(based on knnl problem 15.13) an automotive engineer was interested in the effect of four al- ternative rubber compounds on the life of automobile tires. to carry out the study, five tires were manufactured from each of the four compounds and five automobiles were obtained for testing. with each automobile, the four tire types were assigned at random to the four wheels. each automobile was driven for 40,000 miles and the amount of wear on each of the four tires was recorded. a what is the experimental unit in this study? b what is the experimental factor, and what are the levels of this factor? c what non-experimental (observational) factor is present in this study, and what are the levels of this factor? d are the two factors crossed, nested or neither? explain your answer briefly. e what kind of design is this?

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).