Question

cr v. algebra 1 sem a cr- a and venn diagrams westside high’s 2015 senior-class science enrollment is summarized by the venn diagram. chemistry, biology, and physics class enrollments are denoted by the sets c, b, and p, respectively. how many students are in the 2015 senior class? how many students are taking chemistry and biology, but not physics? how many students are not taking science?

Explanation:

Step1: Find total senior class students

To find the total number of students in the senior class, we sum all the regions in the Venn diagram (including the region outside all three circles, which is 18). The regions inside the circles are: \(9\) (only C), \(5\) (C and B only), \(11\) (only B), \(6\) (C and P only), \(3\) (all three), \(4\) (B and P only), \(7\) (only P), and \(18\) (outside all).
Sum: \(9 + 5 + 11 + 6 + 3 + 4 + 7 + 18\)
Calculate: \(9+5=14\), \(14+11=25\), \(25+6=31\), \(31+3=34\), \(34+4=38\), \(38+7=45\), \(45+18=63\).

Step2: Find students taking chemistry and biology, but not physics

This is the region where C and B overlap, but not P. From the Venn diagram, that region is \(5\).

Step3: Find students not taking science

This is the region outside all three circles (C, B, P), which is \(18\).

Answer:

Total senior class students: \(63\)
Students taking chemistry and biology (not physics): \(5\)
Students not taking science: \(18\)