At a school with 100? students, 33 were taking? arabic, 32 ? bulgarian, and 40 chinese. 9 students take only? arabic, 12 take only? bulgarian, and 20 take only chinese. in? addition, 14 are taking both arabic and? bulgarian, some of whom also take chinese. how many students are taking all three? languages? none of these three? languages?

The answer is 4 and 32.

Step-by-step explanation: Let "A", "B" and "C" represents the set of students who were taking Arabic, Bulgarian and Chinese respectively.

The, according to the given information, we have

Let 'p' represents the number of students who take all the three languages, then

Also,

From here, we get after subtracting equation(c) from (b) that

Therefore,

and from equation (a), we find

Thus,

and

Thus, the number of students who take all the three languages is 4 and the number of students who take none of the languages is 100-68 = 32.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: