Waiting for the Train. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train station. The time, in minutes, that John waits for the train is a variable with density curve y = 1/30 for 0< x< 30, and y = 0 otherwise. a. Graph the density curve of this variable.b. Show that the area under this density curve to the left of any number x between 0 and 30 equals x/30. What percentage of the time does John wait for the trainc. less than 5 minutes?d. between 10 and 15 minutes?e. at least 20 minutes?

The accompanying table shows time-to-speed data for a particular car accelerating from rest to 130 mph. How far had the car traveled by the time it reached this speed? (Use trapezoids to estimate the area under the velocity curve. Notice that intervals vary in length.) Speed change Zero to 30 mph 40 mph 50 mph 60 mph 70 mph 80 mph 90 mph 100 mph 110 mph 120 mph 130 mph Time (sec) 2.2 3.5 5.1 6.8 9.0 11.7 14.5 18.1 23.0 28.9 40.1 The car will travel ft by the time it reaches this speed. (Round the final answer to three decimal places as needed. Round all intermediate values to five decimal places as needed.)

Assume the graph represents the density for body weights (in lb) of cane toads, Bufo marinus.  Find P (X > 3.0) and P (3.0 ≤ X ≤ 5.0).