Answer:
Mom decided to split the prize between my brother and (I).
Explanation:
As there is only two entities (in this case, two people, you and your brother), between would make the most sense. Among can be used in such a state, but it is generally used when there is either more than 2 persons or more than 2 groups of people.
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The first one (facts and details)
Answer:
The giant-impact theory.
Explanation:
The giant-impact theory proposes that the Moon formed in a collision between the Earth another smaller celestial body. It is estimated that the smaller planet was roughly about the size of Mars. The debris from the resulting impact, over time, collected to form a mass that is now, presumably, the Moon.