Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive throughs. certainly the faster the cars get through the drive through, the more opportunity for making money. qsr magazine studied drive through times for fast-food restaurants and found wendy's has the best time, with a mean time spent in the drive through of mu=138.5 second. assuming drive through times are normally distributed with a standard deviation of 29 seconds, answer the following:
(a) what is the probability that a randomly selected car will get through the wendy's drive through in less than 100 seconds, p(x< 100)?
(b) what is the probababily that a car will spend more than 160 seconds in the wendy's drive through, p(x> 160)?
(c) according to our normal model, what is the probababily that a car will spend less than 4 minutes in the wendy's drive through p(x< 240)? (note: you will not be able to get me a precise value for this probability using the table, but you can tell me what is has to be greater than.)
(d) would you say that it is unusual for a car to spend more than 4 minutes in the wendy's drive through? why?

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).