Let's address each part of the question in sequence.
Part 1: Domain of the Function
The function given is:
\[ R(n) = \frac{0.6n}{0.1 + 0.6n} \]
To determine the domain, we need to identify any values for \(n\) that would make the denominator zero since division by zero is undefined.
Setting the denominator equal to zero:
\[ 0.1 + 0.6n = 0 \]
Solving for \(n\):
\[ 0.6n = -0.1 \ n = -\frac{0.1}{0.6} \ n = -\frac{1}{6} \approx -0.1667 \]
Thus, the function is undefined at \( n = -\frac{1}{6} \). Therefore, the domain of the function is "all real numbers except \( n = -\frac{1}{6} \)".
Correct Answer for Part 1: A. All real numbers except \( -\frac{1}{6} \).
Part 2: Values of \(n\) that Make Sense in the Application
The application states that it requires an increase in the size of the test. This implies that \(n\) should be a positive factor for increasing the number of questions.
Given that \(n\) represents the factor by which the number of questions increases:
- Positive values of \(n\) would indicate that the number of questions is being increased.
- Negative values of \(n\) would suggest a decrease or a non-standard interpretation of the number of questions, which does not align with the requirement to increase the test size.
- \( n = 0 \) would mean no increase at all, which would not apply in this context.
Correct Answer for Part 2: B. Positive values of \(n\).