20% of the kids were wearnig orange (32/160)<span />
Answer:
the perimeter is 87
Step-by-step explanation:
You have to use carefully Venn Diagram to solve this problem:
n, here below means number of students
GIVEN
----------
n(Cigarettes) = 645
n(Alcohol) = 859
n(Drugs) = 207
n(Alcohol ∩ Cigarettes) = 397
n(Alcohol ∩ Drugs) = 109
n(Alcohol ∩ Cigarettes ∩ Drugs) = 85
And 274 Students "Clean from any of the above"
Let x be the unknown number, that is n(Cigarettes ∩ Drugs)
Start by drawing 3 intersecting circles, one for Alcohol, another for Cigarettes and the 3rd for Drugs:
1) n( Alcohol ONLY) =859-397-109-85 = 268 (only Alcohol)
2) n( Cigarettes ONLY) =645-397-85 - x= 163 - x (only Cigarettes)
3) n( Drugs ONLY) =207- 109 -85 - x = 13 - x (only Drugs).
(Remember that there are 274 Students clean, not shown in Venn)
Total of students (we need it to solve):
TOTAL n(STUDENT) = Alcohol Alone+ Cigarette Alone+ Drug Alone + 274
TOTAL n(STUDENT) = 268 + (163-x) + (13-x) + 274
TOTAL n(STUDENT) = 718 -2x
(hope you can get the TOTAL n(STUDENT) to be able to find x, which is the
n(Drugs ∩ Cigarettes)
We are asked to determine the numerator of the simplified sum and the answer is the letter "C" which is "4X + 6". To get the answer, the solution is shown below:
We have given equation as:
x / (x²+3x + 2) + 3/(x+1) , we need to factor out the denominator of the first term such as x²+3x+2 = (x+2) (x+1)
x / (x+3)(x+1) + 3/(x+1)
Perform combining of terms such as:
x + 3(x+2) x + 3x +6 4X + 6
------------------- = ----------------- = --------------
(x+2) (x+1) (x+2)(x+1) (x+2)(x+1)
Therefore, the numerator simplified sum is "4X + 6".