Derek is training for a half-marathon. his training plan sets his goal for this week at 18 miles with three short runs and one longer run.

his three short runs total 9.35 miles.

how long will his long run need to be to meet his goal?

enter your answer in the box.

miles

If 90° < θ < 180° and cotθ = -1/3, then cscθ =

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."

The distributive property allows you to say that 3(x − 1) = 3x −