What is the capital state of the state that is bordered by Colorado, Nebraska, Missouri, and Oklahoma? Since that state is Kansas then my answer is Topeka. Is this correct?

Right. :-)

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Yes, your answer is correct. The capital city of the state bordered by Colorado, Nebraska, Missouri, and Oklahoma is indeed Topeka. To arrive at this answer, you correctly identified that the state in question is Kansas, which is bordered by the mentioned states. Then, you identified the capital city of Kansas as Topeka. Well done!