Answer:A
Step-by-step explanation: 6 divided by 420 = 70
To solve this, we are going to use the surface are of a sphere formula:
![A=4 \pi r^2](https://tex.z-dn.net/?f=A%3D4%20%5Cpi%20r%5E2)
where
![A](https://tex.z-dn.net/?f=A)
is the surface area of the sphere
![r](https://tex.z-dn.net/?f=r)
is the radius of the sphere
We know for our problem that
![A=2122.64](https://tex.z-dn.net/?f=A%3D2122.64)
and
![\pi =3.14](https://tex.z-dn.net/?f=%20%5Cpi%20%3D3.14)
, so lets replace those vales in our formula:
![A=4 \pi r^2](https://tex.z-dn.net/?f=A%3D4%20%5Cpi%20r%5E2)
![2122.64=4(3.14)r^2](https://tex.z-dn.net/?f=2122.64%3D4%283.14%29r%5E2)
![2122.64=12.56r^2](https://tex.z-dn.net/?f=2122.64%3D12.56r%5E2)
Now, we just need to solve our equation for
![r](https://tex.z-dn.net/?f=r)
:
![\frac{2122.64}{12.56} =r^2](https://tex.z-dn.net/?f=%20%5Cfrac%7B2122.64%7D%7B12.56%7D%20%3Dr%5E2)
![r^2=\frac{2122.64}{12.56}](https://tex.z-dn.net/?f=%20r%5E2%3D%5Cfrac%7B2122.64%7D%7B12.56%7D)
![r^2=169](https://tex.z-dn.net/?f=r%5E2%3D169)
![r=+or- \sqrt{169}](https://tex.z-dn.net/?f=r%3D%2Bor-%20%5Csqrt%7B169%7D%20)
![r=13](https://tex.z-dn.net/?f=r%3D13)
or
![r=13](https://tex.z-dn.net/?f=r%3D13)
Since the radius of a sphere cannot be a negative number,
![r=13](https://tex.z-dn.net/?f=r%3D13)
.
We can conclude that the radius of a sphere with surface area <span>2,122.64 </span>
![in^2](https://tex.z-dn.net/?f=in%5E2)
is
13 in.
Answer:
Value of the test statistic, ![z_{test} = - 1.17](https://tex.z-dn.net/?f=z_%7Btest%7D%20%20%3D%20-%201.17)
Step-by-step explanation:
Null hypothesis, ![H_{0}: \mu = 53.9](https://tex.z-dn.net/?f=H_%7B0%7D%3A%20%5Cmu%20%3D%2053.9)
Alternative hypothesis, ![H_{a} : \mu \neq 53.9](https://tex.z-dn.net/?f=H_%7Ba%7D%20%3A%20%5Cmu%20%5Cneq%2053.9)
Sample mean, ![\bar{X} = 53.7](https://tex.z-dn.net/?f=%5Cbar%7BX%7D%20%3D%2053.7)
Sample size, n = 110
Standard deviation, ![\sigma = 1.8](https://tex.z-dn.net/?f=%5Csigma%20%3D%201.8)
Significance level, ![\alpha = 0.02](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.02)
The value of the test statistics is given by the formula:
![z_{test} = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n} } } \\z_{test} = \frac{53.7 - 53.9}{\frac{1.8}{\sqrt{110} } } \\z_{test} = - 1.17](https://tex.z-dn.net/?f=z_%7Btest%7D%20%20%3D%20%5Cfrac%7B%5Cbar%7BX%7D%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D%20%5C%5Cz_%7Btest%7D%20%20%3D%20%5Cfrac%7B53.7%20-%2053.9%7D%7B%5Cfrac%7B1.8%7D%7B%5Csqrt%7B110%7D%20%7D%20%7D%20%5C%5Cz_%7Btest%7D%20%20%3D%20-%201.17)
Answer:
<u>12</u>
Step-by-step explanation:
Well, I am pretty sure you are looking for the length.
Since area = length x width, I would say that you could divide as well.
120 = 10 x <u>12</u>
I am pretty sure the length is <u>12.</u>
<u></u>
:)
It will take 2/3 hour or 40 minutes to fill the tank if both pipes are used.
Let pi be pipe 1 and pi2 be pipe 2
pi = 1 / 1
pi2 = 1 / 2
together = 1/1 + 1/2 ;
3/2 time ; 2/3 hour.
It will take 2/3 hour or 40 minutes to fill the tank if both pipes are used.
Problem-solving is the act of defining a problem; figuring out the motive of the problem; identifying, prioritizing, and deciding on alternatives for a solution; and implementing an answer.
Learn more about Problem-solving here: brainly.com/question/13818690
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