Pest Control In an experiment to test the effectiveness of the latest roach trap, the "Roach Resort," 500 roaches were placed in the vicinity of the trap and left there for an hour. At the end of the hour, it was observed that 30 of them had "checked in," while the rest were still scurrying around. (Remember that "once a roach checks in, it never checks out." Let 1 = not checked in, and 2 = checked in.) (a) Set up the transition matrix P for the system with decimal entries. Calculate p2 Calculate p. (b) If a roach begins outside the "Resort," what is the probability of it "checking in" by the end of 1 hour? 2 hours? 3 hours? 1 hour 2 hours 3 hours (c) What do you expect to be the long-term impact on the number of roaches? O Eventually, all the roaches will have checked in. O Eventually, all the roaches will not have checked in. O There is not enough information.
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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