To calculate the speed at which a galaxy is moving away from us, we can use the known expansion rate of the universe, which is given as 73.2 kilometers per second per megaparsec.
If a galaxy is located 100 megaparsecs away, we can calculate its velocity as follows:
\[ \text{Velocity} = \text{Expansion Rate} \times \text{Distance} \] \[ \text{Velocity} = 73.2 , \text{km/s/Mpc} \times 100 , \text{Mpc} \] \[ \text{Velocity} = 7320 , \text{km/s} \]
Now, we also need to consider the uncertainty in the measurement. The uncertainty in the expansion rate is ±1.4 km/s/Mpc. Since we are calculating the velocity for 100 Mpc:
\[ \text{Uncertainty in Velocity} = 1.4 , \text{km/s/Mpc} \times 100 , \text{Mpc} = 140 , \text{km/s} \]
So, the final result for the speed at which the galaxy is moving away from us, including uncertainty, is:
\[ 7320 \pm 140 , \text{km/s} \]
Therefore, the correct response is: 7,320 ± 140 km/s.
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