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Answer:
Step-by-step explanation:
a)Whatis thestochastic matrix for thissituation?
b)Suppose there is a 50% chance of good weather today and 50% of indifferent.What are the chances of badweather tomorrow?
c)Suppose the predicted weather for Monday is 40% indifferent and 60%bad.What are the chances for good weather on Wednesday?
Attached below is the solution :
He can choose as follows:
Only 1 entree: 3 groups
Only 2 entrees: 3 groups
All the 3 entrees: 1 group
total groups of entrees= 3 + 3 + 1 = 7 groups
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First off, we'll move the non-repeating part in the decimal to the left-side, by doing a division by a power of 10.
then we'll equate the value to some variable, and move the repeating part over to the left as well.
anyhow, the idea being, we can just use that variable, say "x" for the repeating bit, let's proceed,
![\bf 0.580\overline{80}\implies \boxed{\cfrac{5.80\overline{80}}{10}}\qquad \textit{now, let's say }x= 5.80\overline{80}\\\\ -------------------------------](https://tex.z-dn.net/?f=%5Cbf%200.580%5Coverline%7B80%7D%5Cimplies%20%5Cboxed%7B%5Ccfrac%7B5.80%5Coverline%7B80%7D%7D%7B10%7D%7D%5Cqquad%20%5Ctextit%7Bnow%2C%20let%27s%20say%20%7Dx%3D%205.80%5Coverline%7B80%7D%5C%5C%5C%5C%0A-------------------------------)
![\bf thus\qquad \begin{array}{llll} 100\cdot x&=&580.80\overline{80}\\ &&575+5.80\overline{80}\\ &&575+x \end{array}\qquad \implies 100x=575+x \\\\\\ 99x=575\implies x=\cfrac{575}{99}\qquad therefore\qquad \boxed{\cfrac{5.80\overline{80}}{10}}\implies \cfrac{\quad \frac{575}{99}\quad }{10} \\\\\\ \cfrac{\quad \frac{575}{99}\quad }{\frac{10}{1}}\implies \cfrac{575}{99}\cdot \cfrac{1}{10}\implies \cfrac{575}{990}\implies \stackrel{simplified}{\cfrac{115}{198}}](https://tex.z-dn.net/?f=%5Cbf%20thus%5Cqquad%20%5Cbegin%7Barray%7D%7Bllll%7D%0A100%5Ccdot%20x%26%3D%26580.80%5Coverline%7B80%7D%5C%5C%0A%26%26575%2B5.80%5Coverline%7B80%7D%5C%5C%0A%26%26575%2Bx%0A%5Cend%7Barray%7D%5Cqquad%20%5Cimplies%20100x%3D575%2Bx%0A%5C%5C%5C%5C%5C%5C%0A99x%3D575%5Cimplies%20x%3D%5Ccfrac%7B575%7D%7B99%7D%5Cqquad%20therefore%5Cqquad%20%5Cboxed%7B%5Ccfrac%7B5.80%5Coverline%7B80%7D%7D%7B10%7D%7D%5Cimplies%20%5Ccfrac%7B%5Cquad%20%5Cfrac%7B575%7D%7B99%7D%5Cquad%20%7D%7B10%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B%5Cquad%20%5Cfrac%7B575%7D%7B99%7D%5Cquad%20%7D%7B%5Cfrac%7B10%7D%7B1%7D%7D%5Cimplies%20%5Ccfrac%7B575%7D%7B99%7D%5Ccdot%20%5Ccfrac%7B1%7D%7B10%7D%5Cimplies%20%5Ccfrac%7B575%7D%7B990%7D%5Cimplies%20%5Cstackrel%7Bsimplified%7D%7B%5Ccfrac%7B115%7D%7B198%7D%7D)
and you can check that in your calculator.
X= 2 ; you can use the fórmula for axis of symmetry , which is -b/2(a)