Answer:
![\cos(\alpha +\beta)=\frac{2}{3}(1-\frac{\sqrt{5}}{5})](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%20%2B%5Cbeta%29%3D%5Cfrac%7B2%7D%7B3%7D%281-%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B5%7D%29)
Step-by-step explanation:
Let the hypotenuse of the smaller triangle be h units.
Then; from the Pythagoras Theorem.
![h^2=4^2+2^2](https://tex.z-dn.net/?f=h%5E2%3D4%5E2%2B2%5E2)
![h^2=16+4](https://tex.z-dn.net/?f=h%5E2%3D16%2B4)
![h^2=20](https://tex.z-dn.net/?f=h%5E2%3D20)
![h=\sqrt{20}](https://tex.z-dn.net/?f=h%3D%5Csqrt%7B20%7D)
![h=2\sqrt{5}](https://tex.z-dn.net/?f=h%3D2%5Csqrt%7B5%7D)
From the smaller triangle;
and ![\sin(\alpha)=\frac{2}{2\sqrt{5} }=\frac{1}{\sqrt{5} }](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%29%3D%5Cfrac%7B2%7D%7B2%5Csqrt%7B5%7D%20%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B5%7D%20%7D)
From the second triangle, let the other other shorter leg of the second triangle be s units.
Then;
![s^2+4^2=6^2](https://tex.z-dn.net/?f=s%5E2%2B4%5E2%3D6%5E2)
![s^2+16=36](https://tex.z-dn.net/?f=s%5E2%2B16%3D36)
![s^2=36-16](https://tex.z-dn.net/?f=s%5E2%3D36-16)
![s^2=20](https://tex.z-dn.net/?f=s%5E2%3D20)
![s=\sqrt{20}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B20%7D)
![s=2\sqrt{5}](https://tex.z-dn.net/?f=s%3D2%5Csqrt%7B5%7D)
![\cos(\beta)=\frac{2\sqrt{5} }{6}=\frac{\sqrt{5} }{3}](https://tex.z-dn.net/?f=%5Ccos%28%5Cbeta%29%3D%5Cfrac%7B2%5Csqrt%7B5%7D%20%7D%7B6%7D%3D%5Cfrac%7B%5Csqrt%7B5%7D%20%7D%7B3%7D)
and
![\sin(\beta)=\frac{4}{6}=\frac{2}{3}](https://tex.z-dn.net/?f=%5Csin%28%5Cbeta%29%3D%5Cfrac%7B4%7D%7B6%7D%3D%5Cfrac%7B2%7D%7B3%7D)
We now use the double angle property;
![\cos(\alpha +\beta)=\cos(\alpha)\cos(\beta) -\sin(\alpha)\sin(\beta)](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%20%2B%5Cbeta%29%3D%5Ccos%28%5Calpha%29%5Ccos%28%5Cbeta%29%20-%5Csin%28%5Calpha%29%5Csin%28%5Cbeta%29)
we plug in the values to obtain;
![\cos(\alpha +\beta)=\frac{2}{\sqrt{5} }\times \frac{\sqrt{5} }{3}-\frac{1}{\sqrt{5} }\times \frac{2}{3}](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%20%2B%5Cbeta%29%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B5%7D%20%7D%5Ctimes%20%5Cfrac%7B%5Csqrt%7B5%7D%20%7D%7B3%7D-%5Cfrac%7B1%7D%7B%5Csqrt%7B5%7D%20%7D%5Ctimes%20%5Cfrac%7B2%7D%7B3%7D)
![\cos(\alpha +\beta)=\frac{2}{3}(1-\frac{\sqrt{5}}{5})](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%20%2B%5Cbeta%29%3D%5Cfrac%7B2%7D%7B3%7D%281-%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B5%7D%29)
Answer:
1. 3/4
2. 1/2
3. 7/12
4. 2/3
5. 1/12
6. 1/2
7. 39/8
8. 59/10
Step-by-step explanation:
For this case, the first thing we must do is define a variable.
We have then:
x: real number
Now we write the expression:
-8 / (x + 3)
The number x can be all real different from minus three.
Answer:
-8 / (x + 3)
With x different from -3.
Answer:
Part A
The probability of the treatment groups mean being greater than the control group mean by 8points or more = (26+8+2)/1000 = 0.036
Part B
Yes, the result is statistically significant because the probability of the difference being 8point or more is less than 5% significant level
Part C
The answers is 0.036 means that there is a very little chance of obtaining difference of 8points or more by random chance. So, if the difference between treatment group mean and control group mean is at least 8 , then the result is significant which means protein shaken is actually helpful in speeding up the weight-10 process