Explanation

Ratio of boys to girls = 2:3

Number of boys = 12

Let's find the multiplier:

2x = 12

x = 6

Now, find the number of girls:

3x = 3 * 6

= 18

Explanation

Given proportion:

4 : 3 = 8 : p

First, let's find the relationship between 4 and 8:

8 = 2 * 4

Now, apply the same relationship to 3:

p = 2 * 3

p = 6

Explanation

To calculate the mean, add all the numbers together and divide by the total number of values.

(10 + 16 + 20 + 22) / 4 = 68 / 4 = 17.

Explanation

120% of 40 = (120/100) * 40

= 1.2 * 40

= 48

Explanation

Given:

Sum of numbers = -8

Product of numbers = 15

The algebraic expression representing this is:

x^2 - (sum)x + (product) = 0

x^2 - (-8)x + 15 = 0

x^2 + 8x + 15 = 0

The correct answer is: x^2 + 8x + 15

Explanation

The car travels 30 km in the first hour and 32 km in the second hour, total distance = 30 + 32 = 62 km.

Total time = 2 hours, so average speed = 62 ÷ 2 = 31 km/h.

Explanation

Arithmetic mean of 2, 4, 6, 8, 10, and 12
A.M = Sum of terms / No. of terms
A.M = (2 + 4 + 6 + 8 + 10 + 12) / 6
A.M = 42 / 6
A.M = 7

Explanation

• To convert a decimal to a percentage, multiply by 100:
  

$0.09\times 100=9\mathrm{\%}$

Explanation

To divide Rs. 2000 in the ratio 3:2, we need to first calculate the total number of shares:

3 + 2 = 5

Then, we divide the total amount (Rs. 2000) by the total number of shares (5):

Rs. 2000 ÷ 5 = Rs. 400

Now, we multiply the share value (Rs. 400) by the respective ratio numbers to find the two shares:

Share 1 (3): 3 × Rs. 400 = Rs. 1200

Share 2 (2): 2 × Rs. 400 = Rs. 800

So, the two shares are Rs. 1200 and Rs. 800.

Explanation