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We offer help in almost all topics in math. A few are mentioned below

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## Simple Examples

**Example 1:-**

Urn ‘A’ contains 4 white and 3 red marbles and Urn B contains 2 white and 5 red marbles. One of the urn is chosen at random and a marble is to be selected from the chosen urn. What is the probability of drawing a white marble?

**Solution: -**

Let A denote the event of choosing first urn, B/A denote the event of drawing a white marble from the first urn Let C denote the event of choosing second urn,

D/C denote the event of drawing a white marble from the second urn

P (A) = 1/2

P (B/A) = 4/7

P (C) = 1/2

P (C/A) = 2/7

P[drawing a white marble from the chosen urn]

= P [choosing the first urn and drawing a white marble or

choosing second urn and drawing a white marble from it]

= P (A) x P (B/A) + P (C) x P (C/A)

=(1/2) x 4/7 + 1/2 x 2/7 = 4/14 = 2/14 = 6/14

= 3/7

**Probability of drawing a white marble =3/7**

**Example 2: -**

Solve the following radical equation.

√4x+ 6 = √5x

**Solution: -**

The expressions 4x+ 6 and 5x are under the radical. We first try to eliminate the radical sign from the equation. For this we square both sides

We get

(4x+ 6) = 5x

Subtracting 4x on both sides, we get

6 = 5x - 4x

That is x = 6

Therefore

**solution of the radical equation is x = 6.**

**Example 3: -**

Draw the graph of the linear polynomial function y = 5x+9

**Solution: -**

First lets find two points on this line. Then plot those points on a graph and join them using a straight line.

Lets put x = 0

Then y = 5(0)+9

= 0+9

= 9

Then the point is (0,9).

Let us find another point on the same line

Put x = 1

Then y = 5(1) + 9

= 5 + 9

= 14

Then the point is (1, 14).

Now we plot the points and join them.

To plot (0, 9) we move 0 points to right and 9 points up and

mark the point.

Similarly, to plot (1, 14), we move 1 point to right and 14

points to right and mark the point.

Now we join the points using straight line.

So the required graph will be

**Example 4: -**

Find the domain of the inverse of the rational function (x^2 - 1)/(x^2 - 2x + 1)

**Solution: -**

Given function is y = (x^2 - 1)/(x^2 - 2x + 1) In this case we can see that there is a common factor (x - 1) among the numerator and denominator. So first we factor the numerator and denominator and cancel out the common factor.

Lets write x in terms of y

Cross multiplying we get

(x - 1)y = x + 1

xy - y = x +-1

xy - x = 1+ y

x(y - 1) = y + 1

That is x = (y + 1)/(y -1)

Replacing y by x we get the inverse of the given function.

To find the domain we first equate the denominator to 0.

Since the denominator is y -1, we omit 1 from the set of real number.

So domain is set of all real numbers except 1. That is

**Domain = { x/ x ε R, x ≠ 1}**