Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
factorization of 45 is 5 x 3 x 3, or 5 x 3^2.
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 ![E[L]=1.375n](https://tex.z-dn.net/?f=E%5BL%5D%3D1.375n)
.
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 ![\mathrm{Var}[L]=1.859n](https://tex.z-dn.net/?f=%5Cmathrm%7BVar%7D%5BL%5D%3D1.859n)
.
Answer: cookbook $40 and science $15
Step-by-step explanation:
Answer:
The vertex form is y = (x + 4)² - 13
The minimum value of the function is -13
Step-by-step explanation:
∵ y = x² + 8x + 3
∵ 8x ÷ 2 = 4x ⇒ (x) × (4)
∴ We need ⇒ x² + 8x + 16 to be completed square
∴ y = (x² + 8x + 16) - 16 + 3 ⇒ we add 16 and subtract 16
∴ y = (x + 4)² - 13 ⇒ vertex form
∵ The vertex form is (x - a)² + b
Where a is the x-coordinate of the minimum point and b is y-coordinate of the minimum point (b is the minimum value of the function)
∴ The minimum value is -13
Associative property moves the parenthesis
Choice B
