The three correct answers that provide evidence of universe expansion supporting the Big Bang Theory are:
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Galaxies are moving away from each other. - This observation, noted by Edwin Hubble, supports the idea of an expanding universe.
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An enormous amount of weak cosmic background radiation has been detected in the universe. - This cosmic microwave background radiation is a remnant from the early universe and is consistent with predictions of the Big Bang Theory.
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The temperature of Cosmic Microwave Background radiation varies widely from one part of the universe to another. - The uniformity and slight variations in the temperature of the cosmic microwave background support the idea of a hot, dense early universe as proposed by the Big Bang Theory.
The other options provided do not align with the evidence supporting the Big Bang Theory.