To find the total length of the connected hoses, we can add their lengths together:
- Brown hose: 10.75 feet
- Green hose: 19.4 feet
- Black hose: 7.5 feet
Adding these lengths:
\[ 10.75 + 19.4 + 7.5 = 37.65 \text{ feet} \]
The total length of the hose is 37.65 feet.
Since Melanie's vegetable garden is 30 feet away from where the hose is connected, we can see that the length of the hose (37.65 feet) is greater than the distance to the garden (30 feet).
Therefore, yes, Melanie will be able to water her vegetables.