Printer allows for optional settings with a panel of sixon-off switches in a row. how many different settings can she select if there are no restrictions on the switches?

There are 2×2×2×2×2×2 = 2⁶ = 64 possible settings.

Each switch can be in 2 positions, and for each of those, the other switches can have all possible settings. 1 switch has 2 settings. 2 switches will have 2×2 settings. 3 switches will have 2×2×2 settings.

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.