problem #1.
you have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. calculate the questions below. note: all of your answers should be expressed as a percentage using one decimal place. for example, a hw value of 0.183 would be 18.3% as an answer. the value 0.183 is a relative frequency, whereas 18.3% is a percentage. while they seem the same, moodle will only accept a certain format for answers as it deems correct for an answer. all answers must have one decimal place. for example, an answer of 10% would need be entered as \10.0\. do not include the % symbol. warning: many people will not get credit for answers simply because they do not read and follow the instructions.
a. the percentage of the \aa\ genotype
b. the percentage of the \a\ allele
c. the percentage of the \a\ allele
d. the percentages of the genotypes \aa\ and \aa.\
e. the percentages of the two possible phenotypes if \a\ is completely dominant over \a.\

problem #2.
cystic fibrosis is a recessive condition that affects about 1 in 2,500 babies in the caucasian population of the united states. please calculate the questions below. note: all of your answers should be expressed as a percentage using one decimal place. for example, a hw value of 0.183 would be 18.3% as an answer. the value 0.183 is a relative frequency, whereas 18.3% is a percentage. while they seem the same, moodle will only accept a certain format for answers as it deems correct for an answer. all answers must have one decimal place. for example, an answer of 10% would need be entered as \10.0\. do not include the % symbol. warning: many people will not get credit for answers simply because they do not read and follow the instructions.
a. the percentage of the recessive allele in the population
b. the percentage of the dominant allele in the population
c. the percentage of heterozygous individuals (carriers) in the population

problem #3.
in a given population, only the \a\ and \b\ alleles are present in the abo system; there are no individuals with type \o\ blood or with o alleles in this particular population. if 200 people have type a blood, 50 have type ab blood, and 50 have type b blood, what are the allele frequencies (expressed as a percentage) of each allele in this population (i.e., what are p and q)? note: you can still use the hw formula here, but in this case \p\ and \q\ are co-dominant alleles, meaning they carry equal dominance and work together to form the blood type \ab\. all of your answers should be expressed as a percentage using one decimal place. for example, a hw value of 0.183 would be 18.3% as an answer. the value 0.183 is a relative frequency, whereas 18.3% is a percentage. while they seem the same, moodle will only accept a certain format for answers as it deems correct for an answer. all answers must have one decimal place. for example, an answer of 10% would need be entered as \10.0\. do not include the % symbol. warning: many people will not get credit for answers simply because they do not read and follow the instructions.

your answers must be uploaded to the link in moodle for credit, but you can keep track of them in the table below.
1a· the percentage of the \aa\ genotype
1b. the percentage of the \a\ allele
1c: the percentage of the \a\ allele
1d the percentage of the genotype \aa\ (or homozygous dominant)
1d: the percentage of the genotype \aa\ (or heterozygous)
1e: the percentage of the dominant phenotype (or \a_\)
1e: the percentage of the recessive phenotype (or \aa\)
2a: the percentage of the recessive allele in the population
2b: the percentage of the dominant allele in the population
2c: the percentage of heterozygous individuals (carriers) in the population
3a. the percentage of the \a\ allele in the population (or \p\ for the hw formula)
3b: the percentage of the \b\ allele in the population (or \q\ for the hw formula)

Question

problem #1.
you have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. calculate the questions below. note: all of your answers should be expressed as a percentage using one decimal place. for example, a hw value of 0.183 would be 18.3% as an answer. the value 0.183 is a relative frequency, whereas 18.3% is a percentage. while they seem the same, moodle will only accept a certain format for answers as it deems correct for an answer. all answers must have one decimal place. for example, an answer of 10% would need be entered as \10.0\. do not include the % symbol. warning: many people will not get credit for answers simply because they do not read and follow the instructions.
a. the percentage of the \aa\ genotype
b. the percentage of the \a\ allele
c. the percentage of the \a\ allele
d. the percentages of the genotypes \aa\ and \aa.\
e. the percentages of the two possible phenotypes if \a\ is completely dominant over \a.\

problem #2.
cystic fibrosis is a recessive condition that affects about 1 in 2,500 babies in the caucasian population of the united states. please calculate the questions below. note: all of your answers should be expressed as a percentage using one decimal place. for example, a hw value of 0.183 would be 18.3% as an answer. the value 0.183 is a relative frequency, whereas 18.3% is a percentage. while they seem the same, moodle will only accept a certain format for answers as it deems correct for an answer. all answers must have one decimal place. for example, an answer of 10% would need be entered as \10.0\. do not include the % symbol. warning: many people will not get credit for answers simply because they do not read and follow the instructions.
a. the percentage of the recessive allele in the population
b. the percentage of the dominant allele in the population
c. the percentage of heterozygous individuals (carriers) in the population

problem #3.
in a given population, only the \a\ and \b\ alleles are present in the abo system; there are no individuals with type \o\ blood or with o alleles in this particular population. if 200 people have type a blood, 50 have type ab blood, and 50 have type b blood, what are the allele frequencies (expressed as a percentage) of each allele in this population (i.e., what are p and q)? note: you can still use the hw formula here, but in this case \p\ and \q\ are co-dominant alleles, meaning they carry equal dominance and work together to form the blood type \ab\. all of your answers should be expressed as a percentage using one decimal place. for example, a hw value of 0.183 would be 18.3% as an answer. the value 0.183 is a relative frequency, whereas 18.3% is a percentage. while they seem the same, moodle will only accept a certain format for answers as it deems correct for an answer. all answers must have one decimal place. for example, an answer of 10% would need be entered as \10.0\. do not include the % symbol. warning: many people will not get credit for answers simply because they do not read and follow the instructions.

your answers must be uploaded to the link in moodle for credit, but you can keep track of them in the table below.
1a· the percentage of the \aa\ genotype
1b. the percentage of the \a\ allele
1c: the percentage of the \a\ allele
1d the percentage of the genotype \aa\ (or homozygous dominant)
1d: the percentage of the genotype \aa\ (or heterozygous)
1e: the percentage of the dominant phenotype (or \a_\)
1e: the percentage of the recessive phenotype (or \aa\)
2a: the percentage of the recessive allele in the population
2b: the percentage of the dominant allele in the population
2c: the percentage of heterozygous individuals (carriers) in the population
3a. the percentage of the \a\ allele in the population (or \p\ for the hw formula)
3b: the percentage of the \b\ allele in the population (or \q\ for the hw formula)

Accepted Answer

### PROBLEM #1 (Using Hardy-Weinberg Equilibrium, $ p^2 + 2pq + q^2 = 1 $ and $ p + q = 1 $, where $ q^2 $ is frequency of "aa", $ q $ is frequency of "a", $ p $ is frequency of "A", $ p^2 $ is "AA", $ 2pq $ is "Aa")

#### 1A: Percentage of "aa" genotype
Given $ q^2 = 0.36 $ (from table, 36% → $ 36.0 $ as per format).
# Explanation:
## Step1: Identify $ q^2 $
$ q^2 = 0.36 $, so percentage is $ 0.36 \times 100 = 36.0 $.
# Answer: 36.0

#### 1B: Percentage of "a" allele ($ q $)
# Explanation:
## Step1: Solve $ q = \sqrt{q^2} $
$ q = \sqrt{0.36} = 0.6 $.
## Step2: Convert to percentage
$ 0.6 \times 100 = 60.0 $.
# Answer: 60.0

#### 1C: Percentage of "A" allele ($ p $)
# Explanation:
## Step1: Use $ p + q = 1 $
$ p = 1 - q = 1 - 0.6 = 0.4 $.
## Step2: Convert to percentage
$ 0.4 \times 100 = 40.0 $.
# Answer: 40.0

#### 1D: Percentage of "AA" genotype ($ p^2 $)
# Explanation:
## Step1: Calculate $ p^2 $
$ p^2 = (0.4)^2 = 0.16 $.
## Step2: Convert to percentage
$ 0.16 \times 100 = 16.0 $.
# Answer: 16.0

#### 1D (Aa genotype, $ 2pq $)
# Explanation:
## Step1: Calculate $ 2pq $
$ 2pq = 2 \times 0.4 \times 0.6 = 0.48 $.
## Step2: Convert to percentage
$ 0.48 \times 100 = 48.0 $.
# Answer: 48.0

#### 1E: Dominant phenotype ("A_", $ p^2 + 2pq $)
# Explanation:
## Step1: Sum $ p^2 + 2pq $
$ 0.16 + 0.48 = 0.64 $.
## Step2: Convert to percentage
$ 0.64 \times 100 = 64.0 $.
# Answer: 64.0

#### 1F: Recessive phenotype ("aa", $ q^2 $)
# Explanation:
## Step1: Use $ q^2 = 0.36 $
$ 0.36 \times 100 = 36.0 $.
# Answer: 36.0

### PROBLEM #2 (Cystic Fibrosis, recessive: $ q^2 = \frac{1}{2500} = 0.0004 $)

#### 2A: Recessive allele ($ q $)
# Explanation:
## Step1: Solve $ q = \sqrt{q^2} $
$ q = \sqrt{0.0004} = 0.02 $.
## Step2: Convert to percentage
$ 0.02 \times 100 = 2.0 $.
# Answer: 2.0

#### 2B: Dominant allele ($ p $)
# Explanation:
## Step1: Use $ p + q = 1 $
$ p = 1 - 0.02 = 0.98 $.
## Step2: Convert to percentage
$ 0.98 \times 100 = 98.0 $.
# Answer: 98.0

#### 2C: Heterozygous carriers ($ 2pq $)
# Explanation:
## Step1: Calculate $ 2pq $
$ 2pq = 2 \times 0.98 \times 0.02 = 0.0392 $.
## Step2: Convert to percentage (1 decimal)
$ 0.0392 \times 100 = 3.92 \approx 3.9 $.
# Answer: 3.9

### PROBLEM #3 (ABO Blood, CO-dominant: Total people = $ 200 + 50 + 50 = 300 $)
- Type A: $ AA $ or $ AO $, but no $ O $, so $ AA $ (count: 200)
- Type AB: $ AB $ (count: 50)
- Type B: $ BB $ (count: 50)

#### 3A: "A" allele frequency ($ p $)
Total "A" alleles: $ (200 \times 2) + 50 = 450 $ (each $ AA $ has 2 A, $ AB $ has 1 A)
Total alleles: $ 300 \times 2 = 600 $
# Explanation:
## Step1: Calculate $ p $
$ p = \frac{450}{600} = 0.75 $.
## Step2: Convert to percentage (1 decimal)
$ 0.75 \times 100 = 75.0 $.
# Answer: 75.0

#### 3B: "B" allele frequency ($ q $)
Total "B" alleles: $ (50 \times 2) + 50 = 150 $ (each $ BB $ has 2 B, $ AB $ has 1 B)
# Explanation:
## Step1: Calculate $ q $
$ q = \frac{150}{600} = 0.25 $.
## Step2: Convert to percentage (1 decimal)
$ 0.25 \times 100 = 25.0 $.
# Answer: 25.0

(Note: Table entries in the image have minor errors; above are corrected using Hardy-Weinberg and allele counting.)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

PROBLEM #1 (Using Hardy-Weinberg Equilibrium, \( p^2 + 2pq + q^2 = 1 \) and \( p + q = 1 \), where \( q^2 \) is frequency of "aa", \( q \) is frequency of "a", \( p \) is frequency of "A", \( p^2 \) is "AA", \( 2pq \) is "Aa")

1A: Percentage of "aa" genotype

Step1: Identify \( q^2 \)

Step1: Solve \( q = \sqrt{q^2} \)

Step2: Convert to percentage

Step1: Use \( p + q = 1 \)

Step2: Convert to percentage

Answer:

1B: Percentage of "a" allele (\( q \))