Answer:
Mizuki is here to help! The answer is D!
Step-by-step explanation:
Ok... So there are 24 students in the class and no other students in the class has the same name right? So the fraction should be  since there are three madisons, which will be 0.125!
 since there are three madisons, which will be 0.125!
Since three people have the same name, everyone else gets less probability of getting called so the answer would be D.
 
        
                    
             
        
        
        
A: tracy's family has greater valiablity because put the number in order
 
        
             
        
        
        
Answer:
−
6
=
3
7
n
Step-by-step explanation:
Rewrite the equation as  
3
7
n
=
−
6
.
3
7
n
=
−
6
Multiply both sides of the equation by  
7
3
.
7
3
⋅
3
7
⋅
n
=
7
3
⋅
−
6
Simplify both sides of the equation.
Tap for more steps...
n
=
−
14
 
        
                    
             
        
        
        
Answer:
9 terms
Step-by-step explanation:
Given:  
1, 8, 28, 56, ..., 1
Required
Determine the number of sequence
To determine the number of sequence, we need to understand how the sequence are generated
The sequence are generated using
![\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dn%26%26r%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D)
Where n = 8 and r = 0,1....8
When r = 0
![\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%260%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-0%29%210%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B8%210%21%7D%20%3D%201)
When r = 1
![\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%261%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-1%29%211%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B7%211%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%21%7D%7B7%21%20%2A%201%7D%20%3D%20%5Cfrac%7B8%7D%7B1%7D%20%3D%208)
When r = 2
![\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%262%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-2%29%212%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B6%212%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%21%7D%7B6%21%20%2A%202%20%2A1%7D%20%3D%20%5Cfrac%7B8%20%2A%207%7D%7B2%20%2A1%7D%20%3D2%208)
When r = 3
![\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%263%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-3%29%213%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B5%213%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%20%2A%205%21%7D%7B5%21%20%2A3%2A%202%20%2A1%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%7D%7B3%20%2A2%20%2A1%7D%20%3D%2056)
When r = 4
![\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%264%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-4%29%214%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B4%213%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%20%2A%205%20%2A%204%21%7D%7B4%21%20%2A4%2A3%2A%202%20%2A1%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%2A5%7D%7B4%2A3%20%2A2%20%2A1%7D%20%3D%2070)
When r = 5
![\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%265%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-5%29%215%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B5%213%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%20%2A%205%21%7D%7B5%21%20%2A3%2A%202%20%2A1%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%7D%7B3%20%2A2%20%2A1%7D%20%3D%2056)
When r = 6
![\left[\begin{array}{c}8&&6\end{array}\right] = \frac{8!}{(8-6)!6!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} = 28](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-6%29%216%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B6%212%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%21%7D%7B6%21%20%2A%202%20%2A1%7D%20%3D%20%5Cfrac%7B8%20%2A%207%7D%7B2%20%2A1%7D%20%3D%2028)
When r = 7
![\left[\begin{array}{c}8&&7\end{array}\right] = \frac{8!}{(8-7)!7!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%267%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-7%29%217%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B7%211%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%21%7D%7B7%21%20%2A%201%7D%20%3D%20%5Cfrac%7B8%7D%7B1%7D%20%3D%208)
When r = 8
![\left[\begin{array}{c}8&&8\end{array}\right] = \frac{8!}{(8-8)!8!} = \frac{8!}{8!0!} = 1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%268%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-8%29%218%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B8%210%21%7D%20%3D%201)
The full sequence is: 1,8,28,56,70,56,28,8,1
And the number of terms is 9
 
        
             
        
        
        
Answer:
-4096
Step-by-step explanation:
8,-16,32,-64,128,-256,512,-1024,2048.-4096