Consider X ∼ Uniform(0,1) as the point where a stick of unit length is broken at random. So after the stick breaks, you will have two sticks of lengths x and 1 − x. Find the probability that x (also called the 5

1−x

odds) is less than 4. Hint: You can treat the inequality inside the probability statement as you would any

other inequality.

What is the y-intercept of the line given by the equation

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (-4, 0) and (6,0). the y-intercept of thefirst parabola is (0, –12). the y-intercept of the second parabola is (0-24). what is the positive difference between the avalues for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth.

D(5, 7). e(4,3), and f(8, 2) form the vertices of a triangle. what is mzdef? oa. 30° ob. 45° oc. 60° od 90°