Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
We need to equalize f' to 0
- k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
- 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
- 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
- ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
- 1/x = e^(1/2)
- x = 1/e^(1/2) = 1/√e ≅ 0.607
Thus, the value of x that gives the maximum transmission is 1/√e.
the ratio in which 42 should be divided is 1:2:3
the sum of the parts of the ratio is - 1 + 2 + 3 = 6
this means that there's a sum of 6 parts
so we need to find how much 1 part is equivalent to
if 6 parts are equivalent to 42
then 1 part is equivalent to - 42/6 = 7
so the ratio should be 1:2:3
1 part - 7
2 parts - 7 x 2 = 14
3 parts - 7 x 3 = 21
therefore 42 divided into 1:2:3 ratio is as follows
7 : 14 : 12
Euler's formula tells us that
Suppose we subtract the two. This eliminates the cosine terms.
Divide both sides by
and you're done.
Answer:
The answer is 1/3 or 0.33
Step-by-step explanation:
Let's consider the following ocurrences:
A: A person has a MasterCard
B: A person has an American Express
The data says:
P(A∩B) = 0.2
P(A without B) = 0.4
P(B without A) = 0.1
Then, P(A) = P(A∩B) +P(A without B) = 0.2+0.4 = 0.6
By conditional probability theory:
P (B/A) = P(A∩B) / P(A) = 0.2 / 0.6 = 1/3 = 0.33
Thus
P(B/A) = 1/3 = 0.33
