Question

THEORY

1 a. In a class of 58 students, 35 offer Biology, 28 offer Economics and 15 offer Physics. Each student offers at least one of the three subjects. If 12 students offer both Biology and Economics , 7 students offer both Biology and Physics and 5 students offer both Economics and Physics, how many students offer all three subjects?

b. A regular polygon with (2m+1) sides has each interior angle equal to 1440 . Find the value of m.

don't spam.

Answer 1

a. In a class of 58 students, 35 students offer Biology, 28 students offer Economics and 15 students offer Physics.

Using the Principle of Inclusion-Exclusion, we can calculate the number of students who offer all three subjects as follows:

The total number of students who offer at least one subject is 35 + 28 + 15 = 78

The number of students who offer Biology and Economics is 12

The number of students who offer Biology and Physics is 7

The number of students who offer Economics and Physics is 5

So the number of students who offer all three subjects is given by:

35 + 28 + 15 - (12 + 7 + 5) = 58 - 24 = 34

Therefore, 34 students offer all three subjects.

b. A regular polygon with (2m + 1) sides has each interior angle equal to 1440.

Each interior angle of a regular polygon with n sides is given by:

angle = (n-2) * 180 / n

So for a regular polygon with (2m + 1) sides, we have:

1440 = (2m + 1 - 2) * 180 / (2m + 1)

Expanding and simplifying:

1440 = 360m / (2m + 1)

Multiplying both sides by (2m + 1):

1440 * (2m + 1) = 360m

Expanding the left side:

2880 + 1440 = 360m

4320 = 360m

Finally, dividing both sides by 360:

m = 12

Therefore, the value of m is 12.