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User interactions with personal assistants like Alexa, Google Home and Siri are typically initiated by a wake term or wakeword. Several personal assistants feature "follow-up" modes that allow users to make additional interactions without the need of a wakeword. For the system to only respond when appropriate, and to ignore speech not intended for it, utterances must be classified as device-directed or non-device-directed. State-of-the-art systems have largely used acoustic features for this task, while others have used only lexical features or have added LM-based lexical features. We propose a directedness classifier that combines semantic lexical features with a lightweight acoustic feature and show it is effective in classifying directedness. The mixed-domain lexical and acoustic feature model is able to achieve 14% relative reduction of EER over a state-of-the-art acoustic-only baseline model. Finally, we successfully apply transfer learning and semi-supervised learning to the model to improve accuracy even further.