Solve
-There Are $n$ People in a Room $N$ Of Possible Handshakes by All the People in the Room

question 21

Multiple Choice

Solve.
-There are $n$ people in a room. The number $N$ of possible handshakes by all the people in the room is given by the function $N ( n ) = \frac { n ( n - 1 ) } { 2 }$ . For what number n of people is $91 \leq N \leq 190$ ?

• A) \(\{ n \mid 13 \leq n \leq 22 \}\)
• B) \(\{ n \mid 15 \leq n \leq 19 \}\)
• C) \(\{ \mathrm { n } \mid 16 \leq \mathrm { n } \leq 19 \}\)
• D) \(\{ n \mid 14 \leq n \leq 20 \}\)

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Definitions:

Wilmot Proviso

An unsuccessful 1846 proposal in the United States Congress that aimed to ban slavery in territory acquired from Mexico in the Mexican War.

Appeal of the Independent Democrats

A document issued in 1854 criticizing the Kansas-Nebraska Act and advocating for anti-slavery policies.

Mexican War

A conflict between the United States and Mexico from 1846 to 1848, resulting in the U.S. annexing territory that includes present-day California, Arizona, and New Mexico.

Foreign Soil

Foreign soil refers to land or territory under the sovereignty of a country other than one’s own.