200 students are taking a survey on weather or not they would prefer the Reading comprehension or the Math comprehension on a test. 150 students said they prefer the reading comprehension. 115 students said they prefer the math comprehension. 20 students said they neither sections and preferred the grammar section. How many students preferred both Reading comprehension and Math section? How do I do this

Rectangle abcd is translated to get rectangle a’b’c’d’. rectangle abcd moves units along the x-axis to get rectangle a’b’c’d’. rectangle abcd moves units along the y-axis to get rectangle a’b’c’d’. the algebraic rule that describes this translation is t(x, y), where x = and y = .

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

Anew test for ra is being developed. the test is administered to 750 patients with ra and 750 without ra. for the sake of the question, assume the prevalence of ra in this population is 50%. of the 750 patients with ra, 575 have a positive result. of the 750 patients without ra, 150 have a positive result. what is the positive predictive value of the new test? a575/(575+150) b. 600/(600+ 150) c. 575/(575+125) d. 600/(600+ 125)