Which would be a case in which a center could NOT provide care for a mildly ill child?

A center typically cannot provide care for a mildly ill child if that child has vomited multiple times, as indicated in the situation described. Vomiting can indicate the presence of a contagious illness, which poses a risk to other children and staff at the center. Even if a child appears to be feeling well otherwise, repeated vomiting typically requires that child to remain at home until they are free of symptoms for a specified period.

In contrast, loose bowel movements may not necessitate exclusion if the child is otherwise well, a temperature of 99.5 degrees Fahrenheit may be considered within the normal range (and not a reason to exclude the child), and a temperature of 100 degrees Fahrenheit taken axillary might be beneath the threshold that necessitates exclusion in some policies, depending on the specific guidelines set forth by health authorities or the center’s policies. Therefore, the repeated vomiting presents the clearest case for exclusion due to both the child's health and the well-being of others in the care environment.