8:
A line can intersect a circle twice. So, two lines intersect one circle 4 times. Two lines can intersect two circles 8 times.
Hope this helps!
Answer:
centroid of the triangle
Step-by-step explanation:
centroid of the triangle
Answer:
The correct option is (a) 0.9780.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
![\mu_{\hat p}=p](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%20p%7D%3Dp)
The standard deviation of this sampling distribution of sample proportion is:
![\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%20p%7D%3D%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D)
As the sample selected is quite large, i.e. <em>n</em> = 110 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample proportion by a Normal distribution.
The mean and standard deviation are:
![\mu_{\hat p}=p=0.70\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.70(1-0.70)}{110}}=0.044](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%20p%7D%3Dp%3D0.70%5C%5C%5C%5C%5Csigma_%7B%5Chat%20p%7D%3D%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%3D%5Csqrt%7B%5Cfrac%7B0.70%281-0.70%29%7D%7B110%7D%7D%3D0.044)
Compute the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 as follows:
![P(0.60](https://tex.z-dn.net/?f=P%280.60%3C%5Chat%20p%3C0.80%29%3DP%28%5Cfrac%7B0.60-0.70%7D%7B0.044%7D%3C%5Cfrac%7B%5Chat%20p-%5Cmu_%7B%5Chat%20p%7D%7D%7B%5Csigma_%7B%5Chat%20p%7D%7D%3C%5Cfrac%7B0.80-0.70%7D%7B0.044%7D%29)
![=P(-2.27](https://tex.z-dn.net/?f=%3DP%28-2.27%3CZ%3C2.27%29%5C%5C%5C%5C%3DP%28Z%3C2.27%29-P%28Z%3C-2.27%29%5C%5C%5C%5C%3D0.98840-0.01160%5C%5C%5C%5C%3D0.9768%5C%5C%5C%5C%5Capprox0.9780)
*Use a <em>z</em>-table.
Thus, the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 is approximately equal to 0.9780.
The correct option is (a).
Answer:
c = 3(b + 1)
Step-by-step explanation:
c = 4b - 1b + 3
4b - 1b = 3b
c = 3b + 3
3 is a common factor of both terms on the right hand side
Factorizing the expression
c = 3(b + 1)