Answer:
Step-by-step explanation:
Given are 3 data sets with values as:
(i) 8 9 10 11 12 ... Mean =10
(ii) 7 9 10 11 13 ... Mean =10
(iii) 7 8 10 12 13 ... Mean =10
We see that data set shows mean deviations as
(i) -2 -1 0 1 2
(ii) -3 -1 0 1 3
(iii) -3 -2 0 2 3
Since variance is the square of std deviation, we find that std deviation is larger when variance is larger.
Variance is the sum of squares of (x-mean). Whenever x-mean increases variance increases and also std deviation.
Hence we find that without calculations also (i) has least std dev followed by (ii) and then (iii)
(i) (ii) (iii) is the order.
b) Between (i) and (ii) we find that 3 entries are the same and 2 entries differ thus increasing square by 9-4 twice. But between (ii) and (iii) we find that
increase in square value would be 4-1 twice. Obviously the latter is less.
3 GB every month..... 21+3=24+3=27+3=30....so 3 GB
Answer:
Alternate Interior Angles
Answer:
See the verification below.
Step-by-step explanation:
Starting expression: 
Extract from the expression on the left of the equal sign the common factor "sin(x)":
![sin^3(x)+sin(x)\,cos^2(x)=sin(x)\\sin(x)[sin^2(x)+cos^2(x)]=sin(x)](https://tex.z-dn.net/?f=sin%5E3%28x%29%2Bsin%28x%29%5C%2Ccos%5E2%28x%29%3Dsin%28x%29%5C%5Csin%28x%29%5Bsin%5E2%28x%29%2Bcos%5E2%28x%29%5D%3Dsin%28x%29)
Now use the Pythagorean trigonometric identity: 
to replace the expression in between square brackets with "1":
![sin(x)[sin^2(x)+cos^2(x)]=sin(x)\\sin(x) \,[1]=sin(x)\\sin(x)=sin(x)](https://tex.z-dn.net/?f=sin%28x%29%5Bsin%5E2%28x%29%2Bcos%5E2%28x%29%5D%3Dsin%28x%29%5C%5Csin%28x%29%20%5C%2C%5B1%5D%3Dsin%28x%29%5C%5Csin%28x%29%3Dsin%28x%29)
Therefore we have verified the identity
The answer is 48π units³ or 150.72 units³.
To find the volume of the cone, use the formula : <u>1/3 × πr²h</u>
We are given that r = 6 and h = 4.
Solving :
- V = 1/3 × π × 6² × 4
- V = 12 × 4 × π
- V = 48π units³ (in terms of π)
- V = 150.72 units³
