Question

4 tall & orange 0 short & orange 1. a farmer knows that most people prefer tall and yellow flowers. if he plans to grow 100 sunflowers from these two parents, how many can be expected to be tall and yellow like he desires? 75 sunflowers 2. what should be the genotypes of the parent flowers (p generation) if he wants to ensure that all of the flowers in the f1 generation are tall and yellow? x possible gametes ty ty ty ty ty ttyy ttyy ttyy ttyy ty ttyy ttyy ttyy ttyy ty ttyy ttyy ttyy ttyy ty ttyy ttyy ttyy ttyy problem b: in humans, free earlobes are dominant to attached earlobes, and a straight thumb is dominant to a hitchhikers thumb. cross two people that are heterozygous for both traits.

Explanation:

Sub - question 1

Step 1: Analyze the Punnett square

First, we need to determine the proportion of tall and yellow flowers from the Punnett square. Looking at the Punnett square, we count the number of genotypes that correspond to tall and yellow. Let's assume that \(T\) is for tall (dominant) and \(Y\) is for yellow (dominant). The genotypes that are tall and yellow would be those with at least one \(T\) and at least one \(Y\). By counting the cells in the Punnett square, we find that out of 16 cells (let's assume the Punnett square is a 4x4 grid, although from the given square, we can see the pattern), the number of tall and yellow genotypes: Let's list the genotypes:

• \(TTYY\): tall and yellow
• \(TTYy\): tall and yellow
• \(TtYY\): tall and yellow
• \(TtYy\): tall and yellow
• \(TTYy\): tall and yellow
• \(TTyy\): tall and non - yellow (so exclude)
• \(TtYy\): tall and yellow
• \(Ttyy\): tall and non - yellow (exclude)
• \(TTYY\): tall and yellow
• \(TTYy\): tall and yellow
• \(TtYY\): tall and yellow
• \(TtYy\): tall and yellow
• \(TTYy\): tall and yellow
• \(TTyy\): tall and non - yellow (exclude)
• \(TtYy\): tall and yellow
• \(Ttyy\): tall and non - yellow (exclude)

Wait, maybe a better way: Let's consider the two traits separately. For the height trait (T - tall, t - short), the parents' gametes suggest that the tall allele is dominant. For the color trait (Y - yellow, y - orange or non - yellow). From the Punnett square, if we look at the ratio of tall (T_) and yellow (Y_). Let's count the number of cells with T_ and Y_:

Looking at the given Punnett square:

Row 1 (TY gamete from one parent and TY from the other):

• \(TTYY\) (T_, Y_), \(TTYy\) (T_, Y_), \(TtYY\) (T_, Y_), \(TtYy\) (T_, Y_)

Row 2 (TY and Ty):

• \(TTYy\) (T_, Y_), \(TTyy\) (T_, y_), \(TtYy\) (T_, Y_), \(Ttyy\) (T_, y_)

Row 3 (TY and TY):

• \(TTYY\) (T_, Y_), \(TTYy\) (T_, Y_), \(TtYY\) (T_, Y_), \(TtYy\) (T_, Y_)

Row 4 (TY and Ty):

• \(TTYy\) (T_, Y_), \(TTyy\) (T_, y_), \(TtYy\) (T_, Y_), \(Ttyy\) (T_, y_)

Now, let's count the number of T_ and Y_ cells. Let's go through each cell:

1. \(TTYY\): yes
2. \(TTYy\): yes
3. \(TtYY\): yes
4. \(TtYy\): yes
5. \(TTYy\): yes
6. \(TTyy\): no
7. \(TtYy\): yes
8. \(Ttyy\): no
9. \(TTYY\): yes
10. \(TTYy\): yes
11. \(TtYY\): yes
12. \(TtYy\): yes
13. \(TTYy\): yes
14. \(TTyy\): no
15. \(TtYy\): yes
16. \(Ttyy\): no

Count the "yes" ones: Cells 1,2,3,4,5,7,9,10,11,12,13,15. That's 12 out of 16? Wait, no, maybe my counting is wrong. Wait, the original answer for the first sub - question was 75 out of 100. So the proportion is \(\frac{3}{4}\) (since \(75=\frac{3}{4}\times100\)). So we assume that the proportion of tall and yellow flowers from the cross is \(\frac{3}{4}\).

Step 2: Calculate the number of sunflowers

If the total number of sunflowers is \(n = 100\) and the proportion of tall and yellow flowers is \(p=\frac{3}{4}\), then the number of tall and yellow sunflowers \(N=n\times p\).

Substitute \(n = 100\) and \(p=\frac{3}{4}\) into the formula: \(N = 100\times\frac{3}{4}=75\)

Step 1: Recall the principles of dominant and recessive traits

For all the F1 generation to be tall and yellow, the parents must be homozygous dominant for the traits that determine tallness and yellowness (assuming that tall (T) and yellow (Y) are dominant traits). So, if we want all offspring to be tall (so they must have at least one T allele, and to ensure all are tall, the parent should be \(TT\)) and all offspring to be yellow (so the parent should be \(YY\)) for the respective traits.

Let's assume that the tall trait is determined by the allele \(T\) (dominant) and short by \(t\) (recessive), and yellow trait is determined by \(Y\) (dominant) and non - yellow by \(y\) (recessive).

To get all F1 offspring as tall (\(T\_\)) and yellow (\(Y\_\)), one parent should be homozygous dominant for tall and homozygous dominant for yellow (\(TTYY\)) and the other parent should also be homozygous dominant for tall and homozygous dominant for yellow (\(TTYY\)) or, alternatively, one parent could be \(TTYY\) and the other could be \(TTYY\) (or other combinations where one parent is \(TTYY\) and the other is, for example, \(TTYY\), \(TTYy\) would not work because if the other parent has a \(y\) allele, there is a chance of getting \(yy\) in offspring. Wait, no. Wait, if we want all offspring to be tall (so genotype \(T\_\)) and yellow (genotype \(Y\_\)).

If we consider the two traits:

For the tall trait: To ensure all offspring are tall, the parents must be such that at least one parent is \(TT\) (because if one parent is \(Tt\) and the other is \(Tt\), there is a chance of \(tt\) offspring). But since we want all to be tall, the parents should be \(TT\) for the tall trait.

For the yellow trait: To ensure all offspring are yellow, the parents must be \(YY\) for the yellow trait (because if one parent is \(Yy\) and the other is \(Yy\), there is a chance of \(yy\) offspring).

So the genotypes of the parent flowers (P generation) should be \(TTYY\) and \(TTYY\) (or \(TTYY\) and \(TTYY\), or other combinations where both parents are homozygous dominant for both traits. But the most straightforward is \(TTYY\) (homozygous tall and homozygous yellow) crossed with \(TTYY\) (homozygous tall and homozygous yellow), or \(TTYY\) crossed with \(TTYY\) (or \(TTYY\) and \(TTYY\)). Wait, actually, if we have one parent as \(TTYY\) and the other as \(TTYY\), all offspring will be \(TTYY\) (tall and yellow). Alternatively, if one parent is \(TTYY\) and the other is \(TTYY\) (or \(TTYY\) and \(TTYY\)).

Wait, another way: Let's think about the Punnett square. If we cross \(TTYY\) (parent 1) with \(TTYY\) (parent 2), all the gametes from parent 1 are \(TY\) and from parent 2 are \(TY\), so all offspring are \(TTYY\) (tall and yellow). If we cross \(TTYY\) with \(TTYy\), then there is a chance of getting \(TTYy\) and \(TTYY\) (still tall and yellow), but wait, no, \(Yy\) would mean that there is a \(y\) allele, but since \(Y\) is dominant, \(Yy\) is still yellow. Wait, maybe I made a mistake. Wait, the question says "all of the flowers in the F1 generation are tall and yellow". So for the yellow trait, as long as the offspring has at least one \(Y\) allele, it will be yellow. So to ensure all offspring have at least one \(Y\) allele, one parent should be \(YY\) (homozygous dominant for yellow) and the other parent should be \(YY\) (or \(Yy\), but if the other parent is \(Yy\), and the first parent is \(YY\), all offspring will be \(Y\_\)). But for the tall trait, to ensure all offspring are tall, the parents should be \(TT\) (homozygous dominant for tal…

Answer:

75

Sub - question 2