Astate gets its money from a state lottery, a property tax, a sales tax of 5%, and an excise tax. this year it projects that it will receive $32 million from the state lottery, $40 million from the property tax, and $10 million from the excise tax. if the state needs $100 million to cover its expenses, how many dollars worth of taxable items must be purchased in the state this year for the state to break even?

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.