How many miles of naoh will completely react with 10.0 ml of 1.0 m hcl?

The reaction between 1 mole of NaOH and 1 mole of HCl creates 1 mole of NaCl and 1 mole of water. Meaning that the moles of HCl needs to equal that of NaOH for the solution to be considered equalized. That being said, you first need to find the numbers miles of HCl by multiplying the volume by the molarity to get 0.01 moles HCl. (1Mx0.01L=0.01). That means that you need 0.01 moles of NaOH. I hope that helps. Let me know if anything is unclear.

V = 10.0 mL / 1000 = 0.01 L

Molarity = number of moles / volume

1.0 = n / 0.01

n = 1.0 * 0.01

n = 0.01 mols of HCl 

hope this helps!