Oooh just to warn you, you may not catch that flight! I had an hour to catch a flight from London to France and thought I could do it, but the plane to London ended up having to circle for 20 minutes before landing, then I had to take the Airport subway to the right terminal, by the time I got to Customs a lady was standing there reading tickets and saying "sorry, it is too late" so I had to wait 6 hours for the next flight. You only have 30 minutes, that isn't even enough time for you to get off the plane! Because when they say "arrival time" that is when you land, not the time it takes to taxi to the gate, lock down the plane, open doors, everyone takes their time getting up from their seats and gathering bags (and oh gosh, their children!).
So I would suggest taking A LOT to do because you may have to wait in Minneapolis for a couple hours (they should give you free food tickets, they gave me one) and tell whoever is picking you up in Seattle that it is a possibility so they know you are coming eventually.