The hundredth number in the series as defined in the task content is; 107.
<h3>What is the 100th Number?</h3>
According to the task content;
The first term of the sequence of numbers is; 8 and evidently, the common difference of the sequence is; 9-8 = 1.
On this note it follows that the 100th number is;
T(100th). = 8 + 99(1) = 107.
Read more on terms in sequence;
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Answer:
The shape and rate parameters are
and
.
Step-by-step explanation:
Let <em>X</em> = service time for each individual.
The average service time is, <em>β</em> = 12 minutes.
The random variable follows an Exponential distribution with parameter,
.
The service time for the next 3 customers is,
<em>Z</em> = <em>X</em>₁ + <em>X</em>₂ + <em>X</em>₃
All the <em>X</em>
's are independent Exponential random variable.
The sum of independent Exponential random variables is known as a Gamma or Erlang random variable.
The random variable <em>Z</em> follows a Gamma distribution with parameters (<em>α</em>, <em>n</em>).
The parameters are:
![\alpha =\lambda=\frac{1}{12}\\n=3](https://tex.z-dn.net/?f=%5Calpha%20%3D%5Clambda%3D%5Cfrac%7B1%7D%7B12%7D%5C%5Cn%3D3)
Thus, the shape and rate parameters are
and
.
Solution:
DF = Initial dilution * Subsequent dilution * Amount Plated
Total Count Per g =
* Colonies Counted
Initial dilution : ![\frac{43}{(43+350)}=\frac{43}{393}](https://tex.z-dn.net/?f=%5Cfrac%7B43%7D%7B%2843%2B350%29%7D%3D%5Cfrac%7B43%7D%7B393%7D)
Subsequent dilution : ![(\frac{1}{6} )*(\frac{1}{90} )*(\frac{1}{61} )](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B6%7D%20%29%2A%28%5Cfrac%7B1%7D%7B90%7D%20%29%2A%28%5Cfrac%7B1%7D%7B61%7D%20%29)
Amount Plated : 0.1
Colonies Counted : 143
DF = ![\frac{43}{393}*\frac{1}{6}*\frac{1}{90}*\frac{1}{61}*0.1](https://tex.z-dn.net/?f=%5Cfrac%7B43%7D%7B393%7D%2A%5Cfrac%7B1%7D%7B6%7D%2A%5Cfrac%7B1%7D%7B90%7D%2A%5Cfrac%7B1%7D%7B61%7D%2A0.1)
DF=![\frac{43}{393}*\frac{1}{6}*\frac{1}{90}*\frac{1}{61}*\frac{1}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B43%7D%7B393%7D%2A%5Cfrac%7B1%7D%7B6%7D%2A%5Cfrac%7B1%7D%7B90%7D%2A%5Cfrac%7B1%7D%7B61%7D%2A%5Cfrac%7B1%7D%7B10%7D)
DF = ![\frac{43}{129454200}](https://tex.z-dn.net/?f=%5Cfrac%7B43%7D%7B129454200%7D)
Total Count Per g = ![(\frac{129454200}{43} )*143](https://tex.z-dn.net/?f=%28%5Cfrac%7B129454200%7D%7B43%7D%20%29%2A143)
Total Count Per g = ![4.3*10^{8}](https://tex.z-dn.net/?f=4.3%2A10%5E%7B8%7D)
You would get 8.333333 boxes full so you would end up getting 9 boxes but only eight full and one not full