few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Your response, in json format:
{
  "explanation": "This problem applies trigonometric identities, including the angle addition formula for cosine.",
  "answer": "A"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS
options: Draw informal comparative inferences about two populations.

Summarize and describe distributions.

Calculate expected values and use them to solve problems.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Use random sampling to draw inferences about a population.

Summarize, represent, and interpret data on a single count or measurement variable.

Understand and evaluate random processes underlying statistical experiments.

Develop understanding of statistical variability.

Investigate patterns of association in bivariate data.

Understand independence and conditional probability and use them to interpret data.

Investigate chance processes and develop, use, and evaluate probability models.

Interpret linear models.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Use probability to evaluate outcomes of decisions.
problem_activity: Problem 1
For the four scatter plots, answer the following questions:
Does there appear to be a relationship between
$$x$$
and
$$y$$
?
If there is a relationship, does it appear to be linear?
If the relationship appears to be linear, is it a positive or negative linear relationship?
If applicable, circle the correct words in this sentence: There is a (positive/negative) association between
$$x$$
and
$$y$$
because as
$$x$$
increases, then
$$y$$
tends to (increase/decrease).
a.
[IMG]
b.
[IMG]
c.
[IMG]
d.
[IMG]
Problem 2
Pablo is curious if there is a relationship between the amount of time high school students spend on social media and their academic achievement. To explore this, he conducts a survey of 30 randomly selected students from his school, and asks them how many minutes they spent on social media yesterday and what their most recent grade point average (GPA) was. Pablo summarized his data in the scatter plot below.
[IMG]
a.   Describe the relationship between the amount of time spent on social media and GPA.
b.   Are there any deviations from the pattern? Explain what you see.
c.   Are there any clusters of data? What do they mean in context?


correct_option_index: 8