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Anastasy [175]
3 years ago
12

A rectangular picture has dimensions x and x + 10. The picture is in a frame 2 inches wide. The total area of the picture and th

e frame is 875 in2. What are the dimensions of the picture? Show your work and explain how you got your answer. (if you can please do it on paper)
Mathematics
1 answer:
GREYUIT [131]3 years ago
7 0

Answer:

Step-by-step explanation:

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A source of information randomly generates symbols from a four letter alphabet {w, x, y, z }. The probability of each symbol is
koban [17]

The expected length of code for one encoded symbol is

\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha\ell_\alpha

where p_\alpha is the probability of picking the letter \alpha, and \ell_\alpha is the length of code needed to encode \alpha. p_\alpha is given to us, and we have

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so that we expect a contribution of

\dfrac12+\dfrac24+\dfrac{2\cdot3}8=\dfrac{11}8=1.375

bits to the code per encoded letter. For a string of length n, we would then expect E[L]=1.375n.

By definition of variance, we have

\mathrm{Var}[L]=E\left[(L-E[L])^2\right]=E[L^2]-E[L]^2

For a string consisting of one letter, we have

\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha{\ell_\alpha}^2=\dfrac12+\dfrac{2^2}4+\dfrac{2\cdot3^2}8=\dfrac{15}4

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"squared" bits per encoded letter. For a string of length n, we would get \mathrm{Var}[L]=1.859n.

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