27% of the students in a school are in grade 6. This is 540 students. How many students are in the school?

Mathematics

1 answer:

Anettt [7]3 years ago

6 0

There are a total of 2,000 students in the school.

1.) There are 540 students in the 6th grade. 540 is only 27% of students compared to the total. To find the total students in the whole school, we divide 540 by 27%.

2.) We first change 27% into a decimal by moving the point two times to the left. (Rule to change the percent into a decimal)

27% = .27

3.) Before we divide, we remove the decimal by moving the decimal two times to the right and so do we to 540.

.27 = 27

540. = 54000.

4.) Now we have 54000 divided by 27 which give us the answer of 2,000.

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→Number of Integers from 1 to 100

=100(50 Odd +50 Even)

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(a)

Number of ways of Selecting 2 integers from 50 Integers ,so that their sum is even,

=Selecting 2 Even integers from 50 Even Integers , and Selecting 2 Odd integers from 50 Odd integers ,as Order of arrangement is not Important, ,

$=_{2}^{50}\textrm{C}+_{2}^{50}\textrm{C}\\\\=\frac{50!}{(50-2)!(2!)}+\frac{50!}{(50-2)!(2!)}\\\\=\frac{50!}{48!\times 2!}+\frac{50!}{48!\times 2!}\\\\=\frac{50 \times 49}{2}+\frac{50 \times 49}{2}\\\\=1225+1225\\\\=2450$

=4900 ways

(b)

Number of ways of Selecting 2 integers from 100 Integers ,so that their sum is Odd,

=Selecting 1 even integer from 50 Integers, and 1 Odd integer from 50 Odd integers, as Order of arrangement is not Important,

$=_{1}^{50}\textrm{C}\times _{1}^{50}\textrm{C}\\\\=\frac{50!}{(50-1)!(1!)} \times \frac{50!}{(50-1)!(1!)}\\\\=\frac{50!}{49!\times 1!}\times \frac{50!}{49!\times 1!}\\\\=50\times 50\\\\=2500$