For valid sources in online research, the following would be considered appropriate:
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the National Archives - Valid source, as it is an official government archive with credible historical documents.
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a weblog of a college history professor about her area of specialty - This can be a valid source if the professor is knowledgeable and provides credible information.
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a gov website - Valid source, as government websites tend to provide reliable and official information.
The other options are less reliable for academic research:
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a weblog of a guy who describes himself as a “history nerd” - This may lack credibility without proper credentials or sources.
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a Wikipedia article - While it can be a starting point, Wikipedia itself is not considered a reliable academic source since its content can be edited by anyone.
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a org website that was last updated in 2008 - The outdated nature makes it less reliable unless the information is still relevant.
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a com website with its own online store - Generally, commercial websites are not seen as credible sources unless they are well-established and provide verifiable information.
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a website with claims that you can’t verify at another source - This is not a reliable source, as claims need external verification to be credible.
In conclusion, the valid sources are the National Archives, the weblog of a college history professor, and a gov website.