There are only blue cubes, yellow cubes and green cubes in a bag. There are
three times as many blue cubes as yellow cubes
and five times as many green cubes as blue cubes
Sarah takes at random a cube from the bag.
What is the probability that Sarah takes a yellow cube.
Give your answer in its simplest form.

Provide an example of a trigonometric function and describe how it is transformed from the standard trigonometric function f(x) = sin x, f(x) = cos x, or f(x) tan x using key features.

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 base of a triangle exceeds the height by 7 centimeters. if the area is 400 square centimeters, find the length of the base and the height of the triangle.