3x+20=5x+12
-3x -3x
20= 2x +12
-12 -12
8=2x
Divide both sides by two
4=x
It will take four days (this is how to solve algebraically)
We know
![\boxed{\sf Surface\:area=4\pi r^2}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20Surface%5C%3Aarea%3D4%5Cpi%20r%5E2%7D)
![\\ \sf\longmapsto 4\pi r^2=7238](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%5Clongmapsto%204%5Cpi%20r%5E2%3D7238)
![\\ \sf\longmapsto 4\times \dfrac{22}{7}r^2=7238](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%5Clongmapsto%204%5Ctimes%20%5Cdfrac%7B22%7D%7B7%7Dr%5E2%3D7238)
![\\ \sf\longmapsto r^2=\dfrac{7238\times 7}{88}](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%5Clongmapsto%20r%5E2%3D%5Cdfrac%7B7238%5Ctimes%207%7D%7B88%7D)
![\\ \sf\longmapsto r^2=\dfrac{5066}{88}](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%5Clongmapsto%20r%5E2%3D%5Cdfrac%7B5066%7D%7B88%7D)
![\\ \sf\longmapsto r^2=575.75](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%5Clongmapsto%20r%5E2%3D575.75)
![\\ \sf\longmapsto r^2\approx576](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%5Clongmapsto%20r%5E2%5Capprox576)
![\\ \sf\longmapsto r\approx\sqrt{576}](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%5Clongmapsto%20r%5Capprox%5Csqrt%7B576%7D)
![\\ \sf\longmapsto r\approx24in](https://tex.z-dn.net/?f=%5C%5C%20%5Csf%5Clongmapsto%20r%5Capprox24in)
<h3>Option b is coreect</h3>
Answer:
The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
![\alpha = \frac{1 - 0.8}{2} = 0.1](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1%20-%200.8%7D%7B2%7D%20%3D%200.1)
Now, we have to find z in the Ztable as such z has a pvalue of
.
That is z with a pvalue of
, so Z = 1.28.
Now, find the margin of error M as such
![M = z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which
is the standard deviation of the population and n is the size of the sample.
![M = 1.28\frac{1.5}{\sqrt{305}} = 0.1](https://tex.z-dn.net/?f=M%20%3D%201.28%5Cfrac%7B1.5%7D%7B%5Csqrt%7B305%7D%7D%20%3D%200.1)
The lower end of the interval is the sample mean subtracted by M. So it is 7.6 - 0.1 = 7.5
The upper end of the interval is the sample mean added to M. So it is 7.6 + 0.1 = 7.7
The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.