Alice (A), Bob (B) and Chris (C) pass a stochastic models textbook to each other. When B gets the book, he sets up two independent "alarm clocks," which ring after independent exponentially distributed times: alarm clock B-A is distributed as EXP(2), i. e. has exponential distribution with parameter 2 (mean 1/2); alarm clock B-C is distributed as EXP(5). If B-A rings first, at that time B passes the book to A; if B-C rings first, at that time B passes the book to C. When C get the book, he behaves analogously, except his alarm clocks to pass the book to A or B are EXP(5) and EXP(3), respectively. Alice (A) behaves differently. When she gets the book, she sets the first independent alarm clock H1 which is distributed as EXP(4). When H1 rings, A with probability 1/4 passes the book to C, and with probability 3/4 sets another independent alarm clock H2 which is distributed as EXP(4). Finally, when H2 rings, Alice passes the book to either B or C with equal probabilities 1/2. Can this process be modeled as a CTMC? If so, what is the state space and transition rates (the Gij ’s)? (25 points) In the long-run, what is the fraction of time that Alice holds the book? (10 points)

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).

What type of symmetry does a rhombus have?

Part a what is the area of triangle i? show your calculation. part b triangles i and ii are congruent (of the same size and shape). what is the total area of triangles i and ii? show your calculation. part c what is the area of rectangle i? show your calculation. part d what is the area of rectangle ii? show your calculation. part e rectangles i and iii have the same size and shape. what is the total area of rectangles i and iii? show your calculation. part f what is the total area of all the rectangles? show your calculation. part g what areas do you need to know to find the surface area of the prism? part h what is the surface area of the prism? show your calculation. part i read this statement: “if you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” is this statement true or false? why? part j read this statement: “if you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” is this statement true or false? why?