The ESV Study Bible's note on Acts 13:48 says it perfectly:
Throughout Acts, Luke affirms the sovereignty of God over all of life while at the same time affirming the significance of human activity, as evidenced by the remarkable human effort and sacrifice involved in proclaiming the gospel. Thus Luke, without contradiction, maintains a dual emphasis on divine election ("appointed") and on human response ("believed") ... The emphasis here in 13:48 is on the way in which divine sovereignty (appointment) results in the belief of the Gentiles, demonstrating that their belief was due to God's grace alone.That's good stuff. THEOparadox approved!