Lose part of mucus plug 40 weeks 4 days

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Haven't had any signs of labor starting until now. I was 1cm dilated at appointment on Tuesday so we scheduled my induction date for Saturday night so baby will be here Sunday hopefully. Well tonight iv been pouring sweat ( not hot in house at all) and I went to bathroom and had part of my mucus plug come out. Been having back cramps and feel constipated but now I'm wondering if labor might be starting soon. Had sex last night to try and get things going but felt fine all day. Anyone else have this happen and labor start?