Which of the following graphs best represents f(x) = −2 sin(4x) + 3? (1 point) graph of a trigonometric function with points at 0, 3 and pi over 8, 5, and pi over 4, 3 and pi over 2, 3
graph of a trigonometric function with points at 0, 3, and pi over 8, 1, and pi over 4, 3 and pi over 2, 3
graph of a trigonometric function with points at 0, 5 and pi over 4, negative 1 and pi over 2, 5
graph of a trigonometric function with points at 0, negative 1 and pi over 4, 5 and pi over 2, negative 1

What kinds of numbers make up the set of numbers called the real numbers? give examples when you explain a number type. there are a limited set of types of numbers, but an unlimited number of examples of these numbers.

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."

In the geometric progression –3, 12, −48… what term is 3,072?