At a school with 100 students, 33 were taking Arabic, 39 Bulgarian, and 40 Chinese. 14 students take only Arabic, 19 take only Bulgarian, and 21 take only Chinese. In addition, 13 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?

6 students are taking all three

20 students are taking none.

Step-by-step explanation:

Please check image attached.

From the total of 33 that are taking Arabic, 14 only take Arabic and 13 take Arabic and Bulgarian (b + d), so the students that take only Arabic and Chinese together is:

a = 33 - 14 - 13 = 6

From the total of 39 that are taking Bulgarian, 19 only take Bulgarian and 13 take Arabic and Bulgarian, so the students that take only Bulgarian and Chinese together is:

c = 39 - 19 - 13 = 7

Now, from the total of 40 that are taking Chinese, 21 only take Chinese, 6 take only Arabic and Chinese and 7 take only Bulgarian and Chinese, so the number of students that take all three languages is:

d = 40 - 21 - 6 - 7 = 6 students

The number of students that take any language is 14 + 19 + 21 + 6 + 7 + 13 = 80 students, so 100 - 80 = 20 students take none of the three languages

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

2

step-by-step explanation: