Which of the following diseases is caused by a virus in a family associated with viral hemorrhagic fevers?

The correct answer, dengue, is associated with the family of viruses known as flaviviruses, which are indeed linked to viral hemorrhagic fevers. Dengue fever can cause severe flu-like symptoms, but in some cases, it can lead to more serious conditions like dengue hemorrhagic fever or dengue shock syndrome, which are characterized by bleeding and capillary leakage, typical of viral hemorrhagic fevers.

On the other hand, rabies is caused by the rabies virus, which belongs to the Lyssavirus genus and does not fit into the category of viral hemorrhagic fevers. Influenza, though a serious viral infection, is caused by the influenza virus, which is part of the Orthomyxoviridae family and is not classified as a hemorrhagic fever. Mumps is caused by the mumps virus from the Paramyxoviridae family and is associated with parotitis rather than hemorrhagic manifestations. Thus, all other options do not align with the characteristics and classifications of viral hemorrhagic fevers like dengue does.