First, let's find the total length of the connected garden hoses by adding their lengths together:
- Brown hose: 10.75 feet
- Green hose: 16.4 feet
- Black hose: 8.5 feet
Now, calculate the total length:
\[ 10.75 + 16.4 + 8.5 = 35.65 \text{ feet} \]
The total length of the hose is 35.65 feet, which you have already stated to be the correct sum.
Next, we need to compare this total length with the distance to Melanie's vegetable garden, which is 33 feet away.
Since 35.65 feet (the length of the hose) is greater than 33 feet (the distance to the garden), Melanie will be able to water her vegetables.
Conclusion: Yes, Melanie will be able to water her vegetables.