# Tutor profile: Spencer B.

## Questions

### Subject: SAT II Biology E/M

Albinism is a recessive condition meaning that heterozygous individuals can carry the gene without showing any sign. Using Hardy-Weinberg, determine the frequency of carriers (heterozygotes) if the frequency of albinos (homozygous recessive) is 0.01

The Hardy-Weinberg equations is as follows, p2 + 2pq + q2 = 1 and p + q = 1 p stands for the frequency of the dominant allele, and q the frequency of the recessive allele. Therefore, p2 is the frequency of homozygous dominant individuals, 2pq is the frequency of heterozygous individuals, and q2 is the frequency of homozygous recessive individuals. It is given that the frequency of homozygous recessive individuals is 0.01, which in terms of the equation means: q2 = 0.01 We can find the frequency of the recessive allele by taking the square root of both sides, solving for q: q = 0.1 From this we can calculate the frequency of the dominant allele by plugging q into the second part of the Hardy-Weinberg equation: p + q = 1 p + (0.1) = 1 p = 0.9 We can now calculate the number of heterozygous individuals (carriers) by finding: 2pq 2(0.9)(0.1) = 0.18 That means that the frequency of carriers for albinism is 0.18

### Subject: Biology

What is endosymbiotic theory? Name the major component/organelle of the animal cell that originated through this process.

Endosymbiotic theory is the proposition that some of the organelles unique to Eukaryotes evolved from ancient bacterial cells living within a larger host cell. The two cells had a mutually beneficial relationship in which the larger cell provided a home for the smaller cell and in return the smaller cell helped the host cell process energy. The mitochondria of animals’ cells originated through this process

### Subject: Algebra

Given the system of equations: 2x – y2 = -3y 4x + 10y = 0 Find x and y:

To start, solve the second equation for 2x, in terms of y: 4x + 10y = 0 - 10y -10y 4x = -10y /2 /2 2x = -5y Substitute -5y for 2x into the first equation and solve for y: 2x – y2 = -3y (-5y) – y2 = -3y +5y +5y - y2 = 2y /y /y -y = 2 y = -2 Now that you know y, plug it into your equation for x: 2x = -5y 2x = -5(-2) 2x = 10 x = 5 Solution: x = 5 y = -2

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