When building a Venn Diagram, I always start from the area with the most overlap to the areas of least overlap. Once you have placed the 3 in the middle, you have counted those people, and therefore you must subtract them from the other surveys. Example: since there are 3 people that like all three subjects, now only have 5 students that like just math and English instead of 8.
Therefore:
A) 36 Students were in the survey
*Add all the numbers within the Venn diagram up. Overlapping doesn't matter because no one is double counted.
B) 6 People liked only Math
*Can't touch any other circle but Math
C) 20 Students liked English and math, but not history
*You add 9+5+6, since these bubbles are not overlapping with history.
I Hope this helps and let me know if you have any further questions!
Step-by-step explanation:
first you have to use the formula for circle is 2πr
22
π= ----
7
and r stands for radius
Answer:
![20a^3b^3](https://tex.z-dn.net/?f=20a%5E3b%5E3)
Step-by-step explanation:
<u>Binomial Series</u>
![(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n](https://tex.z-dn.net/?f=%28a%2Bb%29%5En%3Da%5En%2B%5Cdfrac%7Bn%21%7D%7B1%21%28n-1%29%21%7Da%5E%7Bn-1%7Db%2B%5Cdfrac%7Bn%21%7D%7B2%21%28n-2%29%21%7Da%5E%7Bn-2%7Db%5E2%2B...%2B%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7Da%5E%7Bn-r%7Db%5Er%2B...%2Bb%5En)
<u>Factorial</u> is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.
Example: 4! = 4 × 3 × 2 × 1
Therefore, the fourth term in the binomial expansion (a + b)⁶ is:
![\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bn%21%7D%7B3%21%28n-3%29%21%7Da%5E%7Bn-3%7Db%5E3)
![\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B6%21%7D%7B3%21%286-3%29%21%7Da%5E%7B6-3%7Db%5E3)
![\implies \dfrac{6!}{3!3!}a^{3}b^3](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B6%21%7D%7B3%213%21%7Da%5E%7B3%7Db%5E3)
![\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3](https://tex.z-dn.net/?f=%5Cimplies%20%5Cleft%28%5Cdfrac%7B6%20%5Ctimes%205%20%5Ctimes%204%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%213%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%212%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%211%7D%7B3%20%5Ctimes%202%20%5Ctimes%201%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%213%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%212%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%211%7D%5Cright%29a%5E%7B3%7Db%5E3)
![\implies \left(\dfrac{120}{6}\right)a^{3}b^3](https://tex.z-dn.net/?f=%5Cimplies%20%5Cleft%28%5Cdfrac%7B120%7D%7B6%7D%5Cright%29a%5E%7B3%7Db%5E3)
![\implies 20a^3b^3](https://tex.z-dn.net/?f=%5Cimplies%2020a%5E3b%5E3)
Answer:
that = 8 and if you want to see more you can go on
Answer:
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