Answer:
Hello,
Step-by-step explanation:
0 girls and 8 boys :
![\left(\begin{array}{c}10\\ 8\end{array}\right)=10*9*8*7*6*5*4*3/8!=45\\\\](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C%208%5Cend%7Barray%7D%5Cright%29%3D10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2F8%21%3D45%5C%5C%5C%5C)
1 girl and 7 boys:
![\left(\begin{array}{c}6\\ 1\end{array}\right)*\left(\begin{array}{c}10\\7\end{array}\right)=6*10*9*...*4/7!=6*120=720\\\\](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C%201%5Cend%7Barray%7D%5Cright%29%2A%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C7%5Cend%7Barray%7D%5Cright%29%3D6%2A10%2A9%2A...%2A4%2F7%21%3D6%2A120%3D720%5C%5C%5C%5C)
2 girl and 6 boys:
![\left(\begin{array}{c}6\\ 2\end{array}\right)*\left(\begin{array}{c}10\\6\end{array}\right)=60*210=1260\\](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C%202%5Cend%7Barray%7D%5Cright%29%2A%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C6%5Cend%7Barray%7D%5Cright%29%3D60%2A210%3D1260%5C%5C)
3 girl and 5 boys:
![\left(\begin{array}{c}6\\ 3\end{array}\right)*\left(\begin{array}{c}10\\5\end{array}\right)\\](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C%203%5Cend%7Barray%7D%5Cright%29%2A%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C5%5Cend%7Barray%7D%5Cright%29%5C%5C)
4 girls and 4 boys:
![\left(\begin{array}{c}6\\ 4\end{array}\right)*\left(\begin{array}{c}10\\4\end{array}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C%204%5Cend%7Barray%7D%5Cright%29%2A%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C4%5Cend%7Barray%7D%5Cright%29)
5 girls and 3 bys:
![\left(\begin{array}{c}6\\ 5\end{array}\right)*\left(\begin{array}{c}10\\3\end{array}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C%205%5Cend%7Barray%7D%5Cright%29%2A%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C3%5Cend%7Barray%7D%5Cright%29)
I let you to calculate and make the sum.
x^2 - 2x + 2
x = 1 + i
(1 + i)^2 - 2(1 + i) + 2
<em><u>Distributive property.</u></em>
(1 + i)(1 + i) - 2 - 2i + 2
<em><u>Continue distributive property on left side.</u></em>
1 + i + i + i^2 - 2 - 2i + 2
<em><u>Combine like terms.</u></em>
1 + 2i + i^2 - 2 - 2i + 2
1 + i^2
<em><u>i^2 can be interpreted as -1.</u></em>
1 - 1 = 0
The expression is equal to 0.
Answer:
2x-4. When you take a number- x- and add 2 of them -2x- and subtract 4 from it.
Answer:
x = 114
Step-by-step explanation:
Since p and q are parallel, the angle = 104° is equal to the angle = ( x - 10 )° by alternate exterior angles.
That means 104 = ( x - 10 )
+10 +10
= 114 = x
Sequence: 1, 3, 6, 10, 15, …
If sequence is arithmetic, ![\boxed{\sf \bold{second \ term = \dfrac{first \ term+third \ term}{2} }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20%5Cbold%7Bsecond%20%5C%20term%20%3D%20%5Cdfrac%7Bfirst%20%5C%20%20term%2Bthird%20%5C%20term%7D%7B2%7D%20%7D%7D)
If sequence is geometric, ![\boxed{\sf \bold{second \ term = \sqrt{first \ term \ * \ third \ term} }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20%5Cbold%7Bsecond%20%5C%20term%20%3D%20%5Csqrt%7Bfirst%20%5C%20term%20%5C%20%20%2A%20%5C%20third%20%5C%20term%7D%20%7D%7D)
<u>Check </u>for arithmetic:
![\sf \rightarrow 3 = \dfrac{1+6}{2}](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%203%20%3D%20%5Cdfrac%7B1%2B6%7D%7B2%7D)
Hence, the sequence is not arithmetic
<u>Check </u>for geometric:
![\sf \rightarrow 3 = \sqrt{1*6}](https://tex.z-dn.net/?f=%5Csf%20%5Crightarrow%203%20%3D%20%5Csqrt%7B1%2A6%7D)
Hence, the sequence is not geometric
Solution: