Answer:
y = lnx/ln12
Step-by-step explanation:
Given the function y = 12^x, to find the inverse of the function, we news to write x as a function of y as shown:
Given y = 12^x
Taking ln of both sides
ln y = ln 12^x
ln y = xln12
Divide both sides by ln12
lny/ln12 = xln12/ln12
x = lny/ln12
x = ln(y-12)
Replacing y with x and x with y
The inverse of the function will be:
y = lnx/ln12
Answer:
I think the answer is repeating because it'd be
0.55
Answer:
angles 3 and 4 both equal a 90 degree angle or bisect a 90 degree angle.
angle 5 is 44-degrees because it is complementary or vertical to the 44 degree angle.
x=32 because it is on the same line as the 44-degree angle and a line is 180 so 180-44=136 and to get the rest of x you would do the equation backwards so 136 divided by 4 is 34 and 36-2=32
angle a is 136 described above.
angle b, because it is on the same line as the 46 degree angle is 180-46=134
now im pooped :(
T= Mins
1 hour = 60 mins
60 x 6 = 360
360 - T = x
X= How many minutes he has remaining
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.