An archaeologist discovers a piece of a ceramic plate. She knows that if the plate is from the third century it was probably a regular 16-gon, but if it was from the twelfth century it was probably a regular 18-gon. If one of the angles on the piece she found is 160o , from which century did the plate most likely originate? Why?

If a(0,0,0) and b(2,2,2) are points in coordinate space, how many paths are there from a to b that move from one lattice point to another in the positive x-,y- or z- direction?

You drop a rubber ball off the roof of a 50 meter high building onto a paved parking lot. it bounces back up with every bounce, but not quite all the way back up to you. after the first bounce it bounces back only 80 percent of the distance it was dropped from. the pattern continues, meaning after every bounce it comes up to just 80 percent of the previous maximum height. so if before the first bounce the height is 50 meters, what height does the ball reach after the fifth bounce? round your answer to one decimal place and chose the correct response from the choices below:

The perimeter of a triangle is 69 cm. the first is 5 cm shorter than the second side. the third side is twice as long the first side. find the length of each side