In and . Circle intersects at and at and and at and . Given that and length where and are relatively prime positive integers, and is a positive integer not divisible by the square of any prime. Find .

Jeffery conducted a survey in his school and found that 30 of the 50 eighth grade students' favorite subject is mathematics. based on the results, jeffery concluded that out of the 200 students in his school, 120 students' favorite subject is mathematics. select the statement that is true about jeffery's conclusion. a. jeffery's conclusion is not valid because the sample was biased since only 200 students were surveyed. b. jeffery's conclusion is valid because the sample was random since all of the students were eighth grade students. c. jeffery's conclusion is valid because the sample was random. d. jeffery's conclusion is not valid because the sample was biased since all of the students were eighth grade students.

What is the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen? assume that the cards are not replaced.

The difference between two numbers is one. three times the larger number minus two times the smaller number is 9. what are the two numbers