Solve the following optimization problems. f(x) = x^2 + 3x - 4 subject to r e r. (a) min z (b) min z f (x) = xe" subject to r e r in(x2 x 1) subject to r e r. 1-e subject to r e r. (c) min z f(x) f(r) (d) max z

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.

Which number completes the system of linear inequalities represented by the graph? y> 2x – 2 and x + 4y 2 et 2 3 4

Find the area of the triangle formed by the origin and the points of intersection of parabolas y=−3x^2+20 and y=x^2−16.