Based on these data, state the most appropriate conclusions dr. aguiera could make about the relationships between the following

After conducting her survey, Dr. Aguilera collected quantitative data about the relationship between the following variables. Here are the appropriate conclusions she could make:

The correlation coefficient -.64 indicates medium to strong correlation between anxiety and academic performance. It means that a significant proportion of students who reported that they suffer from anxiety also reported lower academic performance. This relationship may imply causality but does not prove it. Further research with more appropriate methodology would be necessary to identify the causality of poor academic performance and other factors (variable) would have to be taken into account. Dr. Aguilera’s study showed no correlation between hours sleeping per night and academic performance. Meanwhile, it does not prove that there is no causal relationship. Aguilera should have concluded that the questions in her survey do not ask about hours sleeping at day time. She could present a hypothesis that students who compensates for little hours sleep at night with long day time naps do not demonstrate poor academic performance and investigate it with a new study.

You're asking in the ap section, so i'll give the ap calculus-style answer. alternatively, you can find the vertex of the parabola and use the "y"-coordinate as the answer.

the maximum height can occur at a critical number, that is, a number  such that  .

the derivative of  can be calculated as follows:



find a value of  that is a zero of the derivative:


this is parabola that is opening downward; we can assume there is a maximum at  .

to find that maximum, calculate  .