Answer:
try the third option
Step-by-step explanation:
At least I'm trying
Px + qy = r
2px - qy = 2r
----------------add
3px = 3r
x = 3r/3p
x = r/p
You need to first set up the equation:
It would look like 90 divided by 360 multiplied by the given
circumference which is 72 cm.
So 90 / 360 x 72
Simply the fraction above, it will give us:
¼ x 72
So the answer would be 18 cm that is the length of DE (minor
arc)
Answer:
Option 2 is right
Step-by-step explanation:
Given that

We can write this in polar form with modulus and radius

Hence angle = 60 degrees and

Since we have got 5 roots for z, we can write 60, 420, 780, etc. with periods of 360
Using Demoivre theorem we get 5th root would be
5th root of 2 multiplied by 1/5 th of 60, 420, 780,....
![z= \sqrt[5]{2} (cos12+isin12)\\z=\sqrt[5]{2} (cos84+isin84)\\\\z=\sqrt[5]{2} (cos156+isin156)\\\\z=\sqrt[5]{2} (cos228+isin228)\\\\z=\sqrt[5]{2} (cos300+isin300)\\](https://tex.z-dn.net/?f=z%3D%20%5Csqrt%5B5%5D%7B2%7D%20%28cos12%2Bisin12%29%5C%5Cz%3D%5Csqrt%5B5%5D%7B2%7D%20%28cos84%2Bisin84%29%5C%5C%5C%5Cz%3D%5Csqrt%5B5%5D%7B2%7D%20%28cos156%2Bisin156%29%5C%5C%5C%5Cz%3D%5Csqrt%5B5%5D%7B2%7D%20%28cos228%2Bisin228%29%5C%5C%5C%5Cz%3D%5Csqrt%5B5%5D%7B2%7D%20%28cos300%2Bisin300%29%5C%5C)
Out of these only 2nd option suits our answer
Hence answer is Option 2.
Answer:
Step-by-step explanation:
Given that a fair coin is flipped twelve times.
It means the number of possible sequences of heads and tails would be:
2¹² = 4096
We can determine the number of ways that such a sequence could contain exactly 9 tails is the number of ways of choosing 9 out of 12, using the formula

Plug in n = 12 and r = 9


∵ 
∵ 

Thus, the probability will be:



Thus, the probability of the coin landing tails up exactly nine times will be: