Final answer:
Options a and b contain rational numbers which include integers, a perfect square, and terminating decimals. Option c requires clarification on whether the decimal is repeating to confirm if it's a rational number. If the decimal in option c is repeating, then 'All of the above' could be considered rational numbers.
Step-by-step explanation:
To determine which of the provided options are rational numbers, we need to understand that rational numbers are any numbers that can be expressed as a fraction or ratio of two integers, where the denominator is not zero. This includes integers, fractions, and terminating or repeating decimals.
- Option a: 4 is an integer and can be written as 4/1, √25 is 5 and also an integer, 0.12 is a terminating decimal, and 17 is an integer. Hence, all numbers in option a are rational.
- Option b: 3, 2, 114, and 11 are all integers, implying that they are rational as they can be represented as fractions with a denominator of 1.
- Option c: 0.1225762519... without further context may be a non-repeating, non-terminating decimal, which would not be rational. However, if this were a repeating decimal, it would be rational.
So, the answer depends on whether 0.1225762519... is a repeating decimal. Without that information, we cannot be certain it's rational. Therefore, based on the information available, the most accurate answer is either Option a and b are definitely comprised of rational numbers, potentially Option c if the decimal is repeating, so potentially d) All of the above could be rational numbers.