Which individual is legally competent to sign a contract?

The individual who is legally competent to sign a contract is the emancipated minor, in this case, Joan. Emancipation grants a minor the legal rights and responsibilities of an adult, allowing them to enter into contracts, make decisions regarding their personal affairs, and be held accountable under the law. As a result, Joan has the capability to enter binding agreements, as her emancipated status overrides the general rule that minors cannot contract.

In contrast, options like Carol, who has been declared insane, and Mike, who is mentally impaired due to an accident, lack the mental capacity required for contract formation. Contract law emphasizes that individuals must have the ability to understand the consequences of their actions when entering into contracts, which neither Carol nor Mike possesses due to their respective mental states.

Ramona, being addicted to heroin, may also not possess the required mental capacity to understand the nature and consequences of a contract fully, as addiction can impair judgment and decision-making abilities. Therefore, Joan, as an emancipated minor, is the only individual in this scenario who is legally competent to enter into a contract.