Doesn't look like you have anything to worry about. Looks like cold damage to me, and those palms grow so fast, within a couple months, they'll be full of green leaves again. If possible, just prune the dead leaves off, and fertilize with your maintenance fertilizer. If the leaves at the top of the tree(the newest leaves) start to show signs of browning or yellowing this time of year or this summer, then I would be concerned.

By the way, those look to be Washingtonia Filibusta hybrid palms.

It could be cold damage as islandbreeze said and the only thing I would say is find a palm fertilizer with minors so if your palm is potassium deficient that will cover that as well.

One thing to remember, damage on existing fronds can not correct itself. So what you need to watch is the new growth. I agree with the above two posters. Some of your brown fronds are just "old" fronds. When we moved to Florida I bought several books on Palms and asked tuns of questions. Our HD has a master gardener there on Fridays and Saturdays. He was very helpful. A lot of towns have extension offices where you can bring leaves for their review. I would remove the completely brown fronds, and trim only those yellowing fronds that are at or below 9 and 3 o'clock, fertilize and see what happens. You dont want to prune too much.

Thank you for all of the input. It was exactly what I needed. You guys are great!