Expo dry-erase markers are typically considered some of the best in the industry for their clarity and lifespan. A major competitor named Whypo claims that their markers last longer on average than Expo markers and they attempt to show this fact by using a random group of 15 Whypo markers. Whypo finds that their markers have a mean lifespan of 32 days, with a standard deviation of 8 days. Typically, an Expo marker under daily use will have a lifespan of 20 days before needing to be replaced

Check the conditions for Whypo's Hypothesis

If 90° < θ < 180° and cotθ = -1/3, then cscθ =

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.

Evaluate the expression for the given value of the variable 7a - 4a for a =8