To determine which of the given options is a rational number between 5 and 514, we can analyze each option:
- 525 - This is not between 5 and 514.
- 5 Start Fraction 2 over 5 end fraction - This is equivalent to \( 5 + \frac{2}{5} = 5.4 \), which is between 5 and 514.
- 513 - This is also not between 5 and 514 since it is on the upper limit.
- 5 Start Fraction 1 over 3 end fraction - This is equivalent to \( 5 + \frac{1}{3} \approx 5.333 \), which is between 5 and 514.
- 517 - This is not between 5 and 514.
- 5 Start Fraction 1 over 7 end fraction - This is equivalent to \( 5 + \frac{1}{7} \approx 5.142857 \), which is also between 5 and 514.
- 26−−√ - The square root of 26 is approximately 5.099, which is between 5 and 514 but is not a simple rational number.
The options that are rational numbers between 5 and 514 are:
- \( 5 + \frac{2}{5} \) (5.4)
- \( 5 + \frac{1}{3} \) (approximately 5.333)
- \( 5 + \frac{1}{7} \) (approximately 5.142857)
Thus, the correct responses are 5 Start Fraction 2 over 5 end fraction, 5 Start Fraction 1 over 3 end fraction, and 5 Start Fraction 1 over 7 end fraction.