Answer:
35,829,630 melodies
Step-by-step explanation:
There are 12 half-steps in an octave and therefore 
arrangements of 7 notes if there were no stipulations.
Using complimentary counting, subtract the inadmissible arrangements from to get the number of admissible arrangements.
can be any note, giving us 12 options. Whatever note we choose, 
must match it, yielding 
. For the remaining two white key notes, 
and 
, we have 11 options for each (they can be anything but the note we chose for the black keys).
There are three possible arrangements of white key groups and black key groups that are inadmissible:
White key notes can be different, so a distinct arrangement of them will be considered a distinct melody. With 11 notes to choose from per white key, the number of ways to inadmissibly arrange the white keys is 
.
Therefore, the number of admissible arrangements is:
Well, we know the slope is 3/2, what's the midpoint of those anyway?
so, what's the equation of a line whose slope is 3/2 and runs through 2,7?
To solve Az + 17 = -4z - b for z, we begin by combining like terms. We get:
Az + 4z = -b - 17, or z(A+4) = -(b+17).
Dividing both sides by (A+4), we get:
-(b+17)
z = --------------
A+4
Assuming that no overtime was factored into his wages, Alex would have gotten a gross pay of $359.60. This was done by multiplying $7.86 x 45.75 hours.
Assuming that overtime was factored into his wages, Alex would have gotten a gross pay of $382.19. This was done by figuring out how much "time and a half" is for over time. "time" = 7.86; "and a half"= 7.86/2= 3.93
Time AND a half would equal 7.86 + 3.93= 11.79.
So, Alex would get an additional $11.79 for the hours OVER 40 hours which was 5 hours and 75 minutes..
11.79 x 5.75 = 67.79
Total hours for a 40 hour work week for Alex with 7.86 would equal a gross pay of 314.40. Plus 67.79. = 382.19
