Answer :
Let's analyze the given equation and the variables involved:
The equation given is:
[tex]\[ u = 748g \][/tex]
where
- [tex]\( g \)[/tex] represents the total number of gallons of water used.
- [tex]\( u \)[/tex] represents the number of units billed.
To determine which variables are dependent and which are independent, we need to understand their roles in the equation.
### Step-by-Step Analysis:
1. Identification of Variables:
- [tex]\( g \)[/tex] (gallons) and [tex]\( u \)[/tex] (units) are the two variables in question.
2. Understand the Equation Structure:
- The equation expresses [tex]\( u \)[/tex] (units) in terms of [tex]\( g \)[/tex] (gallons).
- Mathematically, we are saying that [tex]\( u \)[/tex] is dependent on [tex]\( g \)[/tex].
3. Dependent vs. Independent Variables:
- Independent Variable: This is the variable that stands alone and isn't changed by the other variables you are trying to measure. In experiments and mathematics, it is the input or cause.
- Dependent Variable: This is the variable that depends on the independent variable. It is the outcome or effect.
4. Applying Definitions to the Equation:
- According to our equation [tex]\( u = 748g \)[/tex]:
- [tex]\( g \)[/tex] is the input value (we decide how many gallons are used).
- [tex]\( u \)[/tex] is directly calculated based on the value of [tex]\( g \)[/tex].
- Thus, [tex]\( u \)[/tex] changes in response to [tex]\( g \)[/tex].
5. Determine the Nature of Each Variable:
- [tex]\( g \)[/tex] is the independent variable since we can choose different values for gallons, and this choice influences the value of units.
- [tex]\( u \)[/tex] is the dependent variable since its value is computed based on the chosen value of [tex]\( g \)[/tex].
6. Conclusion:
- The statement "g is the independent variable" is true.
- The statement "u is the dependent variable" is true.
### Answer Options:
- [tex]\( g \)[/tex] is the dependent variable.
- [tex]\( u \)[/tex] is the dependent variable.
- [tex]\( g \)[/tex] is the independent variable.
- [tex]\( u \)[/tex] is the independent variable.
- The two variables cannot be labeled as independent or dependent without a table of values.
Choosing the correct statements:
- [tex]\( u \)[/tex] is the dependent variable.
- [tex]\( g \)[/tex] is the independent variable.
Thus, the true statements are:
[tex]\[ \boxed{2 \text{ (u is the dependent variable)}, \text{ and } 3 \text{ (g is the independent variable)}} \][/tex]
The equation given is:
[tex]\[ u = 748g \][/tex]
where
- [tex]\( g \)[/tex] represents the total number of gallons of water used.
- [tex]\( u \)[/tex] represents the number of units billed.
To determine which variables are dependent and which are independent, we need to understand their roles in the equation.
### Step-by-Step Analysis:
1. Identification of Variables:
- [tex]\( g \)[/tex] (gallons) and [tex]\( u \)[/tex] (units) are the two variables in question.
2. Understand the Equation Structure:
- The equation expresses [tex]\( u \)[/tex] (units) in terms of [tex]\( g \)[/tex] (gallons).
- Mathematically, we are saying that [tex]\( u \)[/tex] is dependent on [tex]\( g \)[/tex].
3. Dependent vs. Independent Variables:
- Independent Variable: This is the variable that stands alone and isn't changed by the other variables you are trying to measure. In experiments and mathematics, it is the input or cause.
- Dependent Variable: This is the variable that depends on the independent variable. It is the outcome or effect.
4. Applying Definitions to the Equation:
- According to our equation [tex]\( u = 748g \)[/tex]:
- [tex]\( g \)[/tex] is the input value (we decide how many gallons are used).
- [tex]\( u \)[/tex] is directly calculated based on the value of [tex]\( g \)[/tex].
- Thus, [tex]\( u \)[/tex] changes in response to [tex]\( g \)[/tex].
5. Determine the Nature of Each Variable:
- [tex]\( g \)[/tex] is the independent variable since we can choose different values for gallons, and this choice influences the value of units.
- [tex]\( u \)[/tex] is the dependent variable since its value is computed based on the chosen value of [tex]\( g \)[/tex].
6. Conclusion:
- The statement "g is the independent variable" is true.
- The statement "u is the dependent variable" is true.
### Answer Options:
- [tex]\( g \)[/tex] is the dependent variable.
- [tex]\( u \)[/tex] is the dependent variable.
- [tex]\( g \)[/tex] is the independent variable.
- [tex]\( u \)[/tex] is the independent variable.
- The two variables cannot be labeled as independent or dependent without a table of values.
Choosing the correct statements:
- [tex]\( u \)[/tex] is the dependent variable.
- [tex]\( g \)[/tex] is the independent variable.
Thus, the true statements are:
[tex]\[ \boxed{2 \text{ (u is the dependent variable)}, \text{ and } 3 \text{ (g is the independent variable)}} \][/tex]
