<span>Conditional probablility P(A/B) = P(A and B) / P(B). Here, A is sum of two dice being greater than or equal to 9 and B is at least one of the dice showing 6. Number of ways two dice faces can sum up to 9 = (3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6) = 10 ways. Number of ways that at least one of the dice must show 6 = (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6), (6, 5), (6, 4), (6, 3), (6, 2), (6, 1) = 11 ways. Number of ways of rolling a number greater than or equal to 9 and at least one of the dice showing 6 = (3, 6), (4, 6), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6) = 7 ways. Probability of rolling a number greater than or equal to 9 given that at least one of the dice must show a 6 = 7 / 11</span>
Answer:
Step-by-step explanation:
Assuming the image is the shown below, we can use the following formula to find the length of arc :
Where is the angle in the arc and is the radius of the circle.
Since we are not given the value of , we will only work with this.
For :
For :
We firstly need to find the value of this angle, taking into account the whole circumference is :
Finding :
Now, let's calculate the length of arc:
2x^3 + 3x^2 + x + 1
=2x^3 + 3x^2 + 3x^2 - 3x^2 + x + 1
=2x^3 + 6x^2 - 3x^2 + x + 1
=2(x^3 + 3x^2) - 3x^2 + x + 1
=2x^2*(x+3) - 3x^2 -9x + 9x + x +1
=2x^2*(x+3) - 3x(x+3) + 10x +1
=2x^2*(x+3) - 3x(x+3) + 10x + 30 - 30 +1
=2x^2*(x+3) - 3x(x+3) +10(x+3) -29
The first three terms can be divided by (x+3) evenly so the remainder is -29