Answer:1
Step-by-step explanation:2+2=4
4/4=1
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: 1 hour
Step-by-step explanation:
Let the distance they walked be 
in time 
and the distance they walked be 
in time 
,then
Walking speed=
Riding speed=
Also the total time taken=3 hours
∴
...(1)
Since the total distance= 20 km
∴![d_1+d_2=20\\\Rightarrow4t_1+12t_2=20\\\Rightarrow4t_1+12(3-t_1)=20..............[\text{from (1)}]\\\Rightarrow4t_1+36-12t_1=20\\\Rightarrow-8t_1=-8\\\Rightarrow\ t_1=1](https://tex.z-dn.net/?f=d_1%2Bd_2%3D20%5C%5C%5CRightarrow4t_1%2B12t_2%3D20%5C%5C%5CRightarrow4t_1%2B12%283-t_1%29%3D20..............%5B%5Ctext%7Bfrom%20%281%29%7D%5D%5C%5C%5CRightarrow4t_1%2B36-12t_1%3D20%5C%5C%5CRightarrow-8t_1%3D-8%5C%5C%5CRightarrow%5C%20t_1%3D1)
Thus, the they spent 1 hour time in walking.
