Arecipe for fruit punch calls for cranberry juice and sparkling water. the ratio of cups of cranberry juice to cups of sparkling water is 6: 24. according to the recipe, how many cups of cranberry juice are needed for everyone and a half cup of sparkling water? write your answer as a fraction in simplest form. explain how you know.

Our star pitcher, foster enlight, can throw a pitch so fast that it gets to the catcher’s mitt before it leaves foster’s fingers! if the team wins a game then the probability that foster was pitching is 0.8 but only if foster had at least one day’s rest since his last pitching assignment. if foster does not have a day off and the team still wins, the probability that foster was pitching drops by half of what it was on the previous day. if the team wins three games in succession from the toronto tachyons and foster pitched in game #2, what is the probability that he pitched in one or more of the other games? (assume that foster did not pitch on the day before the first game of this three game series.)