Etymology
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baby boom (n.)
coined 1941, from baby (n.) + boom (n.); derivative baby-boomer (member of the one that began in the U.S. in 1945) is recorded by 1974.
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back down (v.)
in figurative sense of "withdraw a charge," 1859, American English, from notion of descending a ladder, etc. (the literal sense by 1849); from back (v.) + down (adv.).
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back off (v.)
"retreat, stop annoying someone," by 1938, from the verbal phrase, from back (v.) + off (adv.).
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back seat (n.)

also back-seat, 1832, originally of coaches, from back (adj.) + seat (n.). Used figuratively for "less or least prominent position" by 1868. Back-seat driver attested by 1923.

You know him. The one who sits on the back seat and tells the driver what to do. He issues a lot of instructions, gives advice, offers no end of criticism and doesn't do a bit of work. ["The Back Seat Driver," Wisconsin Congregational Church Life, May 1923]
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back up (v.)
1767, "stand behind and support," from back (v.) + up (adv.). Meaning "move or force backward" is by 1834. Of water prevented from flowing, by 1837.
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ball and chain (n.)

a type of prisoner's restraint, 1818; used figuratively by 1883 of foolish, wasteful habits; as "one's wife," 1920.

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banana republic (n.)
"small Central American state with an economy dependent on banana production," 1901, American English.
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barbed wire (n.)
also barb wire, "fencing wire with sharp edges or points," 1863, American English; see barb (n.) + wire (n.). Originally for the restraint of animals.
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basket case (n.)
1919, American English, originally a reference to rumors of quadriplegics as a result of catastrophic wounds suffered in World War I (the U.S. military authorities vehemently denied there were any such in its hospitals), from basket (n.) + case (n.2). Probably literal, i.e., stuck in a basket, but basket had colloquial connotations of poverty (begging) and helplessness long before this. Figurative sense of "person emotionally unable to cope" is from 1921.
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Bat Mitzvah 

1941, literally "daughter of command;" a Jewish girl who has reached age 12, the age of religious majority. Extended to the ceremony held on occasion of this.

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