Questions: Children who are especially vulnerable to sexual abuse.

The answer is: live in homes with a constantly changing cast of characters.

Explanation for each option:

1. Are aggressive and hostile: This option is incorrect. While aggressive and hostile behavior in children can be a result of various factors, it is not specifically linked to an increased vulnerability to sexual abuse. Vulnerability to sexual abuse is more closely related to environmental and situational factors rather than the child's behavior.

2. Live in homes with a constantly changing cast of characters: This option is correct. Children who live in homes where there are frequent changes in the people living there (such as different partners of a parent, transient roommates, or frequent visitors) are at a higher risk of sexual abuse. This instability can create opportunities for abusers to exploit the lack of consistent supervision and the child's need for attention and stability.

3. Belong to churches and community organizations: This option is incorrect. While it is true that abuse can occur in any setting, simply belonging to churches and community organizations does not inherently increase a child's vulnerability to sexual abuse. In fact, these organizations often provide protective factors such as supportive relationships and structured activities.

4. Live in a large extended-family household: This option is incorrect. Living in a large extended-family household does not necessarily increase a child's vulnerability to sexual abuse. In many cultures, extended families provide additional layers of supervision and support, which can actually help protect children from abuse. However, the dynamics of any household can vary, and abuse can occur in any setting.

In summary, the most significant risk factor among the options provided is living in homes with a constantly changing cast of characters, as this environment can lead to a lack of stable supervision and increased opportunities for abusers.