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1 year ago

If elephant grows 3 3/4 inched a day, how many inches will it grow in 7 days?

Mathematics

1 answer:

olga nikolaevna [1]1 year ago

4 0

Answer:

26.25, or 26 1/4, inches

Step-by-step explanation:

each day 3.75inches, so in 7 day, it grows 3.75 * 7 = 26.25inches

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This can be modeled as a Markov chain, with two states:

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$\begin{pmatrix} &U&M\\U&0.85&0.15\\M&0.10&0.90\end{pmatrix}$

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$(\pi_U,\pi_M)*\begin{pmatrix}0.85&0.15\\0.10&0.90\end{pmatrix}=(\pi_U,\pi_M)$

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$0.85\pi_U+0.10\pi_M=\pi_U\\\\0.15\pi_U+0.90\pi_M=\pi_M$

We choose one of the equations and solve:

$0.85\pi_U+0.10\pi_M=\pi_U\\\\\pi_M=((1-0.85)/0.10)\pi_U=1.5\pi_U\\\\\\\pi_M+\pi_U=1\\\\1.5\pi_U+\pi_U=1\\\\\pi_U=1/2.5=0.4 \\\\ \pi_M=1.5\pi_U=1.5*0.4=0.6$

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