Answer:
1000
Step-by-step explanation:
if you were rounding it would be 1380, 1400, or 1000 because it isn't over 5
Answer: D
Step-by-step explanation:
Answer:
This is your teacher if you do this again, I will contact your parents and you will get in big trouble.
Step-by-step explanation:
SOH CAH TOA tells you
... cos(B) = a/c
... 4/5 = 8/c
... c = 10 . . . . . multiply by 5c/4
By the Pythagorean theorem,
... b = √c² -a²) = √(10² -8²) = √36 = 6
The lengths of the other two sides are: b = 6, c = 10.
_____
You can tell from the value of the cosine that this is a 3-4-5 right triangle. You can tell from the value of "a" that the scale factor is 2. That means the other two sides are 6 and 10.
Answer:
![Selection = 67249\ ways](https://tex.z-dn.net/?f=Selection%20%3D%2067249%5C%20ways)
Step-by-step explanation:
Given
![Men = 8](https://tex.z-dn.net/?f=Men%20%3D%208)
![Women = 15](https://tex.z-dn.net/?f=Women%20%3D%2015)
![Committee = 6](https://tex.z-dn.net/?f=Committee%20%3D%206)
Required
Determine the number of selections if the committee must have more women
To have more women, the selection has to be:
(4 women and 2 men) or (5 women and 1 man) or (6 women and 0 man)
Where each selection is calculated using:
![^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)
So, the selection is calculated as thus:
![Selection = (^{15}C_4 * ^{8}C_2) + (^{15}C_5 * ^{8}C_1) + (^{15}C_6 * ^{8}C_0)](https://tex.z-dn.net/?f=Selection%20%3D%20%28%5E%7B15%7DC_4%20%20%2A%20%5E%7B8%7DC_2%29%20%2B%20%28%5E%7B15%7DC_5%20%20%2A%20%5E%7B8%7DC_1%29%20%2B%20%28%5E%7B15%7DC_6%20%20%2A%20%5E%7B8%7DC_0%29)
![Selection = (\frac{15!}{(15 - 4)!4!} * \frac{8!}{(8 - 2)!2!}) + (\frac{15!}{(15 - 5)!5!} * \frac{8!}{(8 - 1)!1!}) + (\frac{15!}{(15 - 6)!6!} * \frac{8!}{(8 - 0)!0!})](https://tex.z-dn.net/?f=Selection%20%3D%20%28%5Cfrac%7B15%21%7D%7B%2815%20-%204%29%214%21%7D%20%2A%20%5Cfrac%7B8%21%7D%7B%288%20-%202%29%212%21%7D%29%20%2B%20%28%5Cfrac%7B15%21%7D%7B%2815%20-%205%29%215%21%7D%20%2A%20%5Cfrac%7B8%21%7D%7B%288%20-%201%29%211%21%7D%29%20%2B%20%28%5Cfrac%7B15%21%7D%7B%2815%20-%206%29%216%21%7D%20%2A%20%5Cfrac%7B8%21%7D%7B%288%20-%200%29%210%21%7D%29)
![Selection = (\frac{15!}{11!4!} * \frac{8!}{6!2!}) + (\frac{15!}{10!5!} * \frac{8!}{7!1!}) + (\frac{15!}{9!6!} * \frac{8!}{8!0!})](https://tex.z-dn.net/?f=Selection%20%3D%20%28%5Cfrac%7B15%21%7D%7B11%214%21%7D%20%2A%20%5Cfrac%7B8%21%7D%7B6%212%21%7D%29%20%2B%20%28%5Cfrac%7B15%21%7D%7B10%215%21%7D%20%2A%20%5Cfrac%7B8%21%7D%7B7%211%21%7D%29%20%2B%20%28%5Cfrac%7B15%21%7D%7B9%216%21%7D%20%2A%20%5Cfrac%7B8%21%7D%7B8%210%21%7D%29)
![Selection = (\frac{15 * 14 * 13 * 12}{4 * 3 * 2 * 1} * \frac{8 * 7}{2 * 1}) + (\frac{15 * 14 * 13 * 12 * 11}{5*4*3*2*1} * \frac{8}{1}) + (\frac{15 * 14 * 13 * 12 * 11 * 10}{6*5*4*3*2*1} * \frac{1}{1})](https://tex.z-dn.net/?f=Selection%20%3D%20%28%5Cfrac%7B15%20%2A%2014%20%2A%2013%20%2A%2012%7D%7B4%20%2A%203%20%2A%202%20%2A%201%7D%20%2A%20%5Cfrac%7B8%20%2A%207%7D%7B2%20%2A%201%7D%29%20%2B%20%28%5Cfrac%7B15%20%2A%2014%20%2A%2013%20%2A%2012%20%2A%2011%7D%7B5%2A4%2A3%2A2%2A1%7D%20%2A%20%5Cfrac%7B8%7D%7B1%7D%29%20%2B%20%28%5Cfrac%7B15%20%2A%2014%20%2A%2013%20%2A%2012%20%2A%2011%20%2A%2010%7D%7B6%2A5%2A4%2A3%2A2%2A1%7D%20%2A%20%5Cfrac%7B1%7D%7B1%7D%29)
![Selection = (\frac{32760}{24} * \frac{56}{2}) + (\frac{360360}{120} * 8) + (\frac{3603600}{720})](https://tex.z-dn.net/?f=Selection%20%3D%20%28%5Cfrac%7B32760%7D%7B24%7D%20%2A%20%5Cfrac%7B56%7D%7B2%7D%29%20%2B%20%28%5Cfrac%7B360360%7D%7B120%7D%20%2A%208%29%20%2B%20%28%5Cfrac%7B3603600%7D%7B720%7D%29)
![Selection = (1365 * 28) + (3003 * 8) + (5005)](https://tex.z-dn.net/?f=Selection%20%3D%20%281365%20%2A%2028%29%20%2B%20%283003%20%2A%208%29%20%2B%20%285005%29)
![Selection = 38220 + 24024 + 5005](https://tex.z-dn.net/?f=Selection%20%3D%2038220%20%2B%2024024%20%2B%205005)
![Selection = 67249\ ways](https://tex.z-dn.net/?f=Selection%20%3D%2067249%5C%20ways)