Answer:
4 to the 2nd power is the equivalent to 2 to the 4th power
Step-by-step explanation:
2⁴ = 16 = 4²
If you would like to solve the equation 3 * (3 * x - 1) + 2 * (3 - x) = 0, you can calculate this using the following steps:
3 * (3 * x - 1) + 2 * (3 - x) = 0
3 * 3 * x - 3 * 1 + 2 * 3 - 2 * x = 0
9 * x - 3 + 6 - 2 * x = 0
7 * x + 3 = 0
7 * x = - 3 /7
x = - 3/7
The correct result would be - 3/7.
Answer:
12 two times or 4 eight times
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:
5 rolls of ribbon are needed
Step-by-step explanation:
To find how much ribbon you'll use, multiply 80 by 2 3/4. To multiply them, convert 2 3/4 into an improper fraction 11/4.
Multiply: 80 * 11/4 = 880/4 = 220
This means you need 220 total feet of ribbon. Since each roll has 50 feet, you'll need 5 rolls or 250 feet to wrap every box.
