Answer:
<u>The correct answer is 58 1/2 feet. See below to understand the difference of both methods.</u>
Step-by-step explanation:
1. Let's review the information provided to us for solving the question using both methods:
Area of each student = 4 1/2 square feet
Number of students = 13
2. Let's use the first method to solve the question:
4 1/2 = 9/2 (Improper fraction because the numerator, 9 is bigger than the denominator, 2)
9/2 * 13 = 117/2
<u>117/2 = 58 1/2 square feet</u>
3. Let's use the second method to solve the question:
4 1/2 = 4 + 1/2 (Using addition to rewrite the fraction)
(4 + 1/2) * 13 = (4 * 13) + (1/2 * 13) (Distributive property of the multiplication)
(4 * 13) + (1/2 * 13) = 52 + 13/2 = 52 + 6 1/2
<u>52 + 6 1/2 = 58 1/2 square feet</u>
The expected length of code for one encoded symbol is

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

so that we expect a contribution of

bits to the code per encoded letter. For a string of length
, we would then expect
.
By definition of variance, we have
![\mathrm{Var}[L]=E\left[(L-E[L])^2\right]=E[L^2]-E[L]^2](https://tex.z-dn.net/?f=%5Cmathrm%7BVar%7D%5BL%5D%3DE%5Cleft%5B%28L-E%5BL%5D%29%5E2%5Cright%5D%3DE%5BL%5E2%5D-E%5BL%5D%5E2)
For a string consisting of one letter, we have

so that the variance for the length such a string is

"squared" bits per encoded letter. For a string of length
, we would get
.
Answer:
30
Step-by-step explanation: