The local barber shop is home to three barbers. the barbers appear identical but vary in their ability to provide good haircuts. denote the event that you receive a good haircut by g, the event that you do not receive a good haircut by ng, and the event that your hair is cut by barber i by bi , where i ∈ {1, 2, 3}. the probability that any particular barber cuts your hair is 1/3. the probability that you receive a good haircut from barber 1 is 1. the probability that you receive a good haircut from barber 2 is 1/2. the probability that you receive a good haircut from barber 3 is x, where x lies in the interval [0, 1]. using the bayes theorem calculate the probability that your hair is cut by barber 1 given that you received a good hair cut.

Match the following terms with their definitions. 1. bisector of a segment ray ba and ray bc are opposite rays if a, b, and c are collinear and b (the endpoint of both rays) is between a and c. 2. opposite rays a ray, , is the set of points beginning at point a and going infinitely in the direction of point b. 3. collinear points a line or segment that intersects the segment at its midpoint. 4. betweenness of points a set of two or more points all on the same line. 5. ray the distance between the endpoints of a segment. 6. space point b is between a and c if a, b, and c are collinear and the equation ab + bc = ac is true, where ab, bc, and ac are the distances between points a and b, b and c, and a and c, respectively. 7. midpoint of a segment a set of two or more points all on the same plane. 8. coplanar points the point on a segment that divides the segment into two equal segments. 9. length of a segment the set of all possible points. 10. line segment the set of two different endpoints and all points between them.

Which statement justifies why angle ebc measures 90?

Question 3 (essay worth 10 points) (03.06 mc) part a: max rented a motorbike at $465 for 5 days. if he rents the same motorbike for a week, he has to pay a total rent of $625. write an equation in the standard form to represent the total rent (y) that max has to pay for renting the motorbike for x days. (4 points) part b: write the equation obtained in part a using function notation. (2 points) part c: describe the steps to graph the equation obtained above on the coordinate axes. mention the labels on the axes and the intervals. (4 points)