one day 93 student arrived to take various exams at WAEC of there 56 took history paper in the morning and 59 took geography paper in the afternoon. There were 28 students who took one history and geography papers. find how many students who took none of the exam, find the number of students who took geography but not history paper, find the number of students who took history alone?

28 took only the history paper

31 took only the geography paper

6 didn't do any exam.

Step-by-step explanation:

There is a total of 93 students.

56 took the history paper.

59 took the geography paper

28 students took both of them.

then in the 58 that took the history paper, we are counting the ones that only take the history paper and the 28 that took both papers, then the number of students that only took the history paper is:

56 - 28  = 28 took only the history paper.

We can use the same reasoning for the number of students that only took the geography paper:

59 - 28 = 31 took only the geography paper.

Now let's find the number of students that took neither paper.

First let's calculate the total number of students that took at least one paper, this is:

28 took both papers.

28 took only history

31 took only geography.

Total = 28 + 28 + 31 = 87

And there are 93 students in total, then the number of students that didn't took any paper is equal to the difference between the total number of students, and the number of students that took at least one, this is:

N = 93 - 87 = 6

6 students did not take any paper.

the answe i =−n+5

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240