Point A shows that she is incorrect.
With functions, you can perform the "straight line test through each point. If the line goes through both points, you know it's not a function.
If we plotted point A, it'd fail the straight line test because the given point (-6, 7) already has -6 as an x value.
Hope this helps!
Angle1 +angle2+angle3=180(property of triangle)
Angle1+angel2=angle3(according to question)
Thus,
Angle3+angle3=180
2*angle3=180
Angle3=90
Means this is a right triangle
Now,we can use formula
Side1^2+side2^2=side3^2
Thus,
4*4+5*5=side3^2
Square root(36)=side3
Side3=6
Answer:
The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the zscore that has a pvalue of
.
For this problem, we have that:
![n = 2305, \pi = \frac{339}{2305} = 0.147](https://tex.z-dn.net/?f=n%20%3D%202305%2C%20%5Cpi%20%3D%20%5Cfrac%7B339%7D%7B2305%7D%20%3D%200.147)
95% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 - 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.133](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.147%20-%201.96%5Csqrt%7B%5Cfrac%7B0.147%2A0.853%7D%7B2305%7D%7D%20%3D%200.133)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 + 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.161](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.147%20%2B%201.96%5Csqrt%7B%5Cfrac%7B0.147%2A0.853%7D%7B2305%7D%7D%20%3D%200.161)
The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).