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}{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)
![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
The straight line ON has the following equation :
(x - 18)/(x - 0) = (y - 12)/(y - 0)
Where (18,12) are coordinates of N and (0,0) are coordinates of O.
x - 18/x = y - 12/y
-18y = - 12x
y =12x/18 - - - - - (a)
The coordinates satisfy equation (a) are (7.5, 5)
Therefore D is the correct answer.
Good luck
Answer:
The speed in of the plane is 115.47 m/sec
Step-by-step explanation:
Given:
Height at which the plane is flying = 6000 m
Angle of elevation at the radar base = 30 Degrees
Angle of elevation at the radar base after one minute = 60 Degrees
To Find:
The Speed of the plane in meter per second = ?
Solution:
Let us use the tangent of the angle to find the distance (d) to a point directly below plane:
<u>when the angle is 30 degrees</u>



d1 = 10392.3 meters
<u>when the angle is 60 degrees</u>



d2 = 3464.1 meters
<u>distance travelled by aircraft in 1 min is </u>
=>d1 - d2
=>0392.3 - 3464.1
= 6928.2 m/min
<u>Now converting to m/sec</u>
=>
=>115.47 m/sec
The answer is 9/10
the denominator is on the bottom