Use the quadratic formula to determine the exact solutions to the equation.
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Answer:
Step-by-step explanation:
To create a password, you need to select 8 characters (not necessarily different) from the set {1,3,5,7,9,a,b,c,...,z}. Now, this set has 31 elements: the 26 lowercase letters from the alphabet and the 5 odd numbers (1,3,5,7,9).
Now, there are 31 ways to choose the first character, it can be any element from our set. The second character can also be chosen in 31 ways, because there are not restrictions (repetitions, specific characters, etc). Similarly, the third, fourth, fifth, sixth, seventh and eighth characters have 31 possibilities each one.
The number of passwords is the number of ways of selecting the 8 characters, then by the multiplication principle the number of passwords is 31×31×31×31×31×31×31×31=31^8.