![\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\\\ tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\\\\ -----------------------------\\\\ 2cos(A)=3tan(A)\implies 2cos(A)=3\cfrac{sin(A)}{cos(A)} \\\\\\ 2cos^2(A)=3sin(A)\implies 2[1-sin^2(A)]=3sin(A) \\\\\\ 2-2sin^2(A)=3sin(A)\implies 2sin^2(A)+3sin(A)-2](https://tex.z-dn.net/?f=%5Cbf%20sin%5E2%28%5Ctheta%29%2Bcos%5E2%28%5Ctheta%29%3D1%5Cimplies%20cos%5E2%28%5Ctheta%29%3D1-sin%5E2%28%5Ctheta%29%0A%5C%5C%5C%5C%5C%5C%0Atan%28%5Ctheta%29%3D%5Ccfrac%7Bsin%28%5Ctheta%29%7D%7Bcos%28%5Ctheta%29%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%0A2cos%28A%29%3D3tan%28A%29%5Cimplies%202cos%28A%29%3D3%5Ccfrac%7Bsin%28A%29%7D%7Bcos%28A%29%7D%0A%5C%5C%5C%5C%5C%5C%0A2cos%5E2%28A%29%3D3sin%28A%29%5Cimplies%202%5B1-sin%5E2%28A%29%5D%3D3sin%28A%29%0A%5C%5C%5C%5C%5C%5C%0A2-2sin%5E2%28A%29%3D3sin%28A%29%5Cimplies%202sin%5E2%28A%29%2B3sin%28A%29-2)
![\bf \\\\\\ 0=[2sin(A)-1][sin(A)+2]\implies \begin{cases} 0=2sin(A)-1\\ 1=2sin(A)\\ \frac{1}{2}=sin(A)\\\\ sin^{-1}\left( \frac{1}{2} \right)=\measuredangle A\\\\ \frac{\pi }{6},\frac{5\pi }{6}\\ ----------\\ 0=sin(A)+2\\ -2=sin(A) \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5C%5C%5C%5C%5C%5C%0A0%3D%5B2sin%28A%29-1%5D%5Bsin%28A%29%2B2%5D%5Cimplies%20%0A%5Cbegin%7Bcases%7D%0A0%3D2sin%28A%29-1%5C%5C%0A1%3D2sin%28A%29%5C%5C%0A%5Cfrac%7B1%7D%7B2%7D%3Dsin%28A%29%5C%5C%5C%5C%0Asin%5E%7B-1%7D%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%3D%5Cmeasuredangle%20A%5C%5C%5C%5C%0A%5Cfrac%7B%5Cpi%20%7D%7B6%7D%2C%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5C%5C%0A----------%5C%5C%0A0%3Dsin%28A%29%2B2%5C%5C%0A-2%3Dsin%28A%29%0A%5Cend%7Bcases%7D)
now, as far as the second case....well, sine of anything is within the range of -1 or 1, so -1 < sin(A) < 1
now, we have -2 = sin(A), which simply is out of range for a valid sine, so there's no angle with such sine
so, only the first case are the valid angles for A
Answer:
5/4
Step-by-step explanation:
Make a proportion:
16/4 = 5/x
Cross Multiply:
20 = 16x
x = 5/4
Answer: <em>50°</em>
Step-by-step explanation:
<em>Since angle 3 is in a right triangle we can assume one angle is 90°</em><em> </em><em>and then the other missing angle will be 40°</em>
<em>Because you take 180°-140°(the angle next to it) which will equal 40°</em>
<em>Now every triangle must add up to 180°</em>
<em>so lets take the angles we have now</em>
<em>90° +40°=130°</em>
<em>now take that 130°</em>
<em>180°-130°=</em><em>50°</em>
<em>Now check your work</em>
90°+40°+50°=180°
Angle 3 is 50°
Answer:
<h2>Option 2 is the right answer.</h2>
Step-by-step explanation:
We need to check if the two characteristics, <u>having blue eyes and being deaf are independent of each other or not</u>.
The above two characteristics will be independent if ![[Probability of being deaf with blue eyes] = {Probability of being deaf } {Probability of having blue eyes}](https://tex.z-dn.net/?f=%5BProbability%20of%20being%20deaf%20with%20blue%20eyes%5D%20%3D%20%7BProbability%20of%20being%20deaf%20%7D%20%7BProbability%20of%20having%20blue%20eyes%7D)
Now, the probability of having blue eyes is 
.
The probability that the Dalmatians will be deaf is 
.
The probability of being deaf with blue eyes is 
.
Since, 38 is not equals to 42, the two characteristics are not independent.
Answer:
6
Step-by-step explanation:
quarter and 1
quarter and 2
quarter and 3
quarter and 4
quarter and 5
quarter and 6
