Explanation

To factorize the expression y^2 + y - 6, we need to find two numbers whose product is -6 and whose sum is 1 (the coefficient of the middle term).

These numbers are 3 and -2, so we can write:

y^2 + y - 6 = (y + 3)(y - 2)

Explanation

The given number 0.393939 is a repeating decimal, which can be written as:

0.39 39 39 ...

This is a repeating decimal with a block of 39 repeating indefinitely. To convert this to a fraction, we can use the following steps:

Let x = 0.393939...

Multiply both sides by 100 to get: 100x = 39.3939...

Subtract the original equation from this new equation to get: 99x = 39

Divide both sides by 99 to get: x = 39/99

So, the correct answer is: 39/99

Explanation

The mean of 100 items is 30, so the total sum of all items is:

30 x 100 = 3000

However, two items were wrongly taken as 32 and 12 instead of 23 and 11, which means the correct total sum should be:

3000 - 32 - 12 + 23 + 11 = 2990

Since there are 100 items, the correct mean is:

2990 ÷ 100 = 29.9

So, the correct answer is: 29.9

Explanation

Let third number = x

First number = 120/100 x = 6x/5

Second number = 150/ 100x = 3x/2

Ratio of two numbers = 6x/5 : 3x/2 = 12x : 15x = 4:5

Explanation

The mixture contains 12% copper, which means that 12% of the mixture's weight is copper.

We want to find out how many kg of mixture is required to get 69 kg of copper.

Let's say the weight of the mixture is x kg.

Since 12% of the mixture is copper, the weight of copper in the mixture is 12% of x, which is 0.12x.

We are told that the weight of copper is 69 kg, so we can set up the equation:

0.12x = 69

To solve for x, we can divide both sides by 0.12:

x = 69 / 0.12

x = 575

So, the weight of the mixture is 575 kg.

Explanation

Explanation

Mean of 5 numbers =18

⇒ Sum of these 5 numbers =18×5=90

Let number that has been excluded be x

New mean =490−x​=16

Solving this, we get

90−x=64

∴x=26

Explanation

To evaluate this expression, we can simplify the fraction:

12.1 ÷ 19.8 = 0.61 (approximately)

11/18 = 0.61 (approximately)

Explanation

Let's break this down step by step:

1. Let the man's monthly income be x.
2. He spends Rs. 3500 per month, which means his savings are x - 3500.
3. He saves 12 ½% of his income, which can be written as a decimal: 0.125x.
4. Since his savings are equal to his income minus his expenses, we can set up the equation: 0.125x = x - 3500.
5. Simplify the equation: 0.125x = x - 3500 --> 0.125x - x = -3500 --> -0.875x = -3500.
6. Divide both sides by -0.875: x = 3500 / 0.875 --> x = 4000.

So, the man's monthly income is Rs. 4000.

Explanation

Average of a , b = ( a + b ) /2

16a + 16b = 48

a + b = 3  || divide each term by 16

The average is ( a + b ) / 2 = 3/2

= 1.5