Suppose that vehicles taking a particular freeway exit can turn right (r), turn left (l), or go straight (s). consider observing the direction for each of three successive vehicles. (enter your answers in set notation. enter empty or ∅ for the empty ) list all outcomes in the event a that all three vehicles go in the same direction. a = (b) list all outcomes in the event b that all three vehicles take different directions. b = (c) list all outcomes in the event c that exactly two of the three vehicles turn right. c = (d) list all outcomes in the event d that exactly two vehicles go in the same direction. d = (e) list outcomes in d'.d' = list outcomes in c ∪ d. c ∪ d = list outcomes in c ∩ d. c ∩ d =

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?