few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Your response, in json format:
{
  "explanation": "The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001392

8
options: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ³ 1.

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
problem_activity: Problem 1
The formula for an explicit rule for an arithmetic sequence is given by
$${a_n=a_1+d(n-1)}$$
, where
$$d$$
is the common difference and
$$n$$
is the term number.
Write an explicit rule for the number of tiles in each pattern shown below.
a.
[IMG]
b.
[IMG]
c.
[IMG]
Problem 2
An arithmetic sequence is shown below.
$${29,\space 22,\space15,\space8,\space1,\space…}$$
Write a recursive formula to represent the sequence.
Write an explicit formula to represent the sequence.
Find the 10th term in the sequence.
Find the 100th term in the sequence.
Problem 3
An arithmetic sequence is described by either a recursive or explicit rule below. If given a recursive rule, provide the explicit rule. If given the explicit rule, give the recursive rule.
a.
$${f(n)=6(n-1)+1}$$
, for
$${n\geq1}$$
b.
$${a_{n+1}=a_n-{3\over2}}$$
,
$${a_1=10}$$


correct_option_index: 1