Brad is an athletic boy who is on every sport team in school. stephen loves math and is part of his school's math club. these instances reflect correlations that occur when children seek out environments that they find compatible and stimulating.

1. evocative genotype-environment
2. active (niche-picking) genotype-environment
3. passive genotype-environment
4. influential genotype-environment

2. active (niche-picking) genotype-environment

Explanation:

Active (Niche-Picking) Genotype-Environment Correlations is how children look for the environment that matches their capabilities and stimulate them. Niche-picking refers to how those environment that they choose suit or aligns well with their abilities. It is related to their genotype, meaning they have a heritable drive or traits which make them move towards that direction.

For example athletic Brad is inclined to choose a sport team because he is athletic whilst Stephen who loves math is inclined to choose a math club. Their characteristics drives them towards these unique choices.

the factors that the economies of the muslim empires prosper were:

1- land trade routes-located between three continents  

2- sea trade routes

trade contributed to the spread of muslim empires, and with that islamic culture led to a growing feeling of internationalism resulted in the transfer of technology, science, and other cultural forms.