Is it normal for someones accent to rub off on another?

It happened to me. When I was younger I had a speech impediment so I went to a speech therapist. The speech therapist I was assigned to had a thick Australian accent. I worked with her for 5 years, ages 6-10. Now I'm 19 and people always always always ask me where I'm from and say they can hear a faint Australian accent when I speak. Is this common?
Is it normal for someones accent to rub off on another?
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