Messages arrive to a computer server according to a Poisson distribution with a mean rate of 16 per hour. Determine the length of an interval of time (in seconds) such that the probability that no messages arrive during this interval is 0.78. Round your answers to one decimal place (e. g. 98.7).

Question 2 (essay worth 10 points) (03.02 mc) in δabc shown below, point a is at (0, 0), point b is at (x2, 0), point c is at (x1, y1), point d is at x sub 1 over 2, y sub 1 over 2, and point e is at the quantity of x sub 1 plus x sub 2 over 2, y sub 1 over 2: triangle abc is shown. point d lies on segment ac and point e lies on segment bc. a segment is drawn between points d and e. point a is at the origin. prove that segment de is parallel to segment ab.