sat-dog

The correct answer is $41$. The mean of a data set is computed by dividing the sum of the values in the data set by the number of values in the data set. It’s given that data set A consists of the heights of $75$ objects and has a mean of $25$ meters. This can be represented by the equation $\frac{x}{75}=25$, where $x$ represents the sum of the heights of the objects, in meters, in data set A. Multiplying both sides of this equation by $75$ yields $x=75\left(25\right)$, or $x=\mathrm{1,875}$ meters. Therefore, the sum of the heights of the objects in data set A is $\mathrm{1,875}$ meters. It’s also given that data set B consists of the heights of $50$ objects and has a mean of $65$ meters. This can be represented by the equation $\frac{y}{50}=65$, where $y$ represents the sum of the heights of the objects, in meters, in data set B. Multiplying both sides of this equation by $50$ yields $y=50\left(65\right)$, or $y=\mathrm{3,250}$ meters. Therefore, the sum of the heights of the objects in data set B is $\mathrm{3,250}$ meters. Since it’s given that data set C consists of the heights of the $125$ objects from data sets A and B, it follows that the mean of data set C is the sum of the heights of the objects, in meters, in data sets A and B divided by the number of objects represented in data sets A and B, or $\frac{\mathrm{1,875}+\mathrm{3,250}}{125}$, which is equivalent to $41$ meters. Therefore, the mean, in meters, of data set C is $41$.