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