An archery target is made of 3 concentric circles of radii 1/ √ 3, 1 and √ 3 feet. Arrows striking within the inner circle are awarded 4 points, arrows within the middle ring are awarded 3 points, and arrows within the outer ring are awarded 2 points. Shots outside the target are awarded 0 points. Consider a random variable X, the distance of the strike from the center (in feet), and let the probability density function of X be f(x) =    2 π(1+x 2 ) x > 0 0 otherwise What is the expected value of the score of a single strike?

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.

The radius of the circle below intersects the unit circle at (3/5,4/5). what is the approximate value of theta? 0.6 radians 1.0 radians 36.9 degrees 53.1 degrees

Tell whether the two rates form a proportion