Answer:
115.625 cm³
Step-by-step explanation:
The ratio of the volumes is in proportion with the cube of the proportion of the lengths.
V1/925 = (10/20)³
V1/925 = (1/2)³
V1/925 = 1/8
V1 = 925 ÷ 8
V1 = 115.625 cm³
Answer:
<h2>The y intercept is 0</h2>
Step-by-step explanation:
the equation of a line is given as
where
m= is the slope
c= is the y intercept
their mistake is that they did not recall that if the "c" is not shown, it is assumed to be zero (0)
Let 
denote the number of encounters required to see a new Pokemon after having encountered 
of them. Then 
.
If Gary has already seen Pokemon, that leaves 
still to be encountered, and the next new encounter has a probability of 
of occurring. Then is geometric, with PMF
Then the expectation and variance of are
![E[K_i]=\dfrac1{p_i}=\dfrac m{m-(i-1)}](https://tex.z-dn.net/?f=E%5BK_i%5D%3D%5Cdfrac1%7Bp_i%7D%3D%5Cdfrac%20m%7Bm-%28i-1%29%7D)
![V[K_i]=\dfrac{1-p_i}{{p_i}^2}=\dfrac{m(i-1)}{(m-(i-1))^2}](https://tex.z-dn.net/?f=V%5BK_i%5D%3D%5Cdfrac%7B1-p_i%7D%7B%7Bp_i%7D%5E2%7D%3D%5Cdfrac%7Bm%28i-1%29%7D%7B%28m-%28i-1%29%29%5E2%7D)
is the total number of encounters needed to record all 
Pokemon, so
By linearity of expectation,
![E[K]=\displaystyle\sum_{i=1}^mE[K_i]=\sum_{i=1}^m\frac m{m-(i-1)}=\frac mm+\frac m{m-1}+\frac m{m-2}+\cdots+\frac m1](https://tex.z-dn.net/?f=E%5BK%5D%3D%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5EmE%5BK_i%5D%3D%5Csum_%7Bi%3D1%7D%5Em%5Cfrac%20m%7Bm-%28i-1%29%7D%3D%5Cfrac%20mm%2B%5Cfrac%20m%7Bm-1%7D%2B%5Cfrac%20m%7Bm-2%7D%2B%5Ccdots%2B%5Cfrac%20m1)
![E[K]=m\displaystyle\sum_{i=1}^m\frac1i](https://tex.z-dn.net/?f=E%5BK%5D%3Dm%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5Em%5Cfrac1i)
The are independent, so the variance is
![V[K]=\displaystyle\sum_{i=1}^mV[K_i]=\sum_{i=1}^m\frac{m(i-1)}{(m-(i-1))^2}](https://tex.z-dn.net/?f=V%5BK%5D%3D%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5EmV%5BK_i%5D%3D%5Csum_%7Bi%3D1%7D%5Em%5Cfrac%7Bm%28i-1%29%7D%7B%28m-%28i-1%29%29%5E2%7D)
![V[K]=m\displaystyle\sum_{i=0}^{m-1}\frac i{(m-i)^2}](https://tex.z-dn.net/?f=V%5BK%5D%3Dm%5Cdisplaystyle%5Csum_%7Bi%3D0%7D%5E%7Bm-1%7D%5Cfrac%20i%7B%28m-i%29%5E2%7D)
The third angle is 29 degrees.
180 - 58 - 93 = 29
