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a machine can produce 250 items per hour. if the operator of the machine works 40 hours per week, how many times are made by this machine in one year?

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Assuming that the year has 52 weeks in it, (not a leap year) the machine would produce 520,000. You need to multiply the amount of hours worked by how many items the machine makes in an hour. 40x250=10000. Then you need to multiply the amount of items made in a week by 52 (the number of weeks in a year). 10000x52=520000.
The machine would produce 520,000 in one year

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