Elena is interested in whether music affects plant growth. For a science fair project, she will grow one plant in a room that is normally kept quiet. She will grow another plant in another room that has classical piano music playing all the time. After 2 months, she compares the height of the plants to determine the effect of music on plant growth.

1. What type of study is Elena designing?
2. How could her design be improved to collect data that would be better for answering the question of interest?

Match the description of the study design with the type of study being conducted.

Here are the first 4 stages of a pattern.

Pattern of line segments in 4 stages. Stage 1, the middle third of a segment is removed, 2 segments of equal length remain. Stages 2, 3, 4, continue to remove the middle third of remaining segments. Stage 2, 4 segments of equal length remain. Stage 3, 8 segments of equal length remain. Stage 4, 16 segments of equal length remain.

In Stage 1, the middle third of a segment of length 1 is removed. Each successive stage continues to remove the middle third of remaining segments.

1. What is the total length of the segments remaining in Stage 1?
2. What is the total length of the segments remaining in Stage 2?
3. What is the total length of the segments remaining in Stage 3?
4. Priya says that from each stage to the next, the total length of the remaining segments is multiplied by a factor of \(\frac{2}{3}\). Do you agree with Priya? Explain or show your reasoning.
5. Write an expression for the total length of the remaining segments in Stage \(n\).

Mai is using the quadratic formula to solve two different quadratic equations.

For the first equation, she writes \(x= \dfrac{\text-4 \pm \sqrt{4^2 - 4(4)(1)}}{2(4)}\).

For the second equation, she writes \(x=\dfrac{3 \pm \sqrt{(\text-3)^2 - 4(3)(5)}}{2(3)}\).

How many real solutions will each equation have? Explain how you know.

Here are graphs of two functions \(f\) and \(g\).

Graph of functions f and g on grid. Horizontal x axis from negative 3 to 3, by 1’s. Vertical axis from negative 10 to 20, by 10’s. Function F begins near negative 3 comma negative 3, curves upwards and to the right until 0 comma 10, then curves downwards and to the right until about 3 comma negative 3. Function G begins approximately negative 3 comma 23, curves downwards and to the right until 0 comma 5, then curves upwards and to the right until about 3 comma 23. Functions intersect at approximately negative 1 point 25 comma 8 and 1 point 25 comma 8.

Which statements are true about the graph of \(y = h(x)\), where \(h\) given by \(h(x) = f(x) -g(x)\)? Select all that apply.