Answer:
270 feet
Step-by-step explanation:
For clarity, the image below represents the problem. Let's call h the height of the tower. Notice that it forms 2 triangles that are similar to side-angle-side. So, we can calculate the higher of the tower by similar triangles:
higher1/base1 = higher2/base2
h/135 = 6/3
h/135 = 2
h = 270 ft
Answer:
1/20
Step-by-step explanation:
Remark: Not huge
Total number of Socks: 6 + 6 + 4 = 16
P(First Black Sock): 4/16 = 1/4
The second Sock needs to be discussed a bit. The number of black socks has gone down to 1 and the total will always go down by 1.
Second Sock: 3 Black / 15 Total = 3/15 = 1/5
Combined Probability: 1/4 * 1/5 = 1/20
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:
= A(t) = 120000(1.06)^t t = 1 year
We just add ^12 to equal 1/12 months.
Then use the notation below.
Step-by-step explanation:
We simply want to write an equivalent form of the same equation that will allow for the time period to be calculated in years.
For one year, t = 1, we want it to grow 6% = 1.06
Yearly Rate of Growth annual equation: = 7200
P(i) 7200/ 120000 x 100% = 6% per year growth rate
the yearly growth factor is 1 + appreciation rate = 1+i =1+0.06= 1.06
So time in years can be added to t
= A(t) = 120000(1.06)^t t = 1 year
The yearly growth factor = 1.06
To equate monthly we add the exponent t*12*1/12 before 120000(1.06)^t
then add 1/12 to replace ^t = monthly, or just keep the t= time
A(t) = 120000(1.06)^12t