Acomputer system uses passwords that contain exactly 4 characters, and each character is 1 of the 26 lowercase letters (a–z) or 26 uppercase letters (a–z) or 10 integers (0–9). let ω denote the set of all possible passwords, and let a and b denote the events that consist of passwords with only letters or only integers, respectively. determine the number of passwords that contain at least 1 integer. report the exact number.

The number of passwords that contain at least one integer is 9,533,120.

Step-by-step explanation:

If you have a 4 char password, we can calculate the number of passwords that start with an integer:

We have 10 integers to choose, and then 10+26+26 = 62 possibilities for each of the remaining characters.

So we have:

10*62*62*62 = 2,383,280 possibilities

Because we can have integers in anyone of the four characters, we can multiply this number by 4

2,383,280 * 4 = 9,533,120 possibilities

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: