Say we add 5 to each element. We sum them up and divide by the number of elements (compute mean). Well we added 5n to that total sum and are dividing by n. So if the mean was 10 before, now it’s 15. (We had 10 datapoints added too 100, but we added 50, dividing by 10 we get 15).
Now every single data point is just as close to the mean as it was before. The mean shifted with 5, but so did the datapoints. Remember, variance is the sum of squared errors divided by n, or n-1 for sample. Well, the sum of squared errors did not change. So our estimate of variance remains the same as well as our estimate of standard deviation.
This is without assuming normality. (ie through the equation of mean and standard deviation themselves). In general expected values shift with constants, and variances remain stable.
Answer:
C.
Step-by-step explanation:
A. Is false because citizens do not lose their citizenship if they fail to pay taxes.
B. Is false because not every tax paying citizen receives government assistance gets benifits like food stamps.
D. Is false because taxes don't go directly back to the people as cash payouts.
Answer:
A=140m² and P=54m
Step-by-step explanation:
In order to find the perimeter or area, we are going to first need to find the lenghts of the missing sides. There are two of them, we are going to refer to one as the shorter one and the other as the longer one.
Shorter One = 12-8
Shorter One = 4
Longer One = 15-5
Longer One = 10
From this we can then add the side lengths to find the perimeter of the figure.
Perimeter=5+15+12+8+4+10
Perimeter=20+20+14
Perimeter=54
The perimeter of the figure is 54m, therefore we can eliminate two of the answer choices.
Next, we need to find the area of the figure. The easiest way is to cut the figure into two pieces, I chose to do it by cutting a long rectangle, and then add their areas together.
A=(5*12)+(10*8)
A=60+80
A=140
Therefore the correct answer choice is A=140m² and P=54m