Answer:
64 is the perfect square
Step-by-step explanation:
its the perfect square because the square root is 8 and 8 is a whole number therefore 64 is the perfect square here.
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Answer:
There are 220 choices
Step-by-step explanation:
Given
![People = 12](https://tex.z-dn.net/?f=People%20%3D%2012)
(President, Treasurer and Secretary)
Required
Determine number of selection (if no restriction)
This is calculated using the following combination formula:
![^nC_r = \frac{n!}{(n - r)!r!}](https://tex.z-dn.net/?f=%5EnC_r%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n%20-%20r%29%21r%21%7D)
Where
![n = 12](https://tex.z-dn.net/?f=n%20%3D%2012)
![r= 3](https://tex.z-dn.net/?f=r%3D%203)
So, we have:
![^nC_r = \frac{n!}{(n - r)!r!}](https://tex.z-dn.net/?f=%5EnC_r%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n%20-%20r%29%21r%21%7D)
![^{12}C_3 = \frac{12!}{(12 - 3)!3!}](https://tex.z-dn.net/?f=%5E%7B12%7DC_3%20%3D%20%5Cfrac%7B12%21%7D%7B%2812%20-%203%29%213%21%7D)
![^{12}C_3 = \frac{12!}{9!3!}](https://tex.z-dn.net/?f=%5E%7B12%7DC_3%20%3D%20%5Cfrac%7B12%21%7D%7B9%213%21%7D)
![^{12}C_3 = \frac{12*11*10*9!}{9!3!}](https://tex.z-dn.net/?f=%5E%7B12%7DC_3%20%3D%20%5Cfrac%7B12%2A11%2A10%2A9%21%7D%7B9%213%21%7D)
![^{12}C_3 = \frac{12*11*10}{3!}](https://tex.z-dn.net/?f=%5E%7B12%7DC_3%20%3D%20%5Cfrac%7B12%2A11%2A10%7D%7B3%21%7D)
![^{12}C_3 = \frac{12*11*10}{3*2*1}](https://tex.z-dn.net/?f=%5E%7B12%7DC_3%20%3D%20%5Cfrac%7B12%2A11%2A10%7D%7B3%2A2%2A1%7D)
![^{12}C_3 = \frac{12*11*10}{6}](https://tex.z-dn.net/?f=%5E%7B12%7DC_3%20%3D%20%5Cfrac%7B12%2A11%2A10%7D%7B6%7D)
![^{12}C_3 = 2*11*10](https://tex.z-dn.net/?f=%5E%7B12%7DC_3%20%3D%202%2A11%2A10)
![^{12}C_3 = 220\ ways](https://tex.z-dn.net/?f=%5E%7B12%7DC_3%20%3D%20220%5C%20ways)
<em>There are 220 choices</em>
Answer:
The answer to this inequality would be x>2
In order to form triangle PQT and quadrilateral TQRS, point T must lie on line PS which is 16 cm. long.
If the ratio of PT to TS is 5:3 and the total length of PS is 16, then PT must be 10 and TS must be 6 (10 + 6 =16) and 10:6 is the same ratio as 5:3. Another way to think about it is 5/3 = 10/6.
Now you have all the lengths that you need to find the areas of the quadrilateral and the triangle.
Make sure you draw a diagram of it!!
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