What I gather from the question is that
has second moment
and variance
, and you're asked to find the expectation and variance of the random variable
.
From the given second moment and variance, we find the expectation of
:

Expectation is linear, so

Using the same variance identity, we have

and

so that

Alternatively, we can use the identity

12 possible outcomes
any number less than 9 is 8 and below
8 sides of the dice are less than 9 out of 12 total sides
8/12 is the chance you’ll roll lower than 9
2/3 or 66% chance you’ll roll a number lower than 9
The solution would be like this for this specific problem:
Volume of a cylinder = pi * r^2 * h
Volume of a cone = 1/3 * pi * r^2 * h
Total Height = 47
Height of the cone = 12
Height of the cylinder = 35
If the top half is filled with sand, then:
volume (sand) = pi * 4^2 * 36
volume (cone) = 1/3 * pi * 4^2 * 12
Total volume = 1960.353816 cubic millimeters
353816 / (10 * pi) = 62.4 seconds.
It will take 62.4 seconds until all of the sand has dripped to the bottom of the hourglass.
Answer:

Step-by-step explanation:
Given:
19x + 9y = 15
Required:
Rewrite in slope-intercept form, y = mx + b
SOLUTION:
19x + 9y = 15
Subtract 19x from both sides
9y = -19x + 15
Divide both sides by 9
y = -19x/9 + 15/9
