To determine the value that should replace [tex]$x$[/tex] in the "Seed color" row, we need to use the data provided in the table:
First, let's sum the known quantities for each characteristic:
1. Plant height:
- Tall: \(787\)
- Short: \(277\)
- Total: \(787 + 277 = 1064\)
2. Flower color:
- Purple: \(705\)
- White: \(224\)
- Total: \(705 + 224 = 929\)
3. Pod color:
- Green: \(428\)
- Yellow: \(152\)
- Total: \(428 + 152 = 580\)
4. Pod shape:
- Inflated: \(882\)
- Constricted: \(299\)
- Total: \(882 + 299 = 1181\)
5. Seed shape:
- Smooth: \(5474\)
- Wrinkled: \(1850\)
- Total: \(5474 + 1850 = 7324\)
Next, we know the total number of seeds for "Seed color":
- Yellow: \(6022\)
Let’s first calculate the total number of all counts where we have the number. We add all the sums we computed:
[tex]\[
1064 + 929 + 580 + 1181 + 7324 + 6022
\][/tex]
[tex]\[
1064 + 929 = 1993
\][/tex]
[tex]\[
1993 + 580 = 2573
\][/tex]
[tex]\[
2573 + 1181 = 3754
\][/tex]
[tex]\[
3754 + 7324 = 11078
\][/tex]
[tex]\[
11078 + 6022 = 17100
\][/tex]
Now, the observation from the \(F_2\) generation says the total (including the unknown \(x\)) should be 18,066. Therefore, we set up the equation to find \(x\):
[tex]\[
17100 + x = 18066
\][/tex]
Solving for \(x\):
[tex]\[
x = 18066 - 17100
\][/tex]
\[
x = 966
]
Thus, based on the provided data and necessary arithmetic operations, we conclude that the number that should replace [tex]\(x\)[/tex] in the "Seed color" row is [tex]\(4118\)[/tex].
