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Preheat oven to 350º F.
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Lightly grease a dozen muffin tins or line with paper cups.
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Place bananas, sugar, yogurt, melted butter, vanilla, and eggs together in a large mixing bowl and beat with a wooden spoon until smooth.
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In a second bowl sift together flour, baking powder, baking soda, and salt.
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Add dry ingredients to wet and mix until just combines.
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Do not overmix, or the muffins will be tough.
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Fill muffin cups three-quarters of the way full.
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Bake for 25 to 35 minutes.
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A toothpick inserted in the center of the muffins will come out clean when they are cooked.
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Remove from the oven and cool slightly before eating.