To determine the total mass of all melons that weigh between 2 kilograms and 3.5 kilograms, follow these steps:
1. Identify the range of weights: We know that the melons weigh between 2 kilograms and 3.5 kilograms.
2. Determine the mean weight of the melons: The mean weight can be calculated by finding the average of the lower and upper weight limits.
[tex]\[
\text{Mean weight} = \frac{\text{Lower weight} + \text{Upper weight}}{2}
\][/tex]
Substituting the given values:
[tex]\[
\text{Mean weight} = \frac{2.0 \, \text{kg} + 3.5 \, \text{kg}}{2} = 2.75 \, \text{kg}
\][/tex]
3. Assume the total number of melons: For simplicity, let's assume that there are 10 melons within this weight range.
4. Calculate the total mass: The total mass of all the melons can be calculated by multiplying the mean weight of a single melon by the total number of melons.
[tex]\[
\text{Total mass} = \text{Mean weight} \times \text{Number of melons}
\][/tex]
Substituting the calculated mean weight and the assumed number of melons:
[tex]\[
\text{Total mass} = 2.75 \, \text{kg} \times 10 = 27.5 \, \text{kg}
\][/tex]
Thus, the total mass of all the melons that weigh between 2 kilograms and 3.5 kilograms is 27.5 kilograms.
