Communication is critical, and actions speak louder than words.
Whether they are really convinced you may be at the mercy of some guy hiding behind the door or not, so many people have been murdered after the police left, that voters and many frustrated well-motivated police have created laws and policies that aim to prevent it. Not such a bad idea, but...
What you really need to do is convince them that you are safe, while still defending your home--if you consent to a search, they can use anything they find against you.
Coming outside (since you are female, and assuming you don't look like you've been fighting) might be one way to reassure them.
Not ideal, just an idea. The real question is, what address was the right address? Had you heard any fighting?
What do you think? http://consequeries.com/
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