The Hardy-Weinberg principle is a theory that describes how allele frequencies may change within a population absent of evolutionary mechanisms. The theorem is based on certain assumptions regarding the population in question. These assumptions include random mating, large population size, sexual reproduction, and the absence of migration, mutation and selection. It is exceedingly rare for all the Hardy-Weinberg assumptions to be met in nature, but this theory is a tool used to study allele frequencies within populations. 

In the Hardy-Weinberg theory, the two equations used are:

Here,  refers to the frequency of the dominant allele and  refers to the frequency of the recessive allele. Subsequently,  refers to the frequency of the homozygous dominant genotype,  refers to the frequency of the homozygous recessive genotype, and  refers to the frequency of the heterozygous genotype.

In Hardy-Weinberg equilibrium, deviations are violations of the assumptions of the Hardy-Weinberg theory. The assumptions of the Hardy-Weinberg theoru include random mating, large population size, sexual reproduction, and the absence of migration, mutation and selection. Therefore, deviations from the Hardy-Weinberg equilibrium from the options are mutation and migration.

The genetic make up of populations can be measured over time. While genetic changes only occur at the individual level, it is only populations that evolve since genetic changes take many generations to develop into phenotypic changes that may be observed as changing allele frequencies over time.

The five answers listed are all assumptions of Hardy-Weinberg equilibrium except for the population being small. In fact, the population must be large so that random chance during mating and death will not result in certain alleles changing their proportion in the population.

In order to answer this question, you must remember the Hardy-Weinberg equations. 

In the above equations,  stands for the frequency of the dominant allele and  stands for the frequency of the recessive allele. 

It is also important to realize that  stands for the homozygous dominant population,  stands for the homozygous recessive population, and  stands for the heterozygous population. 

We are told that 9% of the population is brown eyed, or homozygous recessive. Let's solve for .

Now let's solve for .

The question asks for the percent of the population that is heterozygous. In order to do this, we look at the first equation and plug in known values.

Thus, our answer is 42%.

Under the Hardy-Weinberg Principle, there is no change in the frequency of alleles or genotypes in a population because there are no changes to the population, such as: natural selection, mutations, migration, or chance events. In addition, mating must be random. Therefore, is it easy to see that most populations do not meet the requirements of this principle.  

For problems of this type, we need to understand the Hardy-Weinberg equations:

Here,  represents the frequency of the dominant allele, while c refers to the frequency of the recessive allele.  and  denote the proportion of homozygous dominant and recessive phenotypes, respectively. Finally, the proportion of heterozygotes is denoted by .

We already know that , and if only two alleles are present in the population,  must be equal to .

Using the values for and , we can solve for the proportion of heterozygotes using the term of the Hardy-Weinberg equation.