Answer:
See the proof below.
Step-by-step explanation:
For this case we just need to apply properties of expected value. We know that the estimator is given by:
And we want to proof that 
So we can begin with this:
And we can distribute the expected value into the temrs like this:
And we know that the expected value for the estimator of the variance s is 
, or in other way 
so if we apply this property here we have:
And we know that 
so using this we can take common factor like this:
And then we see that the pooled variance is an unbiased estimator for the population variance when we have two population with the same variance.
Answer:
The size of Isabella's pool is 220 liters.
Step-by-step explanation:
Let the size of Isabella's pool be 
liters, 
be the rate of fill, 
be the time of fill and 
be the volume of water filled in the pool.
As the rate of fill is constant,
Therefore, volume of water filled in the pool can be given as,
Volume of water left is given as 
From the table,
Volume of water left after 
minutes is 184 liters.
So, 
-------- 1
Volume of water left after 
minutes is 4 liters.
So, 
------------2
Multiply equation 1 by 6 and equation 2 by -1, we get
Now, we add the above equations, we get
Therefore, the size of Isabella's pool is 220 liters.
Answer:
5
Step-by-step explanation:
First off this is a complementary angle so it will add up to 90 degrees so the answer is 5 because 8 x 5 = 40 and
40 + 50 = 90 Hope this helps!
All numbers means it will either be a > or < or =. So all numbers at least 3 units from -1. so -4 and below and 2+. So write it like this. I <-4, >2 I
