and
∑f(x) = (3/4)∑(1/4)^x = (3/4)* [ 1/(1-1/4)] = (3/4)*(4/3) = 1
then f represents a probability mass function
a) P(X = 2)= f(x=2) = (3/4)(1/4)^2 = 3/64 = 0.046 (4.6%)
b) P(X ≤ 2) = ∑f(x) = f(x=0)+ f(x=1) + f(x=2) = (3/4) + (3/4)(1/4) + 3/64 = 63/64 = 0.9843 (98.43%)
c) P(X > 2)= 1- P(X ≤ 2) = 1 - 63/64 = 1/64 = 0.015 (1.5%)
d) P(X ≥ 1) = 1 - P(X < 1) = 1 - f(x=0) = 1- 3/4 = 1/4 = 0.25 (25%)
Answer:
A
Step-by-step explanation:
∆ABC is similar to ∆DEF if and only if the ratio of their corresponding side lengths are the same.
Let's find out:
DE/AB = 10/5 = 2
EF/BC = 8/4 = 2
FD/CA = 12/6 = 2
The ratio of their corresponding side lengths are equal, therefore, ∆ABC is similar to ∆DEF based on the SSS Similarity Theorem.
Answer:
560 seconds.
Step-by-step explanation:
<span>322,000 meters. Because there is 1,000 meters in a kilometer.</span>
Answer:
Step-by-step explanation:
Required
Find m and n
Considering the given angle, we have:
This gives:
Make m ths subject
So, we have:
Considering the given angle again, we have:
This gives:
Make n the subject
So, we have:
