Mathematics, 20.07.2019 03:00 GILLIG6003

a mole has two alleles for fur color, b = brown fur and b = white fur. in a population of 100 moles, 12 have white fur. a) what is the brown fur allele frequency? b) the mole population is at hardy-weinberg equilibrium. how does the gene pool of the population change over time?

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I'll assume $\mathrm B$ is completely dominant over $\mathrm b$ . Recall the Hardy-Weinberg equations:

$\begin{cases}p^2+2pq+q^2=1\\p+q=1\end{cases}$

where

represents the allele frequency for brown fur, or the number of copies of the allele $\mathrm B$ within the population; and

represents the allele frequency for white fur, or the number of copies of $\mathrm b$ . In the first equation, the squared terms refer to the frequencies of the corresponding homozygous individuals, while 2pq

is the frequency of the heterozygotes.

We're told that 12 individual moles have white fur, so we know for sure that there are 12 homozygous recessive individuals, which means

$q^2=\dfrac{12}{100}=\dfrac3{25}\implies q=\dfrac{\sqrt3}5\approx0.346$

from which it follows that

$p=1-\dfrac{\sqrt3}5\approx0.654$

Over time, H-W equilibrium guarantees that the allele frequencies (p,q)

do not change within the population. For example, suppose we denote the frequency of the $\mathrm B$ allele in generation

. Then

$p_n={p_{n-1}}^2+\dfrac{2p_{n-1}q_{n-1}}2$

That is, the frequency $\mathrm B$ in the

-th generation has to match the frequency of $\mathrm B$ attributed to the $\mathrm{BB}$ and half the $\mathrm{Bb}$ individuals of the previous generation.

$p_n={p_{n-1}}^2+p_{n-1}q_{n-1}=p_{n-1}(p_{n-1}+q_{n-1})=p_{n-1}$

The same goes for q_n

Answer from: Quest

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

the function given is y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 = -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

Answer from: Quest

step-by-step explanation:

What is the length of ab round to the nearest 10th?

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a mole has two alleles for fur color, b = brown fur and b = white fur. in a population of 100 moles,...

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