To determine which numbers are irrational, let's break down the options provided:

A. $\frac{9}{4}$

This is a fraction of two integers, which makes it a rational number.

B. $11$

This is an integer, and all integers are rational numbers.

C. $-14$

This is also an integer, so it is a rational number.

D. $0.151155111555...$

This number has a non-repeating and non-terminating decimal pattern. Any number that cannot be expressed as a ratio of two integers and has a non-repeating, non-terminating decimal expansion is an irrational number. So this is irrational.

E. $\frac{5}{7}$

This is a fraction of two integers, so it is a rational number.

Conclusion:

The irrational number in the list is D.

Would you like more details or have any questions?

Here are 5 related questions:

1. What makes a number irrational versus rational?
2. Can a repeating decimal be an irrational number?
3. How do you convert a rational number into a decimal?
4. Are all square roots irrational?
5. Can you give examples of irrational numbers beyond this question?

Tip: Irrational numbers are often identified by their non-repeating, non-terminating decimal expansions!