a = 5 in
b = 12 in
c = 15 in
the lengths of the sides a, b and c
the perimeter is P = a + b + c = 5 + 12 + 15 = 32 in
let the dimensions of the new triangle be
a1 = (1/5)*5 in
b1 = (1/5)*12 in
c1 = (1/5)*15 in
the perimeter is P1 = a1 + b1 + c1 = (1/5)5 + (1/5)12 + (1/5)15 = (1/5)(5 + 12 + 15) = (1/5)P1
P1 = (1/5)P
P1/P = 1/5 = a/a1 = b/b1 = c/c1
the ratio of the perimeters is equal to the ratio of the corresponding sides.
Answer:
The sample standard deviation is 393.99
Step-by-step explanation:
The standard deviation of a sample can be calculated using the following formula:
![s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B%20%5D%7B%5Cfrac%7B1%7D%7BN-1%7D%20%5Csum_%7Bi%3D1%7D%5E%7BN%7D%28x_%7Bi%7D-%7B%5Cdisplaystyle%20%5Ctextstyle%20%7B%5Cbar%20%7Bx%7D%7D%7D%29%20%5E%7B2%7D%20%7D)
Where:
Sample standart deviation
Number of observations in the sample
Mean value of the sample
and 
simbolizes the addition of the square of the difference between each observation and the mean value of the sample.
Let's start calculating the mean value:
Now, let's calculate the summation:
So, now we can calculate the standart deviation:
![s=\sqrt[ ]{\frac{1}{15-1}*(2173160)}](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B%20%5D%7B%5Cfrac%7B1%7D%7B15-1%7D%2A%282173160%29%7D)
![s=\sqrt[ ]{\frac{2173160}{14}}](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B%20%5D%7B%5Cfrac%7B2173160%7D%7B14%7D%7D)
The sample standard deviation is 393.99
