The value of b is -6.
Explanation:
The expression is 
To determine the value of b, we shall solve the expression.
Applying exponent rule, 
, we get,
Applying exponent rule, 
, we have,
The expression is of the form, 
then 
Applying this rule, we get,
Dividing both sides by 4, we have,
Hence, the value of b is -6.
Answer:
There can be 14,040,000 different passwords
Step-by-step explanation:
Number of permutations to order 3 letters and 2 numbers (total 5)
(AAANN, AANNA,AANAN,...)
= 5! / (3! 2!)
= 120 / (6*2)
= 10
For each permutation, the three distinct (English) letters can be arranged in
26!/(26-3)! = 26!/23! = 26*25*24 = 15600 ways
For each permutation, the two distinct digits can be arranged in
10!/(10-2)! = 10!/8! = 10*9 = 90 ways.
So the total number of distinct passwords is the product of all three permutations,
N = 10 * 15600 * 90 = 14,040,000
Half of the total members are men. For every on women there is one man.
So if there was a total of 100 people in the library and the ratio of man to women was 1:1 there would be 50 women and 50 men.
