Answer:
Step 1: 12-2a=3a-18
Step 2: 12-5a=-18
Step 3: -5a=-30
Step 4: a=6
I hope this helps!
pls ❤ and give brainliest pls
You simplify a fraction by finding it's greatest common factor. A greatest common factor is what both numbers are divisible by. If they can both be divided by two, then you've simplified them a little bit. Keep going until you can't find a common number that can be divided by the two, and you've got your simplified fraction. For example, 10/5 = 1/2 since both 10 and 5 is divisible by 5.
Benji’s error is that the division should happen BEFORE subtracting 3. 3 should be subtracted from the quotient.
The correct response should be: (n/9)-3
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)
Answer:
7 6/7
Step-by-step explanation:
To find the area, multiply 2 1/7 by 3 2/3. Then, simplify to get the answer of 7 6/7.