I want proof of trigonometric ratios of double and half angles

Agraph of a trapezoid can have diagonals with slopes that are negative reciprocals and two pairs of adjacent sides that are congruent, true or false, and why

The number if marbles of different colors stored in a hat is listed below: 4 red marbles 10 green marbles 7 blue marbles. without looking in the hat, dan takes out a marble at random. he replaces the marble and then takes out another marble from the hat. what is the probability that dan takes out a blue marble in both draws?

Neoli is a nurse who works each day from 8: 00 am to 4: 00 pm at the blood collection centre. she takes 45 minutes for her lunch break. on average, it takes neoli 15 minutes to collect each sample and record the patient's details. on average, how many patients can neoli see each day?