Josie needs ⅛ cup of sugar to make a dessert. Sophia says that she should fill a ¾ cup with sugar and then pour enough to fill a ½ cup. She says that ⅛ cup of sugar should be left in the ¾ cup.

Abilliard ball is struck by a cue. it travels 1 0 0 cm 100cm before ricocheting off a rail and traveling another 1 2 0 cm 120cm into a corner pocket. the angle between the path as the ball approaches the rail and the path after it strikes the rail is 4 5 ∘ 45 ∘ . how far is the corner pocket from where the cue initially struck the ball? do not round during your calculations. round your final answer to the nearest centimeter.