Particles are a major component of air pollution in many areas. It is of interest to study the sizes of contaminating particles. Let X represent the diameter, in micrometers, of a randomly chosen particle. Assume that in a certain area, the probability density function of X is inversely proportional to the volume of the particle ; that is, assume that fX(x) = c x 3 , x > 1, where c is a constant. (a) Find the value of c so that fX is a probability density function. (b) The term PM10 refers to particles 10 µ m or less in diameter. What proportion of contaminating particles are PM10 ? (c) The term PM2.5 refers to particles 2.5 µ m or less in diameter. What proportion of contaminating particles are PM2.5 ? (d) What proportion of the PM10 particles are PM2.5 ?

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.

Simplify the expression. -2/5(10+15m-20n)

Ann and betty together have $60 ann has $9 more than twice betty’s amount how much money dose each have