\begin{tabular}{|c|c|c|c|c|c|}
\hline \multicolumn{6}{|c|}{\begin{tabular}{l}
When Mandated Reporters in California \\
Must Report Sexual Intercourse to Child- \\
Abuse Authorities
\end{tabular}} \\
\hline \begin{tabular}{c}
Age of \\
partner
\end{tabular} & 13 & 14 & 15 & 16 & 17 \\
\hline \begin{tabular}{c}
Age of \\
patient
\end{tabular} & & & & & \\
\hline 13 & [tex]$N$[/tex] & [tex]$Y$[/tex] & [tex]$Y$[/tex] & [tex]$Y$[/tex] & [tex]$Y$[/tex] \\
\hline 14 & [tex]$Y$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] \\
\hline 15 & [tex]$Y$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] \\
\hline 16 & [tex]$Y$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] \\
\hline 17 & [tex]$Y$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] & [tex]$N$[/tex] \\
\hline
\end{tabular}

According to this table, which instance of sexual intercourse must be reported in California?

A. A 14-year-old with a 17-year-old
B. A 15-year-old with a 13-year-old
C. A 16-year-old with a 14-year-old
D. A 17-year-old with a 15-year-old

Let's analyze the table to understand in which scenarios sexual intercourse must be reported to child-abuse authorities according to California law.

Given four instances to check:
1. a 14-year-old with a 17-year-old
2. a 15-year-old with a 13-year-old
3. a 16-year-old with a 14-year-old
4. a 17-year-old with a 15-year-old

We will compare each instance with the information provided in the table.

### Instance 1: a 14-year-old with a 17-year-old
- The row representing a 14-year-old as the patient and the column representing a 17-year-old as the partner shows "Y".
- This means that this instance must be reported.
- So, the first instance is reported.

### Instance 2: a 15-year-old with a 13-year-old
- The row representing a 15-year-old as the patient and the column representing a 13-year-old as the partner shows "Y".
- This means that this instance must be reported.
- So, the second instance is reported.

### Instance 3: a 16-year-old with a 14-year-old
- The row representing a 16-year-old as the patient and the column representing a 14-year-old as the partner shows "N".
- This means that this instance should not be reported.
- So, the third instance is not reported.

### Instance 4: a 17-year-old with a 15-year-old
- The row representing a 17-year-old as the patient and the column representing a 15-year-old as the partner shows "N".
- This means that this instance should not be reported.
- So, the fourth instance is not reported.

### Conclusion

- Instance 1: a 14-year-old with a 17-year-old must be reported.
- Instance 2: a 15-year-old with a 13-year-old must be reported.
- Instance 3: a 16-year-old with a 14-year-old should not be reported.
- Instance 4: a 17-year-old with a 15-year-old should not be reported.

So, the instances of sexual intercourse that must be reported in California are:
1. a 14-year-old with a 17-year-old
2. a 15-year-old with a 13-year-old