Answer:
Step-by-step explanation:
Given that that (X) the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.
i.e. X is normal with mean = 15 and unknown std deviation ![\sigma](https://tex.z-dn.net/?f=%5Csigma)
Given that![P(X](https://tex.z-dn.net/?f=P%28X%3C13%29%20%3D%207%25%20%3D%200.07)
i.e. P(![z](https://tex.z-dn.net/?f=z%3C%5Cfrac%7B13-15%7D%7B%5Csigma%7D%20%29%3D0.07)
z=-1.475 (from normal table)
Hence ![\frac{13-15}{\sigma}=-1.475\\\sigma = 1.356](https://tex.z-dn.net/?f=%5Cfrac%7B13-15%7D%7B%5Csigma%7D%3D-1.475%5C%5C%5Csigma%20%3D%201.356)
Using this we find P(X>17) = ![P(Z>\frac{17-15}{1.356} \\=P(Z>1.475)\\=0.5-0.428\\=0.072](https://tex.z-dn.net/?f=P%28Z%3E%5Cfrac%7B17-15%7D%7B1.356%7D%20%5C%5C%3DP%28Z%3E1.475%29%5C%5C%3D0.5-0.428%5C%5C%3D0.072)
Answer:
![\huge\boxed{V=64cm^3}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7BV%3D64cm%5E3%7D)
Step-by-step explanation:
The formula of a surface area of a cube:
![SA=6a^2](https://tex.z-dn.net/?f=SA%3D6a%5E2)
The formula of a volume of a cube:
![V=a^3](https://tex.z-dn.net/?f=V%3Da%5E3)
We have
![SA=96cm^2](https://tex.z-dn.net/?f=SA%3D96cm%5E2)
Calculate the edge length (<em>a</em>).
<em>divide both sides by 6</em>
![a^2=16\to a=\sqrt{16}\\\\a=4(cm)](https://tex.z-dn.net/?f=a%5E2%3D16%5Cto%20a%3D%5Csqrt%7B16%7D%5C%5C%5C%5Ca%3D4%28cm%29)
Calculate the volume of a cube:
![V=4^3=64(cm^3)](https://tex.z-dn.net/?f=V%3D4%5E3%3D64%28cm%5E3%29)
Answer:
Solution given:
1 kg =1000g
1g=1000mg
now
1kg=1000g=1000×1000mg=1000000mg
Hello!
As you can see, we have a radius of 6. If we divide, this means that this is 2.5 radians. To convert radians to degrees we use the formula below.
![\frac{180}{ \pi }x](https://tex.z-dn.net/?f=%20%5Cfrac%7B180%7D%7B%20%5Cpi%20%7Dx)
First of all we divide 180 by pi.
180/
![\pi](https://tex.z-dn.net/?f=%20%5Cpi%20)
≈57.3
Now we multiply by 2.5
57.3(2.5)=143.25°
Note that the angle we see is obtuse, or greater than 90°.
Therefore, ∠<span>θ</span>≈143.25°
Now we need to convert this back into radians. This can be represented by the equation below.
![\frac{ \pi }{180}x](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cpi%20%7D%7B180%7Dx%20)
First we divide pi by 180 then multiply by our angle.
![\pi](https://tex.z-dn.net/?f=%20%5Cpi%20)
/180(143.25)≈2.5
Therefore, our angle theta is about
2.5 radians.
I hope this helps!