Certainly! Let’s go through each part of the question step-by-step.
### Part (a): Determine the value of [tex]$A$[/tex] in the table
Given the table:
[tex]\[
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
Number of cans of \\
\hline
Income in Bands & 0 & 50 & 375 & $A$ & 1000 & 1250 \\
\hline
\end{tabular}
\][/tex]
From the provided data, we observe the values of income bands. To determine the value of [tex]$A$[/tex]:
We see the numbers 0, 50, 375, 1000, and 1250. We will assume a pattern or a progression in these bands.
Given the data, it appears there might be an incremental factor or a progression. Without detailed calculation provided by additional context, a reasonable assumption may lead to:
The value of [tex]$A$[/tex] in the income band could be interpolated or patterned incrementally as [tex]$0$[/tex]. This assumption is made prior to more context or detailed data.
So the value for [tex]$A$[/tex] is:
[tex]\[ A = 0 \][/tex]
### Part (b): Write down the equation that can be used to calculate the income
To calculate the income based on the number of cans, consider that we might need a linear relationship (simplified approach):
The linear form of the equation can be represented as:
[tex]\[ \text{Income} = m \cdot n + c \][/tex]
Where:
- [tex]\( m \)[/tex] is the rate or slope (income per can)
- [tex]\( n \)[/tex] is the number of cans
- [tex]\( c \)[/tex] is a constant (initial income when zero cans are sold, likely [tex]$0$[/tex] in this scenario)
In the context of the given data without numerical specifics:
[tex]\[ \text{Income} = m \cdot n + c \][/tex]
Where [tex]\( m \)[/tex] and [tex]\( c \)[/tex] are to be replaced with specific values drawn from the dataset.
### Part (c): Identify the independent variable
In this income calculation scenario:
Given:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Cans} & \text{Income} \\
\hline
n & \text{Income} \\
\hline
\end{array}
\][/tex]
The independent variable—the variable we control or change—would be the number of cans.
Thus, the independent variable is:
[tex]\[ n \][/tex]
In summary:
- [tex]\( A = 0 \)[/tex]
- Equation: [tex]\(\text{Income} = m \cdot n + c \)[/tex]
- Independent variable: [tex]\( n \)[/tex] (number of cans)
