30 POINTS To study the effect of cell phone use on the time it takes to fall asleep, two experimental treatments are planned: one-hour cell phone use before bedtime for one group versus two-hour cell phone use for another. Which of the following groups would serve best as a control for this study?

A third group that uses a cell phone randomly for one hour or two hours before bedtime
A third group that uses a cell phone for 30 minutes before bedtime
A third group that uses a cell phone only if awoken in the middle of the night
A third group in which each subject chooses to use a cell phone for one hour or two hours before bedtime
A third group that does not use a cell phone before bedtime

Lorenzo ate 2/5 of his bag of almonds. his 4 friends ate equal shares of the remaining bag of almonds?

Find the area of the triangle shown 3 by 6

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).