Solve the following word problem using any method. show your work.
courtney finds a company willing to send her meals-ready-to-eat (mres) at a discounted price. cases of small portion meals are $20.00 each and cases of large portion meals are $30.00 each. she buys a total of 20 cases and spends a total of $450.00. how many of each case did she purchase?
courtney purchased cases of small portion meals
and cases of large portion meals.

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.

Cot(90° − x) = 1 the value of x that satisfies this equation is °. a. 60 b. 135 c. 225 d. 315

Ahypothesis is: a the average squared deviations about the mean of a distribution of values b) an empirically testable statement that is an unproven supposition developed in order to explain phenomena a statement that asserts the status quo; that is, any change from what has been c) thought to be true is due to random sampling order da statement that is the opposite of the null hypothesis e) the error made by rejecting the null hypothesis when it is true