Mike and Molly are having an argument about domain. If f(x)=x−1−−−−−√ and g(x)=x2, what is the domain of g(f(x))\)? Mike says that since g(f(x))=g(x−1−−−−−√)=(x−1−−−−−√)2=x −1, the domain of g(f(x)) is all real numbers. Molly says that he is wrong since f(x) has a restricted domain. Who is correct here? Mike or Molly? If Molly is correct, what is the domain of g(f(x))?

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.

Identify the number 127 as a rational or irrational. explain

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.