Answer:
Both get the same results that is,
![\left[\begin{array}{ccc}140\\160\\200\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D140%5C%5C160%5C%5C200%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Given :
![\bf M=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]](https://tex.z-dn.net/?f=%5Cbf%20M%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D)
and initial population,
![\bf P=\left[\begin{array}{ccc}130\\300\\70\end{array}\right]](https://tex.z-dn.net/?f=%5Cbf%20P%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D130%5C%5C300%5C%5C70%5Cend%7Barray%7D%5Cright%5D)
a) - After two times, we will find in each position.
![P_2=[P].[M]^2=[P].[M].[M]](https://tex.z-dn.net/?f=P_2%3D%5BP%5D.%5BM%5D%5E2%3D%5BP%5D.%5BM%5D.%5BM%5D)
![M^2=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]\times \left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]](https://tex.z-dn.net/?f=M%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D)
![=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B25%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%267%267%5C%5C8%268%268%5C%5C10%2610%2610%5Cend%7Barray%7D%5Cright%5D)
![\therefore\;\;\;\;\;\;\;\;\;\;\;P_2=\left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right] \times\left[\begin{array}{ccc}130\\300\\70\end{array}\right] = \left[\begin{array}{ccc}140\\160\\200\end{array}\right]](https://tex.z-dn.net/?f=%5Ctherefore%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3BP_2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%267%267%5C%5C8%268%268%5C%5C10%2610%2610%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D130%5C%5C300%5C%5C70%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D140%5C%5C160%5C%5C200%5Cend%7Barray%7D%5Cright%5D)
b) - With in migration process, 500 people are numbered. There will be after a long time,
![After\;inifinite\;period=[M]^n.[P]](https://tex.z-dn.net/?f=After%5C%3Binifinite%5C%3Bperiod%3D%5BM%5D%5En.%5BP%5D)
![Then,\;we\;get\;the\;same\;result\;if\;we\;measure [M]^n=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]](https://tex.z-dn.net/?f=Then%2C%5C%3Bwe%5C%3Bget%5C%3Bthe%5C%3Bsame%5C%3Bresult%5C%3Bif%5C%3Bwe%5C%3Bmeasure%20%5BM%5D%5En%3D%5Cfrac%7B1%7D%7B25%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%267%267%5C%5C8%268%268%5C%5C10%2610%2610%5Cend%7Barray%7D%5Cright%5D)
![=\left[\begin{array}{ccc}140\\160\\200\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D140%5C%5C160%5C%5C200%5Cend%7Barray%7D%5Cright%5D)
Answer:
what grade is this
Step-by-step explanation:
I'm very confused is this algebra?
Answer:
The answer is cosx cot²x ⇒ the first answer
Step-by-step explanation:
∵ cot²x = cos²x/sin²x
∵ secx = 1/cosx
∴ cot²x secx - cosx = (cos²x/sin²x)(1/cosx) - cosx
= (cosx/sin²x) - cosx
Take cosx as a common factor
∴ cosx[(1/sin²x) - 1] ⇒ use L.C.M
∴ cosx[1-sin²x/sin²x]
∵ 1 - sin²x = cos²x
∴ cosx(cos²x/sin²x) = cosx cot²x
Answer:
an = -6n + 5.
Step-by-step explanation:
This is an arithmetic sequence with first term a1 = -1 and common difference d = -6
an = a1 + d(n-1)
an = -1 + -6(n - 1)
an = -1 -6n + 6
an = -6n + 5.
<h2 /><h2>Here we go ~ </h2>
According to given information there are :
<h3>1. what is the probability that the ball chosen is red ?</h3>
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<h3>2. what is the probability that the ball chosen is blue ?</h3>
<h3>3. what is the probability that the ball chosen is yellow ?</h3>
<h3>4. what is the probability that the ball chosen is green ?</h3>
<h3>5. what is the probability that the ball chosen is not green ?</h3>
