What is the minimum force required to prevent a ball weighing 22.6 lb from rolling down a ramp which is inclined at 39.0 with the horizontal

It's a ball, so we don't have to worry about friction.  Wouldn't it just be 22.6sin(39) = 14.22 pounds of force?  Conceptually, at an angle 0 (flat), we would need 22.6sin(0) = 0 pounds of force, and at angle 90 (vertical), we would need 22.6sin(90) = 22.6 pounds (all of it).  So it should be 14.22 pounds.  And since this is a mathematical question, rather than physics, I'm assuming you don't need to convert to newtons or anything.

Sis less than or equal to 75 (bottom left)