Let the radius of the circle be r. Then the line from the external point through the center of the circle which extends to the far point on the circle has length 3r .By the tangent - secant theorem

t^2 = 3r * r = 3r^2 ( where t is the length of the tangent).

So t = √(3r^2) = √3r answer.

7 0

2 years ago

Two fair number cubes are rolled. What is the probability the numbers are equal or the sum is odd?

Marat540 [252]

Answer:

0.6667 = 66.67%

Step-by-step explanation:

If each number cube has 6 numbers, the two cubes have a total of 6 * 6 = 36 results.

To have equal numbers in each cube, the cases are:

(1,1), (2,2), (3,3), (4,4), (5,5), (6,6) -> 6 cases

To have a odd sum, the cases are:

(1,2), (1,4), (1,6),

(2,1), (2,3), (2,5),

(3,2), (3,4), (3,6),

(4,1), (4,3), (4,5),

(5,2), (5,4), (5,6),

(6,1), (6,3), (6,5). -> 18 cases

So we have a total of 18 + 6 = 24 cases, then the probability is:

P = 24 / 36 = 0.6667 = 66.67%

5 0

2 years ago