I'll start all the way back at the beginning here
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then they can tell us how the carnivores were fed
You forget that all carnvores are fuly capible of being sustained on herbivoric food.
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how herbivores were fed (man that's a lot of food)
Man, that's a big Ark! The ark was 450 feet long, 75 feet wide, and 45 feet high. That's more then big enough for all the animals and their food.
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how the boat stayed afloat in waters that could have overturned cruisse ships
I'll anwser that with a quote
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The rectangular dimensions of the Ark show an advanced design in ship-building. Its length of six times its width and 10 times its height would have made it amazingly stable on the ocean. Remember it was made more for floating than sailing, because it wasn't headed anywhere. The famous rock formation near Mount Ararat that some think is Noah's Ark is almost certainly not! The Ark was made to withstand a turbulent ocean voyage, not to be at a certain place at a certain time.
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and how insects, like the fig wasp, that live for 3 days and require the fig fruit of the fig tree to reproduce, survived
Do to have proof that the fig wasp in it's individual species, exhisted back during the flood?
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how insects like fruit flies and mosquitos, that reproduce unimaginably quickly, were kept from being a monstrous pest
I do not have the anwser to that off the top of my head, however, the ark wasn't meant to be a pleasure cruse.
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how Noah was able to repopulate the entire planet in 300 years
Who says he did?
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how he was able to restore all cultures to their pre-flood state
There was only one culture before the flood - the Tower of Babel (post-flood) split the people into different languages and cultures.
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how noah and other biblical figures were able to live for 100s of yearsa, despite the finding of the contrary after the examination of mummies)
Before the flood the earth was covered by a heavy water canopy (the waters of the heavens), this accounts for the fact that there was an equal, nearly tropical climate everywhere. Because of the canopy the O2 level in the air was much higher thus resulting in age increase and gigantism (the humble 18in Sloth used to be 16ft tall). When the canopy dissapered, the higher concintration of O2 left and age decreased. We know for a fact that there did use to be a much higher concintration of O2 because of air trapped in amber.
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how noah was able to collect all the animals
Due to the all around equal climate there would have been no problem with having all different species of animals in one area. Besides, God made the animals, God can collect them.
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how all the animals were able to move from turkey to australia, the americas, etc. without food (all vegetation would have been wiped out during the flood, and would have taken many years to regrow)...
The animals and Noah had to wait 6 months before they could leave tha Ark, that was by far enough time to let all the plants re-grow and vegitation to spread.
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how marine mammals survived
Flood = water
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how coral survived (coral core measuring goes well beyond the estimated time of the flood, about 4000 years ago)
Just because there was a flood doesn't mean there was rough seas. And besides, all coral can survive underwater.
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how the americans and chinese and egyptians, not to mention their fabulous structures, survived...
I believe I alread anwsered that. Babel.