Question
If a test that has reliability 0.7 has the number of questions increased by a factor n, the reliability R of the new test is given by Upper R left parenthesis n right parenthesis equals StartFraction 0.6 n Over 0.1 plus 0.6 n EndFraction
.
a. What is the domain of the function defined by this equation?
b. If the application used requires that the size of the test be increased, what values of n make sense in the application?
Question content area bottom
Part 1
a. What is the domain of the function defined by this equation? Choose the correct answer below.
A.
All real numbers except
enter your response here.
B.
All real numbers.
Part 2
b. If the application used requires that the size of the test be increased, what values of n make sense in the application?
A.
Negative values of n
B.
Positive values of n
C.If a test that has reliability 0.7 has the number of questions increased by a factor n, the reliability R of the new test is given by Upper R left parenthesis n right parenthesis equals StartFraction 0.6 n Over 0.1 plus 0.6 n EndFraction
.
a. What is the domain of the function defined by this equation?
b. If the application used requires that the size of the test be increased, what values of n make sense in the application?
Question content area bottom
Part 1
a. What is the domain of the function defined by this equation? Choose the correct answer below.
A.
All real numbers except
enter your response here.
B.
All real numbers.
Part 2
b. If the application used requires that the size of the test be increased, what values of n make sense in the application?
A.
Negative values of n
B.
Positive values of n
C.
nequals0
nequals0
.
a. What is the domain of the function defined by this equation?
b. If the application used requires that the size of the test be increased, what values of n make sense in the application?
Question content area bottom
Part 1
a. What is the domain of the function defined by this equation? Choose the correct answer below.
A.
All real numbers except
enter your response here.
B.
All real numbers.
Part 2
b. If the application used requires that the size of the test be increased, what values of n make sense in the application?
A.
Negative values of n
B.
Positive values of n
C.If a test that has reliability 0.7 has the number of questions increased by a factor n, the reliability R of the new test is given by Upper R left parenthesis n right parenthesis equals StartFraction 0.6 n Over 0.1 plus 0.6 n EndFraction
.
a. What is the domain of the function defined by this equation?
b. If the application used requires that the size of the test be increased, what values of n make sense in the application?
Question content area bottom
Part 1
a. What is the domain of the function defined by this equation? Choose the correct answer below.
A.
All real numbers except
enter your response here.
B.
All real numbers.
Part 2
b. If the application used requires that the size of the test be increased, what values of n make sense in the application?
A.
Negative values of n
B.
Positive values of n
C.
nequals0
nequals0
Answers
GPT-4o mini
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 \(n\).
### 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 \(n\).