Answer:
(2)
Step-by-step explanation:
Our logarithmic expression is:
.
Remember the logarithmic property that ln(a/b) = lna - lnb. So, we can write this as:
![ln(\frac{\sqrt{e} }{y^3} )=ln(\sqrt{e} )-ln(y^3)](https://tex.z-dn.net/?f=ln%28%5Cfrac%7B%5Csqrt%7Be%7D%20%7D%7By%5E3%7D%20%29%3Dln%28%5Csqrt%7Be%7D%20%29-ln%28y%5E3%29)
Also, we can write square roots as powers of one-half, so √e =
. There's another log property that:
. We can apply that here for both the √e and the y³:
![ln(\sqrt{e} )-ln(y^3)=\frac{1}{2} ln(e)-3ln(y)](https://tex.z-dn.net/?f=ln%28%5Csqrt%7Be%7D%20%29-ln%28y%5E3%29%3D%5Cfrac%7B1%7D%7B2%7D%20ln%28e%29-3ln%28y%29)
Finally, note that ln(e) is just 1, so we have:
![\frac{1}{2} ln(e)-3ln(y)=\frac{1}{2} -3ln(y)=\frac{1-6ln(y)}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20ln%28e%29-3ln%28y%29%3D%5Cfrac%7B1%7D%7B2%7D%20-3ln%28y%29%3D%5Cfrac%7B1-6ln%28y%29%7D%7B2%7D)
The answer is thus (2).
<em>~ an aesthetics lover</em>
Answer:
6x+2
-2x+1
=
4x+1
just find the area of each and subtract the non-shaded one from the shades area.
Answer:
The 90% confidence interval of the population proportion is (0.6523, 0.7477).
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 = 250, \pi = \frac{X}{n} = \frac{175}{250} = 0.7](https://tex.z-dn.net/?f=n%20%3D%20250%2C%20%5Cpi%20%3D%20%5Cfrac%7BX%7D%7Bn%7D%20%3D%20%5Cfrac%7B175%7D%7B250%7D%20%3D%200.7)
90% 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}} = 0.7 - 1.645\sqrt{\frac{0.7*0.3}{250}} = 0.6523](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.7%20-%201.645%5Csqrt%7B%5Cfrac%7B0.7%2A0.3%7D%7B250%7D%7D%20%3D%200.6523)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7 + 1.645\sqrt{\frac{0.7*0.3}{250}} = 0.7477](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.7%20%2B%201.645%5Csqrt%7B%5Cfrac%7B0.7%2A0.3%7D%7B250%7D%7D%20%3D%200.7477)
The 90% confidence interval of the population proportion is (0.6523, 0.7477).
The club made $16,214.72 at the fundraiser. you just add them together.