Circles C, B, and P overlap. Circle C contains 9, circle B contains 11, and circle P contains 7. The overlap of circles C and P contains 6, the overlap of circles C and B contains 5, and the overlap of circles B and P contains 4. The overlap of all 3 circles contains 3. 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, an 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?

9514 1404 393

Step-by-step explanation:

The number of students in the class is the total of all numbers on the diagram:

  9 +5 +11 +6 +3 +4 +7 +18 = 63 . . . students in the 2015 senior class

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Students taking Chem or Biology, but not Physics are those in the colored area, excluding those in the green:

  9 +5 +11 = 25 science students not taking Physics

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Students not taking science are those outside the colored areas:

  18 students are not taking science

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116