To find out how many students do not take the school bus, you can first calculate how many do take it and then subtract that number from the total number of students.
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Calculate the number of students who take the school bus: \[ \text{Number of students taking the bus} = 680 \times 0.55 = 374 \]
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Now, subtract the number of students taking the bus from the total number of students: \[ \text{Number of students not taking the bus} = 680 - 374 = 306 \]
So, 306 students do not take the school bus.