Question

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1 2 3 4 5
266\frac{2}{3}
373\frac{1}{3} 35
426\frac{2}{3} 40
586\frac{2}{3} 55
what is the approximate number of hours in 72 days on saturn?
603\frac{2}{3}
658\frac{2}{3}
743
768

Explanation:

Step1: Find the relationship between days and hours

From the table, we can see that when the number of days increases, the number of hours also increases proportionally. We can assume a linear relationship \(y = kx\), where \(y\) is the number of hours, \(x\) is the number of days, and \(k\) is the constant of proportionality.

Let's take two points from the table. For example, when \(x = 35\), \(y=373\frac{1}{3}=\frac{373\times3 + 1}{3}=\frac{1120}{3}\). Then \(k=\frac{y}{x}=\frac{\frac{1120}{3}}{35}=\frac{1120}{3\times35}=\frac{32}{3}\)

Step2: Calculate the number of hours for 72 days

Substitute \(x = 72\) into the equation \(y=\frac{32}{3}x\). Then \(y=\frac{32}{3}\times72\)

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Answer:

768