Answer: The required number of passwords that can be created is 175760.
Step-by-step explanation: Given that a company needs temporary passwords for the trial of a new payroll software.
Each password will have one digit followed by three letters and the letters can be repeated.
We are to find the number of passwords that can be created using this format.
For the one digit in the password, we have 10 options, 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Since there are 26 letters in English alphabet and letters can be repeated, so the number of options for 3 letters is
26 × 26 × 26 = 17576.
Therefore, the total number of ways in which passwords can be created using the given format is
Thus, the required number of passwords that can be created is 175760.
Answer:
So then the integral converges and the area below the curve and the x axis would be 5.
Step-by-step explanation:
In order to calculate the area between the function and the x axis we need to solve the following integral:
For this case we can use the following substitution 
and we have 
And if we solve the integral we got:
And we can rewrite the expression again in terms of x and we got:
And we can solve this using the fundamental theorem of calculus like this:
So then the integral converges and the area below the curve and the x axis would be 5.
A² + b² = c²
5² + 8² = x²
x² = 25 + 64
x² = 89
x = √89
x = 9.43
A = event the person got the class they wanted
B = event the person is on the honor roll
P(A) = (number who got the class they wanted)/(number total)
P(A) = 379/500
P(A) = 0.758
There's a 75.8% chance someone will get the class they want
Let's see if being on the honor roll changes the probability we just found
So we want to compute P(A | B). If it is equal to P(A), then being on the honor roll does not change P(A).
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A and B = someone got the class they want and they're on the honor roll
P(A and B) = 64/500
P(A and B) = 0.128
P(B) = 144/500
P(B) = 0.288
P(A | B) = P(A and B)/P(B)
P(A | B) = 0.128/0.288
P(A | B) = 0.44 approximately
This is what you have shown in your steps. This means if we know the person is on the honor roll, then they have a 44% chance of getting the class they want.
Those on the honor roll are at a disadvantage to getting their requested class. Perhaps the thinking is that the honor roll students can handle harder or less popular teachers.
Regardless of motivations, being on the honor roll changes the probability of getting the class you want. So Alex is correct in thinking the honor roll students have a disadvantage. Everything would be fair if P(A | B) = P(A) showing that events A and B are independent. That is not the case here so the events are linked somehow.
A=3,500×(1+0.03÷2)^(2×20)
A=6,349.06
