Explanation

The perfect square between 40 and 50 is 49 (7 × 7 = 49).

Explanation

The perfect square among these is 81 (since 9 × 9 = 81).

Explanation

To find the average, add up all the numbers and divide by the total count.

Step 1: Calculate the sum

Sum = 0 + 0 + 4 + 10 + 5 + 5

= 24

Step 2: Calculate the average

Average = Sum / Count

= 24 / 6

= 4

Explanation

75.5 is an average of the first 150 natural numbers or positive integers

Sum of first 150 numbers

1+ 2 + 3 +4………………147 + 149 + 150 = 11325

Find average
11325/150 = 75.5

Explanation

Ratio of boys to girls = 3:2

Total students = 60

Total parts = 3 + 2 = 5

Number of girls = (2/5) × 60 = 24

Explanation

Let the two numbers be 5x and 6x, where x is their HCF.

Step 1: Calculate the LCM

The LCM of 5x and 6x is 30x.

Step 2: Find x

Given that the LCM is 480, we can set up the equation:

30x = 480

x = 480 / 30

x = 16

Explanation

The sum of the first n natural numbers is given by the formula:

Sum = n(n + 1) / 2

Step 1: Calculate the sum

n = 100

Sum = 100(100 + 1) / 2

= 100 * 101 / 2

= 5050

Explanation

This is an arithmetic sequence with first term a = 2, last term l = 100, and common difference d = 2.

Step 1: Find the number of terms (n)

The nth term of an arithmetic sequence is given by: l = a + (n - 1)d

100 = 2 + (n - 1)2

100 = 2 + 2n - 2

100 = 2n

n = 50

Step 2: Calculate the sum of the sequence

Sum = n/2 * (a + l)

= 50/2 * (2 + 100)

= 25 * 102

= 2550

Explanation

This is an arithmetic series:

2, 6, 10, 14, ...

First term (a) = 2

Common difference (d) = 6 - 2 = 4

Number of terms (n) = 12

Sum of n terms of an arithmetic series:

S = n/2 × [2a + (n - 1)d]

S = 12/2 × [2×2 + (12 - 1)×4]

S = 6 × [4 + 44] = 6 × 48 = 288

Explanation

Step 1: Solve the inequality

x + 3 < 9

x < 9 - 3

x < 6