For this case we have that by definition, the slope of a line is given by:
![m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%20%7By_%20%7B2%7D%20-y_%20%7B1%7D%7D%20%7Bx_%20%7B2%7D%20-x_%20%7B1%7D%7D)
Where:
and
are two points through which the line passes.
According to the image we have:
![(x_ {1}, y_ {1}): (-5,3)\\(x_ {2}, y_ {2}): (3, -3)](https://tex.z-dn.net/?f=%28x_%20%7B1%7D%2C%20y_%20%7B1%7D%29%3A%20%28-5%2C3%29%5C%5C%28x_%20%7B2%7D%2C%20y_%20%7B2%7D%29%3A%20%283%2C%20-3%29)
Substituting we have:
![m = \frac {-3-3} {3 - (- 5)} = \frac {-6} {3 + 5} = \frac {-6} {8} = - \frac {3} {4}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%20%7B-3-3%7D%20%7B3%20-%20%28-%205%29%7D%20%3D%20%5Cfrac%20%7B-6%7D%20%7B3%20%2B%205%7D%20%3D%20%5Cfrac%20%7B-6%7D%20%7B8%7D%20%3D%20-%20%5Cfrac%20%7B3%7D%20%7B4%7D)
Thus, the slope of the line is:
![m = - \frac {3} {4}](https://tex.z-dn.net/?f=m%20%3D%20-%20%5Cfrac%20%7B3%7D%20%7B4%7D)
Answer:
![m = - \frac {3} {4}](https://tex.z-dn.net/?f=m%20%3D%20-%20%5Cfrac%20%7B3%7D%20%7B4%7D)
Answer:
0.15
Step-by-step explanation:
6 divided by 24 equals 0.25
12 divided by 30 equals 0.4
0.4 minus 0.25 is 0.15
Answer:
There is a significant difference between the two proportions.
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for difference between population proportions is:
![CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}](https://tex.z-dn.net/?f=CI%3D%28%5Chat%20p_%7B1%7D-%5Chat%20p_%7B2%7D%29%5Cpm%20z_%7B%5Calpha%2F2%7D%5Ctimes%5Csqrt%7B%5Cfrac%7B%5Chat%20p_%7B1%7D%281-%5Chat%20p_%7B1%7D%29%7D%7Bn_%7B1%7D%7D%2B%5Cfrac%7B%5Chat%20p_%7B2%7D%281-%5Chat%20p_%7B2%7D%29%7D%7Bn_%7B2%7D%7D%7D)
Compute the sample proportions as follows:
![\hat p_{1}=\frac{80}{250}=0.32\\\\\hat p_{2}=\frac{40}{175}=0.23](https://tex.z-dn.net/?f=%5Chat%20p_%7B1%7D%3D%5Cfrac%7B80%7D%7B250%7D%3D0.32%5C%5C%5C%5C%5Chat%20p_%7B2%7D%3D%5Cfrac%7B40%7D%7B175%7D%3D0.23)
The critical value of <em>z</em> for 90% confidence interval is:
![z_{0.10/2}=z_{0.05}=1.645](https://tex.z-dn.net/?f=z_%7B0.10%2F2%7D%3Dz_%7B0.05%7D%3D1.645)
Compute a 90% confidence interval for the difference between the proportions of women in these two fields of engineering as follows:
![CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}](https://tex.z-dn.net/?f=CI%3D%28%5Chat%20p_%7B1%7D-%5Chat%20p_%7B2%7D%29%5Cpm%20z_%7B%5Calpha%2F2%7D%5Ctimes%5Csqrt%7B%5Cfrac%7B%5Chat%20p_%7B1%7D%281-%5Chat%20p_%7B1%7D%29%7D%7Bn_%7B1%7D%7D%2B%5Cfrac%7B%5Chat%20p_%7B2%7D%281-%5Chat%20p_%7B2%7D%29%7D%7Bn_%7B2%7D%7D%7D)
![=(0.32-0.23)\pm 1.645\times\sqrt{\frac{0.32(1-0.32)}{250}+\frac{0.23(1-0.23)}{175}}\\\\=0.09\pm 0.0714\\\\=(0.0186, 0.1614)\\\\\approx (0.02, 0.16)](https://tex.z-dn.net/?f=%3D%280.32-0.23%29%5Cpm%201.645%5Ctimes%5Csqrt%7B%5Cfrac%7B0.32%281-0.32%29%7D%7B250%7D%2B%5Cfrac%7B0.23%281-0.23%29%7D%7B175%7D%7D%5C%5C%5C%5C%3D0.09%5Cpm%200.0714%5C%5C%5C%5C%3D%280.0186%2C%200.1614%29%5C%5C%5C%5C%5Capprox%20%280.02%2C%200.16%29)
There will be no difference between the two proportions if the 90% confidence interval consists of 0.
But the 90% confidence interval does not consists of 0.
Thus, there is a significant difference between the two proportions.
S= Sydney
devaughn= s-13
so s+s-13=75
2s-13=75
now I think you can solve the rest.
Answer:
A literary work credited with advancing ancient Indian civilization because it set rules for the organization of Buddhist monasteries.
Step-by-step explanation: