Since the order in which the members are selected matters (i.e., the mayor, treasurer, and secretary are distinct positions in the leadership team), we can use the permutation formula to calculate the number of possible teams:
P(n,r) = n! / (n-r)!
where n is the total number of members and r is the number of members to be selected.
In this case, n = 9 (the total number of council members) and r = 3 (the number of members to be selected for the leadership team). Therefore, we have:
P(9,3) = 9! / (9-3)!
P(9,3) = 9! / 6!
P(9,3) = (9 x 8 x 7 x 6!) / 6!
P(9,3) = 9 x 8 x 7
P(9,3) = 504
Therefore, there are 504 possible leadership teams that the city council can appoint.