In a solution labeled "0.10 m hno3," which is correct? [h3o +]

When 0.1 M HNO₃ is added to water it dissociates as follow,

                                           HNO₃   →    H₃O⁺   +   NO₃⁻

Let us calculate the pH of this acid in order to know its strength,
As,
                                              pH  =  -log [H₃O⁺]

Putting H⁺ concentration value,

                                              pH  =  -log [0.1]

                                              pH  =  1
It is highly acidic,
And being strong acid it completely ionizes in water producing only H₃O⁺ and NO₃⁻.
So,
              The concentration of H₃O⁺   =  0.1 M
and,
              The concentration of NO₃⁻   =  0.1 M

While unproven, it uses facts to support part of a conclusion. it is still factual and has predictive power, however.