A rumor is a false statement that has been passed around and a fact is something that is true. For example, if a girl is passing secrets around then that is considered a rumor. A fact is something that you found from a reliable source such as the internet, books, or the encyclopedia.
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A fact most of the time is 100% correct and a opinion you can argue
nothing, but there is a rumor saying boys have better eye sight than girls and girls have better hearing than boys
a hypothesis is a scientific word for prediction. An opinion is something someone says that is not a fact.
A fact is something that is known for sure, like "My hat is green". A hypothesis is a guess like "if I melt ice with salt, it will melt faster".
The difference between an inference and a fact is that an inference is generally something which is worked out or deduced from other factual information (but can also relate to something being suggested, although in this case I think the original definition applies), whereas a fact is something which is known to be a true piece of information, without necessarily relying on other information to support this.