Customers who purchase a certain make of car can order an engine in any of three sizes. Of all cars sold, 45% have the smallest engine, 35% have the medium-sized one, and 20% have the largest. Of cars with the smallest engine, 10% fail and emissions test within two years of purchase, while 12% of those with the medium size and 15% of those with the largest engine fail. Required:
a. What is the probability that a randomly chosen vehicle will fail an emission test within two years?
b. If a vehicle chosen at random fails an emission test, what is the probability that it has a small engine?
c. If you choose 20 vehicles at random from the total population of vehicles, what is the probability that you choose at most 2 with the largest engine?
d. If you choose 5 vehicles at random from the total population of vehicles every day for 4 days, what is the probability that you choose one vehicle exactly each day with the largest engine?

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).