To find out how many times higher the number of library visits before examination day is compared to the average weekly visits, we can perform the following calculation:
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Identify the number of visits before examination day: \( 2 \times 10^3 = 2000 \) visits.
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Identify the number of average weekly visits: \( 5 \times 10^2 = 500 \) visits.
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Now, divide the number of visits before examination day by the number of average weekly visits: \[ \text{Number of times higher} = \frac{2000}{500}. \]
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Simplifying the division: \[ \frac{2000}{500} = 4. \]
Thus, the number of library visits before examination day is 4 times higher than the number of visits in an average week.