Explanation

Given expression = (3a + 2b) / (3a - 2b)

= [3(a/b) + 2] / [3(a/b) - 2]

= [3 x 1/3 + 2] / [3 x 1/3 - 2]

= 3 / -1

=-3

Explanation

The word pentagon is derived from a Greek word, pente, meaning five sides or a five-sided polygon.

Explanation

Explanation

To find the fourth proportional, we need to set up a proportion:

60 : 48 :: 30 : x

Where x is the fourth proportional.

We can rewrite this as: 60/48 = 30/x

Cross-multiplying, we get: 60x = 30 × 48

Simplifying, we get: 60x = 1440

Dividing both sides by 60, we get: x = 24

So, the fourth proportional is 24.

Explanation

For one digit number 1 to 9

→1 × 9 = 9

For two digit number 10 to 99

→ 2 × 90 = 180

For three digit number 100 to 300

→3 × 201 = 603

Hence, total number of required digits

= 9 + 180 + 603 = 792

Explanation

Sum of m numbers = mn^2

Sum of n numbers = nm^2

∴ Average of (m + n) numbers

= mn(m+n)/(m+n)

= mn

Explanation

Let's break this down logically:

(i) A toothpaste is useful.

(ii) Useful things are valuable.

From (i), we know that a toothpaste is useful. And from (ii), we know that useful things are valuable.

Therefore, since toothpaste is useful (from i), and useful things are valuable (from ii), we can conclude that toothpaste is valuable.

Thus, statement (iii) "A toothpaste is valuable" follows logically from (i) and (ii).

The correct answer is:

(a) True

Explanation

Explanation

The median of a data set is the middle value when the values are written in numerical order.

Explanation

The result of the expression $4^3 - frac{4^2}{2^2}$ is 60. ​