James concurs that since D is the midpoint of AB, E is the midpoint of BC, and F is the midpoint of CA, then the perimeter of triangle DEF will be half the perimeter of triangle ABC Determine if James is correct or incorrect. Justity, your answer

David must install fencing around a lot that is shaped like a right angle. the side of lot that runs east-west is 200 ft long. the side of the lot runs north-south is 125 ft long. calculate how many feet of fencing he will need to surround the entire lot.

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."

Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. if he spends 3x−5 dollars on rent, how much does he spend on electricity? for which value(s) of x is the amount the shopkeeper spends on electricity less than $100? explain how you found the value(s).