The average number of claims submitted to an insurance firm is 12 per day. the amount of each claim follow exponential distribution with mean 100.

by defining the random variables and stating their distributions, find the probability that

(a) not more than 3 claims submitted arrived in a day;

(b) the waiting time between the 5th and the 6th claims is less than one hour;

(c) more than 400 claims submitted in 30 days;

(d) more than 3 days in which no claim is submitted in a week.

(e) the amount of the fifth claim is more than 200;

(f) the seventh claim is the forth claim that the amount of claim is more than 200.

(g) the total amount of five claims is more than 600.

It took alice 5 5/6 hours to drive to her grandparents' house for . on the way home, she ran into traffic and it took her 7 3/8 hours. how much longer did the return trip take? write your answer as a proper fraction or mixed number in simplest form. the trip home took __hours longer. ?

If a 36 inch yardstick casts a 21 foot shadow, how tall is a building whose shadow is 168 feet? what is the scale factor

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).