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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?

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

Solve the following radical equation.

√4x+ 6 = √5x

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

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

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

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

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