Jason believes that the sales of coffee at his coffee shop depend upon the weather. he has taken a sample of 6 days. below you are given the results of the sample.

cups of coffee sold temperature

350 50

200 60

210 70

100 80

60 90

40 100

a. which variable is the dependent variable?

b. develop a scatter diagram and explain what it shows regarding the relationship between sales and temperature.

c. compute and interpret the least squares estimated line.

d. intepret the coeeficient of determination between temperature and the sales of coffee.

e. is there a significant relationship between the sales of coffee and temperature? use a .05 level of significance. be sure to state the null and alternative hypotheses.

f. predict sales of a 90 degree day.

g. develop a 95% confidence interval for predicting the average sales of a 90 degree day.

h. how would a 95% prediction interval for an individual value of cups sold on a 90 degree day compare with your results in part "g".

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).