Answer:
He needs 785 more minutes
Step-by-step explanation:
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:
The number of the cups of uncooked rice is 3 cups
The number of the cups of water is
cups
Step-by-step explanation:
* Let us read the recipe of Nasi Gorang
- 2 cups of uncooked rice need
cups of water to
make
cups of cooked rice
- Joseph needs
cups of cooked rice
- We need to know how many cups of uncooked rice Joshep needs
for this recipe and how much water should be added
* We can solve this problem by using the ratio method
⇒ uncooked cups : water cups : cooked cups
⇒ 2 :
: 
⇒ x : y : 
- By using cross multiplication
∵ x (
) = 2 (
)
∵
= 
∵
= 
∴ x (
) = 2 (
)
∴
x = 13
- Divide both sides by 
∴ x = 3
∴ The number of the cups of uncooked rice is 3 cups
- By using cross multiplication
∵ y (
) = (
)(
)
∵
= 
∵
= 
∵
= 
∴
y = (
)(
)
∴
y =
- Divide both sides by 
∴ y = 
∴ The number of the cups of water is
cups