Penelope is playing in a 32-player chess tournament. The probability of her playing exactly 1 game is 3/16, exactly 2 games is %, exactly 3 games is 3/8, exactly 4 games is 1/8, and exactly 5 games is 1/16. Determine Penelope's expected value.
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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.

How do the number line graphs of the solutions sets of -23 > x and x-23 differ?

What is the y-intercept of the line with the equation 3x + 4y = 12?