If someone offers you a lottery ticket that has a 25 percent chance of winning $100, a 50 percent chance of winning $200, and a 25 percent chance of winning $1,000, what is the expected value of that lottery ticket?

What is the arc length when θ =pi over 3 and the radius is 5 cm? (5 points) 5 pi over 3 cm 10 pi over 3 cm 16 pi over 3 cm pi over 3 cm

One side of a rectangle is 7 feet shorter than seven times the other side. find the length of the shorter side if we also know that the perimeter of the rectangle is 306 feet.

Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. they randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training. which statistical analysis should be performed to answer the researchers' question?