1) The equation of a circle is: (x - a)² + (y - b)² = r², wnere: a is the x-coordinate of the center of the circleb is the y-coordinate of the center of the circler is the radius of the circle 2) Since the points (-7,-1) and (-5,9) define a diameter, you can find the center of the circle as the mid point of the diameter: x-coordinate of the mid point = (-7 - 5) / 2 = - 12 / 2 = - 6 y-coordinate of the mid point = (-9 - 1)/ 2 = - 10 / 2 = - 5
Therefore, the center of the circle is (-6,-5)
3) The radius of the center is half the diameter. The length of the diameter is found using the formula for the distance between two points applied to the two endopoints given: diameter² = (7 - 5)² + (- 1 + 9)² = 2² + 8² = 4 + 64 = 68
⇒diameter = √68 = 2√17
⇒ radius = diamter / 2 = 2√17 / 2 = √17
4) Now you can replace the coordinates of the center and the radius into the equation: (x + 6)² + (y + 5)² = 17
There are 6 ways we can roll doubles out of a possible 36 rolls (6 x 6), for a probability of 6/36, or 1/6, on any roll of two fair dice. So you have a 16.7% probability of rolling doubles with 2 fair six-sided dice.
