y-intercept is -6 (0,-6) and the x-intercept is -3 (-3,0)
Answer: 0.52
Step-by-step explanation: 8 out of the 15 years were in the 90s. So 8/15 is 0.52
Answer:
a. Fail to reject the null hypothesis.
Step-by-step explanation:
Here we test the claim that proportion of reachers is really 41%
![H_0: p =0.41\\H_a: p \neq 0.41](https://tex.z-dn.net/?f=H_0%3A%20p%20%3D0.41%5C%5CH_a%3A%20p%20%5Cneq%200.41)
(Two tailed test at 1% significance level)
Observed proportion = 0.36
Sample size n = 100
Std error of proportion = ![\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.41*0.59}{100} } \\=0.0492](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D%20%5C%5C%3D%5Csqrt%7B%5Cfrac%7B0.41%2A0.59%7D%7B100%7D%20%7D%20%5C%5C%3D0.0492)
p difference = 0.36-0.41 =- 0.05
Test statistic Z = p diff/std error =-1.0166
p value=0.286
Since p >0.01 we accept null hypothesis.
a. Fail to reject the null hypothesis.
Recall the fundamental rule of trig:
![\sin^2(x)+\cos^2(x)=1 \quad\forall x \in \mathbb{R}](https://tex.z-dn.net/?f=%5Csin%5E2%28x%29%2B%5Ccos%5E2%28x%29%3D1%20%5Cquad%5Cforall%20x%20%5Cin%20%5Cmathbb%7BR%7D)
So, there exists an angle
such that
![(0.6,0.35)=(\sin(t),\cos(t))](https://tex.z-dn.net/?f=%280.6%2C0.35%29%3D%28%5Csin%28t%29%2C%5Ccos%28t%29%29)
if and only if
![\sin^2(t)+\cos^2(t)=0.6^2+0.35^2=1](https://tex.z-dn.net/?f=%5Csin%5E2%28t%29%2B%5Ccos%5E2%28t%29%3D0.6%5E2%2B0.35%5E2%3D1)
Working out the numbers, we get
![0.6^2+0.35^2=0.36+0.1225=0.4825\neq 1](https://tex.z-dn.net/?f=0.6%5E2%2B0.35%5E2%3D0.36%2B0.1225%3D0.4825%5Cneq%201)
So, there doesn't exist a number
such that
![(0.6,0.35)=(\sin(t),\cos(t))](https://tex.z-dn.net/?f=%280.6%2C0.35%29%3D%28%5Csin%28t%29%2C%5Ccos%28t%29%29)