Consider a game in which a player rules a number cube to determine the number of points earned. if a player rolls a number greater than or equal to 4 the number of roll is added to the total points. any other roll is deducted from the players total. what is the expected value of the points earned on a single roll in this game?

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?