The point (1,4) lies on a circle that is centered at (1, 1). Which statements are correct? Check all that apply.
The circle's radius is 2 units.
The circle's radius is 3 units.
The circle's radius is 9 units.
The point (-2, 1) lies on the circle.
The point (3,3) lies on the circle.

Which of these numbers of simulations of an event would be most likely to produce results that are closest to those predicted by probability theory? 15, 20, 5, 10

If m∠abc = 70°, what is m∠abd? justify your reasoning.  using the addition property of equality, 40 + 70 = 110, so m∠abd = 110°.  using the subtraction property of equality, 70 − 30 = 40, so m∠abd = 30°.  using the angle addition postulate, 40 + m∠abd = 70. so, m∠abd = 30° using the subtraction property of equality.  using the angle addition postulate, 40 + 70 = m∠abd. so, m∠abd = 110° using the addition property of equality.

Events a and b are independent. the probability of a occurring is 2/5. the probability of b occurring is 1/4. what is p(a and b)?