Answer:
132°
Step-by-step explanation:
∠AOB = ∠EOD = 3x ( vertical angles )
∠AOB + ∠BOC = 90, that is
3x + 0.5x + 34 = 90
3.5x + 34 = 90 ( subtract 34 from both sides )
3.5x = 56 ( divide both sides by 3.5 )
x = 16
∠AOE + ∠EOD = 180 ( straight angle )
∠AOE + 3x = 180
∠AOE + (3 × 16) = 180
∠AOE + 48 = 180 ( subtract 48 from both sides )
∠AOE = 132°
Answer: 2343 / 256
Explanation
I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.
1) Adding the terms:
4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0
= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =
= 2343 / 256
2) Using the formula:
n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0
Here n - 1 = 4 => n = 5
r = 3/4
A = 3
Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =
= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =
= (3 * 781) / (4^5) / (1/4) = 3 * 781 / (4^4) = 2343 / 256
So, no doubt, the answer is 2343 / 256
Answer:
18900 watt-hours
Step-by-step explanation:
3600 x 24 (hours in a day) = 150
150 x 6 (hours) = 900
3600 (watt hours per day) x 5 (days) = 18000
18000 x 900 = 18900
total= 18900
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:
Step-by-step explanation:
130+5x=180
130-130+5x=180-130
5x=50
x=10
