What does the sword and the scales symbolize in the woman's hand that represents civic education?

Usually the image that you are describing is used in justice department things. The woman is Justice. She is blindfolded to all things so as not to be swayed by anything other than the truth. The scales represent the ability to weigh the facts, circumstances, etc. The sword is the means of executing the sentence. Pretty grim visuals, but, it's hard to depict monetary damages.

While it goes by many names, the most popular are Lady Justice, Scales of Justice, and Blind Justice. The statue dates it origins from ancient Greek and Roman times as the lady represented is Themis, the goddess of justice and law. Well known for her clear sightedness, she typically holds a sword in one hand and scales in the other.

The scales that she holds represent the impartiality with which justice is served and the sword signifies the power that is held by those making the decision. During the 16th century, artists started showing the lady blindfolded to show that justice is not subject to influence. From this, the statue earned the name Blind Justice.

I believe that woman is called "Justice." The scales represent
impartiality and a sword symbolize power.

Sword symbolizes authority and scale for just judgment of the facts.

The woman is in fact justice minus the blindfold. The concept for using this symbol I believe is linked to the belief that any democracy is only as good as the citizens which compose said democracy. Many of the framers especially Jefferson and Franklin endorsed this belief and hence public education and libraries were created and endorsed in the US. So in a round about way I believe they are inferring that through civic education justice is achieved for all americans. When you take into account that we have legal system which consists of a jury of peers this becomes more of a tangible concept.