Assume c is a circle centered at the origin, oriented counterclockwise, that encloses disk r in the plane. complete the following steps for the vector field bold upper fequalsleft angle 7 x superscript 5 baseline y comma xy superscript 4 baseline plus 6 x superscript 6 right angle. a. calculate the two-dimensional curl of bold upper f. b. calculate the two-dimensional divergence of bold upper f. c. is bold upper f irrotational on r? d. is bold upper f source free on r?

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.

Abag of jelly beans contain 13 pink, green, 20 yellow, 10 black, 7 red, and 11 orange jelly beans. approximately what percent of the jelly beans are pink and yellow?

Ab and bc form a right angle at point b. if a= (-3,-1) and b= (4,4) what is the equation of bc?