Answer:
(4x3-6x) + (8x-12)= 2x
(4x3+8x) + (-6x2-12)= 2(2x-3) (x^2+2)
Step-by-step explanation:
All you have to do is simplify.
Answer:
18a(2bc + 3d)
Step-by-step explanation:
36abc + 54ad
Step 1: Find the Highest Common Factor of each
36abc = 2×2×3×3×a×b×c = 18a × 2bc
54ad = 2×3×3×3×a×d = 18a × 3d
HCF = 2×3×3×a = 18a
Step 2: Factor out with HCF
18a(2bc + 3d)
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
.
5 × x = 1/4 x = 1/4 ÷ 5 x = 1/20
If x is the amount of time Gillian takes,
1/10 - 1/x = 1/25
Therefore, the answer is A