[tex] \huge \fbox{\mathbb{ \pink{ANSWER}}} \\ \\ \: \: \rightarrow \bold{14.17} \: kg[/tex]
Step-by-step explanation:
To find the new mean mass, we can add the mass of the new backpack to the total mass of the existing backpacks and then divide by the total number of backpacks.
Given:
Mean mass of 14 backpacks = 14.5 kg
Mass of new backpack = 9.5 kg
To calculate the new mean mass, we need to consider the total mass of 15 backpacks.
Total mass of 14 backpacks
= 14.5 kg * 14 = 203 kg
Total mass of 15 backpacks
= 203 kg + 9.5 kg = 212.5 kg
Now, we divide the total mass of 15 backpacks by the new total number of backpacks (15) to find the new mean mass:
New mean mass = Total mass of 15 backpacks / 15
= [tex] \large \frac{212.5 \: \: kg}{15} [/tex]
= 14.17 kg (rounded to two decimal places)
Therefore, the new mean mass of the backpacks, including the new one, would be approximately 14.17 kg.
