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Sagot :
Let's address the questions step-by-step:
### 1.2.1 Determine the formula to represent the cost for 16-seater minibus:
The cost for hiring a 16-seater minibus can be broken down into the fixed amount and the variable cost per kilometer. The formula is:
[tex]\[ \text{Cost} = \text{Fixed amount} + (\text{Cost per km} \times \text{Number of km}) \][/tex]
For the 16-seater minibus, the fixed amount is [tex]\( R2000 \)[/tex] and the cost per km is [tex]\( R12 \)[/tex]. Thus, the formula can be represented as:
[tex]\[ \text{Cost} = 2000 + 12 \cdot (\text{Number of km}) \][/tex]
### 1.2.2 Calculate the value of [tex]\( A, B \)[/tex] and [tex]\( C \)[/tex]:
Values from Table and their calculations:
Given that the values in the Python code were successfully computed, the results are:
- For [tex]\( K \)[/tex] minibus at 180 km:
[tex]\[ A = 6160 \, \text{R} \][/tex]
- For [tex]\( K \)[/tex] minibus at 300 km:
[tex]\[ B = 7600 \, \text{R} \][/tex]
- For [tex]\( K \)[/tex] minibus at 250 km:
[tex]\[ C = 7000 \, \text{R} \][/tex]
### 1.2.3 Identify the dependent variable and independent variable:
- The independent variable is the number of kilometers traveled (km).
- The dependent variable is the cost of hiring the minibus (Cost).
### 1.2.4 Verify Mr. Moloi's claim for 180 km for a 14-seater bus vs 16-seater bus:
- 14-Seater Minibus (G):
From the table, the cost for a 14-seater minibus at 180 km is provided as [tex]\( R8500 \)[/tex].
- 16-Seater Minibus (K):
According to our formula:
[tex]\[ \text{Cost for 16-seater at 180 km} = 2000 + 12 \cdot 180 \][/tex]
[tex]\[ \text{Cost} = 2000 + 2160 \][/tex]
[tex]\[ \text{Cost} = 4160 \][/tex]
Compare the costs:
- Cost for 14-seater at 180 km = [tex]\( R8500 \)[/tex]
- Cost for 16-seater at 180 km = [tex]\( R4160 \)[/tex]
Mr. Moloi's claim is verified. The 16-seater minibus is indeed cheaper than the 14-seater minibus for 180 km.
### 1.2.5 Draw the graph of 14-seater minibus cost:
This part involves plotting the values from the provided table for the 14-seater minibus costs against their corresponding kilometers on the attached answer sheet.
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of km} & \text{Cost for 14-seater} \\ \hline 0 & 0 \\ 50 & 1250 \\ 100 & 2500 \\ 150 & 3750 \\ 250 & 6250 \\ 300 & 8500 \\ 340 & 10500 \\ \hline \end{array} \][/tex]
### 1.2.6 Explain the type of relationship represented by the graph:
The relationship represented by the graph is a linear relationship. This can be explained by the fact that the cost increases at a constant rate as the number of kilometers increases. Therefore, the graph will be a straight line, indicating a proportional relationship between the distance traveled and the cost incurred.
### 1.2.1 Determine the formula to represent the cost for 16-seater minibus:
The cost for hiring a 16-seater minibus can be broken down into the fixed amount and the variable cost per kilometer. The formula is:
[tex]\[ \text{Cost} = \text{Fixed amount} + (\text{Cost per km} \times \text{Number of km}) \][/tex]
For the 16-seater minibus, the fixed amount is [tex]\( R2000 \)[/tex] and the cost per km is [tex]\( R12 \)[/tex]. Thus, the formula can be represented as:
[tex]\[ \text{Cost} = 2000 + 12 \cdot (\text{Number of km}) \][/tex]
### 1.2.2 Calculate the value of [tex]\( A, B \)[/tex] and [tex]\( C \)[/tex]:
Values from Table and their calculations:
Given that the values in the Python code were successfully computed, the results are:
- For [tex]\( K \)[/tex] minibus at 180 km:
[tex]\[ A = 6160 \, \text{R} \][/tex]
- For [tex]\( K \)[/tex] minibus at 300 km:
[tex]\[ B = 7600 \, \text{R} \][/tex]
- For [tex]\( K \)[/tex] minibus at 250 km:
[tex]\[ C = 7000 \, \text{R} \][/tex]
### 1.2.3 Identify the dependent variable and independent variable:
- The independent variable is the number of kilometers traveled (km).
- The dependent variable is the cost of hiring the minibus (Cost).
### 1.2.4 Verify Mr. Moloi's claim for 180 km for a 14-seater bus vs 16-seater bus:
- 14-Seater Minibus (G):
From the table, the cost for a 14-seater minibus at 180 km is provided as [tex]\( R8500 \)[/tex].
- 16-Seater Minibus (K):
According to our formula:
[tex]\[ \text{Cost for 16-seater at 180 km} = 2000 + 12 \cdot 180 \][/tex]
[tex]\[ \text{Cost} = 2000 + 2160 \][/tex]
[tex]\[ \text{Cost} = 4160 \][/tex]
Compare the costs:
- Cost for 14-seater at 180 km = [tex]\( R8500 \)[/tex]
- Cost for 16-seater at 180 km = [tex]\( R4160 \)[/tex]
Mr. Moloi's claim is verified. The 16-seater minibus is indeed cheaper than the 14-seater minibus for 180 km.
### 1.2.5 Draw the graph of 14-seater minibus cost:
This part involves plotting the values from the provided table for the 14-seater minibus costs against their corresponding kilometers on the attached answer sheet.
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of km} & \text{Cost for 14-seater} \\ \hline 0 & 0 \\ 50 & 1250 \\ 100 & 2500 \\ 150 & 3750 \\ 250 & 6250 \\ 300 & 8500 \\ 340 & 10500 \\ \hline \end{array} \][/tex]
### 1.2.6 Explain the type of relationship represented by the graph:
The relationship represented by the graph is a linear relationship. This can be explained by the fact that the cost increases at a constant rate as the number of kilometers increases. Therefore, the graph will be a straight line, indicating a proportional relationship between the distance traveled and the cost incurred.
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