Using the z-distribution, it is found that 3,007 passengers must be surveyed.
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:
![\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:
is the sample proportion.
The margin of error is given by:
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In this problem, we have a 90% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 1.645.
In this problem, we desired a margin of error of M = 0.015, with no prior estimate, hence
, then we solve for n to find the minimum sample size.
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
![0.015 = 1.645\sqrt{\frac{0.5(0.5)}{n}}](https://tex.z-dn.net/?f=0.015%20%3D%201.645%5Csqrt%7B%5Cfrac%7B0.5%280.5%29%7D%7Bn%7D%7D)
![0.015\sqrt{n} = 1.645(0.5)](https://tex.z-dn.net/?f=0.015%5Csqrt%7Bn%7D%20%3D%201.645%280.5%29)
![\sqrt{n} = \frac{1.645(0.5)}{0.015}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.645%280.5%29%7D%7B0.015%7D)
![(\sqrt{n})^2 = \left(\frac{1.645(0.5)}{0.015}\right)^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%5Cleft%28%5Cfrac%7B1.645%280.5%29%7D%7B0.015%7D%5Cright%29%5E2)
n = 3007.
More can be learned about the z-distribution at brainly.com/question/25890103
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The radius and height, in two decimal places are mathematically given as
r=10.60
<h3>What is the radius and height, in two decimal places?</h3>
Generally, the equation for the volume is mathematically given as
![V=\pi r^{2} h+\frac{2}{3} \pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E%7B2%7D%20h%2B%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D)
Therefore
![5000 &=\pi 0^{2} h+\frac{2}{3} \pi r^{3}](https://tex.z-dn.net/?f=5000%20%26%3D%5Cpi%200%5E%7B2%7D%20h%2B%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D)
![V(r, h) &=\pi r^{2} h+\frac{2}{3} \pi r^{3}-5000 \\\nabla V &=\left\langle 2 \pi r h+2 \pi r^{2}, \pi r^{2}\right\rangle \\](https://tex.z-dn.net/?f=V%28r%2C%20h%29%20%26%3D%5Cpi%20r%5E%7B2%7D%20h%2B%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D-5000%20%5C%5C%5Cnabla%20V%20%26%3D%5Cleft%5Clangle%202%20%5Cpi%20r%20h%2B2%20%5Cpi%20r%5E%7B2%7D%2C%20%5Cpi%20r%5E%7B2%7D%5Cright%5Crangle%20%5C%5C)
![\cos t &=100\left(2 \pi r^{2}\right)+75(2 \pi r h) \\\\\cos t &=200 \pi r^{2}+150 \pi r h \\\\\nabla C(r, h) &=\langle 400 \pi r+150 \pi h, 150 \pi r\rangle](https://tex.z-dn.net/?f=%5Ccos%20t%20%26%3D100%5Cleft%282%20%5Cpi%20r%5E%7B2%7D%5Cright%29%2B75%282%20%5Cpi%20r%20h%29%20%5C%5C%5C%5C%5Ccos%20t%20%26%3D200%20%5Cpi%20r%5E%7B2%7D%2B150%20%5Cpi%20r%20h%20%5C%5C%5C%5C%5Cnabla%20C%28r%2C%20h%29%20%26%3D%5Clangle%20400%20%5Cpi%20r%2B150%20%5Cpi%20h%2C%20150%20%5Cpi%20r%5Crangle)
Using Lagrange method
![$\langle 400 \pi \gamma+150 \pi \gamma h, 150 \pi \gamma\rangle=\lambda\left\langle 2 \pi \gamma h+2 \pi \gamma^{2}, \pi r^{2}\right\rangle$](https://tex.z-dn.net/?f=%24%5Clangle%20400%20%5Cpi%20%5Cgamma%2B150%20%5Cpi%20%5Cgamma%20h%2C%20150%20%5Cpi%20%5Cgamma%5Crangle%3D%5Clambda%5Cleft%5Clangle%202%20%5Cpi%20%5Cgamma%20h%2B2%20%5Cpi%20%5Cgamma%5E%7B2%7D%2C%20%5Cpi%20r%5E%7B2%7D%5Cright%5Crangle%24)
![$400 \pi r+150 \pi r=\left(2 \pi r h+2 \pi r^{2}\right) \lambda$](https://tex.z-dn.net/?f=%24400%20%5Cpi%20r%2B150%20%5Cpi%20r%3D%5Cleft%282%20%5Cpi%20r%20h%2B2%20%5Cpi%20r%5E%7B2%7D%5Cright%29%20%5Clambda%24)
![$400 \pi \gamma+150 \pi h=300 \pi h+300 \pi r \\\\](https://tex.z-dn.net/?f=%24400%20%5Cpi%20%5Cgamma%2B150%20%5Cpi%20h%3D300%20%5Cpi%20h%2B300%20%5Cpi%20r%20%5C%5C%5C%5C)
![$400 \pi r-300 \pi r=150 \pi h$](https://tex.z-dn.net/?f=%24400%20%5Cpi%20r-300%20%5Cpi%20r%3D150%20%5Cpi%20h%24)
![$160 \pi r=150 \pi h \quad \\\\\\](https://tex.z-dn.net/?f=%24160%20%5Cpi%20r%3D150%20%5Cpi%20h%20%5Cquad%20%5C%5C%5C%5C%5C%5C)
with
![h=\frac{2}{3} r $](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B2%7D%7B3%7D%20r%20%24)
![$\pi r^{2} h+\frac{2}{3} \pi r^{3}=5000$](https://tex.z-dn.net/?f=%24%5Cpi%20r%5E%7B2%7D%20h%2B%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D%3D5000%24)
![\pi r}\left(\frac{2}{3} r \right)+\frac{2}{3} \pi^{3}=5000$](https://tex.z-dn.net/?f=%5Cpi%20r%7D%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%20r%20%5Cright%29%2B%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%5E%7B3%7D%3D5000%24)
![$\frac{4 \pi \gamma^{3}}{3}=5000 \quad](https://tex.z-dn.net/?f=%24%5Cfrac%7B4%20%5Cpi%20%5Cgamma%5E%7B3%7D%7D%7B3%7D%3D5000%20%5Cquad)
![r^{3}=\left(\frac{5000 \times 3}{4 \pi}\right)$](https://tex.z-dn.net/?f=r%5E%7B3%7D%3D%5Cleft%28%5Cfrac%7B5000%20%5Ctimes%203%7D%7B4%20%5Cpi%7D%5Cright%29%24)
r=10.60
In conclusion, the radius and height, in two decimal places is
r=10.60
Read more about radius
brainly.com/question/13449316
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Answer:
46.875
Step-by-step explanation:
A= l x w x h so you multiple all three numbers together and get your answer
You can fit 3 in there 13 whole times. After you do that,
the 40 is not quite full yet, but it only has room for 1 more,
so you cannot stuff the whole 3 in there again.