A university requires its Biology majors to take a course called BioResearch. The prerequisite for this course is that all students must have taken either a Statistics course or a computer course. By the time they are juniors, 52% of the Biology majors have taken Statistics, 23% have had a computer course and 7% have both. What percentage of students have also taken a computer course given they have taken Statistics?

(1) Subtracting the 7% from both is incorrect. This is easy to see by drawing a large circle to represents all bio majors, a mid-size circle (inside the big-circle) that takes up 52% of the area of the big circle to represent those bio majors who take stat, and a small-circle (inside the big-circle) that overlaps the mid-size circle to represent those bio majors who take computer science. The area of overlap of the mid-size circle and the small-circle is 7% of the total area of the large circle.

Now add the none overlap areas of the mid-size and small circle, and to that add the overlap:

You get (in percent) 52 + 23 - 7 = 68 %. That's .68.

(2) Consider only the students who have taken statistics. That's the mid-size circle in (1). And for these students what fraction have taken computer science? The fraction is 7/52 (and not 7% since we have limited the question to a specific group of students).

09-04-2011 at 10:50 pm

Step-by-step explanation:

unless if u could do my questions, if not i wouldn't want to

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2