Two ants, red ant and black ant, creeping along lines in 3-space. at time t, red ant is at point on the line
x=3-t , y-2=2t , z-2t=6 and at the same time t, black ant is at the point on the line
2x=t , y-3t=2 , z=2+t a) find the starting distance between red and black ants before they travel.
b) is that possible red ant and black ant will collide each other? if yes, when and where will the collision happen?

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Need now max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

In need of in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.