The exact circumference of the circle is ![7 \frac{49}{150} k m](https://tex.z-dn.net/?f=7%20%5Cfrac%7B49%7D%7B150%7D%20k%20m)
The approximate circumference of the circle is ![7.33 k m](https://tex.z-dn.net/?f=7.33%20k%20m)
Explanation:
The diameter of the circle is ![2 \frac{1}{3} \mathrm{km}](https://tex.z-dn.net/?f=2%20%5Cfrac%7B1%7D%7B3%7D%20%5Cmathrm%7Bkm%7D)
Now, we shall find the circumference of the circle.
The formula to determine the circumference of the circle is given by
![C=\pi d](https://tex.z-dn.net/?f=C%3D%5Cpi%20d)
Where C is the circumference ,
is 3.14 and
is the diameter of the circle.
The exact circumference of the circle is given by
![\begin{aligned}C &=\pi d \\&=(3.14)\left(2 \frac{1}{3}\right) \\&=(3.14)\left(\frac{7}{3}\right) \\&=\frac{21.98}{3}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DC%20%26%3D%5Cpi%20d%20%5C%5C%26%3D%283.14%29%5Cleft%282%20%5Cfrac%7B1%7D%7B3%7D%5Cright%29%20%5C%5C%26%3D%283.14%29%5Cleft%28%5Cfrac%7B7%7D%7B3%7D%5Cright%29%20%5C%5C%26%3D%5Cfrac%7B21.98%7D%7B3%7D%5Cend%7Baligned%7D)
Multiply both numerator and denominator by 100, we get,
![C=\frac{2198}{300} \\C=\frac{1099}{150}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B2198%7D%7B300%7D%20%5C%5CC%3D%5Cfrac%7B1099%7D%7B150%7D)
Converting
into mixed fraction, we get,
![C=7 \frac{49}{150}](https://tex.z-dn.net/?f=C%3D7%20%5Cfrac%7B49%7D%7B150%7D)
Thus, the exact circumference of the circle is ![7 \frac{49}{150} k m](https://tex.z-dn.net/?f=7%20%5Cfrac%7B49%7D%7B150%7D%20k%20m)
The approximate value of the circumference can be determined by dividing the value ![\frac{1099}{150}](https://tex.z-dn.net/?f=%5Cfrac%7B1099%7D%7B150%7D)
![C=\frac{1099}{150}=7.327](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B1099%7D%7B150%7D%3D7.327)
![C=7.33km](https://tex.z-dn.net/?f=C%3D7.33km)
Thus, the approximate circumference of the circle is ![7.33 k m](https://tex.z-dn.net/?f=7.33%20k%20m)
The answer is 105 and 105 because they did not tell you that one had more than the other, so it's equal. Plus, it could not be 210 or over or 0 or less. It was spilt up equally between both alternate angles, and the lines are parallel, so the angles are equal. So just do 210/2 and get what one of the angles would be. Great question!
Explanation:
Lets interpret Z with M trials. First we have M trials, each trial can be a success or not. The number of success is called N. Each trial that is a success becomes a trial, and if it is a success it becomes a success for Z. Thus, in order for a trial to be successful, it needs first to be successful for the random variable N (and it is with probability q), and given that, it should be a success among the N trials of the original definition of Z (with probability p).
This gives us that each trial has probability pq of being successful. Note that this probability is pq independently of the results of the other trials, because the results of the trials of both N and the original definition of Z are independent. This shows us that Z is the total amount of success within M independent trials of an experiment with pq probability of success in each one. Therefore, Z has Binomial distribution with parameters pq and M.