Fact: Census (1900) Magisterial District 4, Carter, Kentucky, United States
Sources
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M9WG-VK1 : accessed 6 February 2017), Francis Smith in household of Haden Smith, Magisterial District 4, Carter, Kentucky, United States; citing enumeration district (ED) 30, sheet 11A, family 196, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,240,514.
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DNA Connections
It may be possible to confirm family relationships with Francis by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Francis:
~1.56%John Hale :
AncestryDNA, GEDmatch FV9234828[compare], yourDNAportal JOHd90a1a43, Ancestry member hrtznmi1
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Family Tree DNA Family Finder, GEDmatch FV9234828[compare], yourDNAportal JOHd90a1a43, FTDNA kit #212709
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Autosomal DNA Test, yourDNAportal JOHd90a1a43