At what time between 7 and 8 o'clock are the hands of a clock in a straight line, but not together (i.e., they are opposite each other)?(a) 5 minutes past 7(b) 5 5/11 minutes past 7(c) 5 2/11 minutes past 7(d) 5 3/11 minutes past 7(e) 5 1/11 minutes past 7

For the hands to be opposite, the angle between them must be 180 degrees. At 7 o'clock, the minute hand is at 12 and the hour hand is at 7 (210 degrees). The minute hand must gain 5 minutes of space relative to the hour hand to be opposite. The formula is M = (2/11) * (30*H +/- 180). For H=7, M = (2/11) * (210 - 180) = (2/11) * 30 = 60/11 = 5 5/11 minutes past 7.