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

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!

127

whether it's diameter, or radius, i believe if i remember correctly from school, every amount has to always add up to 180. so if you take 53, and starting adding, long story short, taking 127 and adding it to 53, gives you 180.