Answer:
30+2+.8+.07+.004
Step-by-step explanation:
i mathed then i mathed then i ate then i mathed some more
Answer:
0.4060
Step-by-step explanation:
To calculate the sample proportion, phat, we take the ratio of the number of preferred outcome to the total number of trials ;
Phat = number of times coin lands on head (preferred outcome), x / total number of trials (total coin flips), n
x = 406
n = 1000
Phat = x / n = 406/ 1000 = 0.4060
![\int_{0}^{1}\frac{1}{1+x^2}dx](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7B1%7D%5Cfrac%7B1%7D%7B1%2Bx%5E2%7Ddx)
The integral above is definite so we must first calculate for indefinite one.
![\int{\frac{1}{1+x^2}dx}](https://tex.z-dn.net/?f=%5Cint%7B%5Cfrac%7B1%7D%7B1%2Bx%5E2%7Ddx%7D)
Rule:
![\int{\frac{1}{a^2+b^2}dx}=\frac{1}{b}\times\arctan(\frac{a}{b})](https://tex.z-dn.net/?f=%5Cint%7B%5Cfrac%7B1%7D%7Ba%5E2%2Bb%5E2%7Ddx%7D%3D%5Cfrac%7B1%7D%7Bb%7D%5Ctimes%5Carctan%28%5Cfrac%7Ba%7D%7Bb%7D%29)
.
Now we apply this rule and get:
![\int{\frac{1}{1+x^2}}=\frac{1}{1}\times\arctan(\frac{x}{1})](https://tex.z-dn.net/?f=%5Cint%7B%5Cfrac%7B1%7D%7B1%2Bx%5E2%7D%7D%3D%5Cfrac%7B1%7D%7B1%7D%5Ctimes%5Carctan%28%5Cfrac%7Bx%7D%7B1%7D%29)
Or just simply:
![\arctan(x)](https://tex.z-dn.net/?f=%5Carctan%28x%29)
Now we integrate:
![\arctan(x)\Big\vert_{0}^{1}](https://tex.z-dn.net/?f=%5Carctan%28x%29%5CBig%5Cvert_%7B0%7D%5E%7B1%7D)
![\arctan(1)-\arctan(0)](https://tex.z-dn.net/?f=%5Carctan%281%29-%5Carctan%280%29)
Pythagorean theorem
A^2 + 144 = 169
A^2 = 25
A = 5in.