Answer:
Number of trees which are tall and have smooth peas are 4
Explanation:
The easiest way to explain this problem is by using venn diagram that is attached to my answer.
Now let's start with explanations.
1. Both tall, green peas and smooth peas trees = 3. So, put it in the middle, at the intercection of all three circles.
2. Both Tall and Green peas trees = 8. So put it at the intersection of T and G circles.
3. Both Green peas and Smooth peas trees = 16. Put it at the intersection of G and S.
4. Let's assume that both Tall and Smooth peas trees amount to X (for calculation purposes). Locate it at the intersection of T and S. This X is what we need to identify.
5. Totally Tall trees amount to 22. This means that in the remaining region we can locate such equation as 22 - 8 - 3 - X = 11 - X
6. Totally Green peas trees amount to 30. So, remaing area will be equal to 30 - 8 - 3 - 16 = 3
7. Totally Smooth peas trees amount to 34. Remaining area is 34 - X -3 -16 = 15 - X.
8. Now we can add up all our calculated numbers and equations and equate it to overall number of trees, 61.
* Also, we have 6 trees which have none of the charecteristics.
So,
61 = (11-x)+8+3+x+3+16+(15-x) + 6
x=1
The intersection of T and S is x+3 ⇒ 1+3=4
The number of plants that were tall and had smooth peas is 4. We can find this through the help of a Venn-diagram.
A Venn-diagram is a diagram that uses circles to show relationship between things. The things that possess similar traits are intersected.
Venn-diagrams visually represent similarities and difference between two or more concepts.
Given:
Total plants are 61
Tall plants are 22
Green peas plants are 30
Smooth peas plants are 34
Tall and had green peas plants are 8
Green peas and smooth peas plants are 16
Plants with all 3 characters are 3
Plants with none of the character are 6
The Venn-diagram to illustrate the situation is given in the attachment.
The number of tall and smooth peas plants are taken as x.
Therefore the tall plants will be:
[tex]\rm Tall \:plants = 22 - 8-3-x\\\\\rm Tall \:plants = 11-x[/tex]
Similarly the smooth peas plants will be:
[tex]\rm Smooth \:peas \:plants = 34-16-3-x\\\\\rm Smooth \:peas \:plants =15-x[/tex]
The green peas plants will be [tex]30-8-3-16=3[/tex]
The total plants having characteristics are [tex]61-6=55[/tex]
Therefore it can be written as:
[tex]\begin{aligned}\rm 11-x + 8+3+16+3+15-x&=55\\\\\rm x &= 1\end[/tex]
Therefore the plants that are tall and have smooth peas are 1+3 = 4
Learn more about Venn-diagram here:
brainly.com/question/8760190
