The light in a restroom operates with a 15-minute timer that is reset every time the door opens as a person goes in or out of the room. Thus, after someone enters or exits the room, the light remains on for only 15 minutes unless the door opens again and resets the timer for another 15 minutes. If the times listed above are the times at which the door opened from 8:00 to 10:00, approximately how many minutes during this two-hour period was the light off?

How many ordered pairs of positive integers satisfy xy=32?

City l has a temperature of −3 °f. city m has a temperature of −7 °f. use the number line shown to answer the questions: number line from negative 8 to positive 8 in increments of 1 is shown. part a: write an inequality to compare the temperatures of the two cities. (3 points) part b: explain what the inequality means in relation to the positions of these numbers on the number line. (4 points) part c: use the number line to explain which city is warmer. (3 points)

F(x) = x^2+x-2/x^2-3x-4 what is the domain and range, x-and y-intercepts, horizontal asymptotes, and vertical asymptotes?