Answer:
0.231
Step-by-step explanation:
first off, let's recall that a cube is just 6 squares stacked up to each other, like in the picture below. Since we know its volume, we can find how long each side is.
part A)
![\bf \textit{volume of a cube}\\\\V=x^3~~\begin{cases}x=side\\[-0.5em]\hrulefill\\V=64\end{cases}\implies 64=x^3\implies \sqrt[3]{64}=x\implies 4=x](https://tex.z-dn.net/?f=%20%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20cube%7D%5C%5C%5C%5CV%3Dx%5E3~~%5Cbegin%7Bcases%7Dx%3Dside%5C%5C%5B-0.5em%5D%5Chrulefill%5C%5CV%3D64%5Cend%7Bcases%7D%5Cimplies%2064%3Dx%5E3%5Cimplies%20%5Csqrt%5B3%5D%7B64%7D%3Dx%5Cimplies%204%3Dx%20)
part B)
they have a painting with an area of 12 ft², will the painting fit flat against a side? Well, it can only fit flat if the sides of the painting are the same length or smaller than the sides of the crate, we know the crate is a 4x4x4, so are the painting's sides 4 or less?
![\bf \textit{area of a square}\\\\A=s^2~~\begin{cases}s=side\\[-0.5em]\hrulefill\\A=12\end{cases}\implies 12=s^2\implies \sqrt{12}=s\implies \stackrel{yes}{3.464\approx s}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Ctextit%7Barea%20of%20a%20square%7D%5C%5C%5C%5CA%3Ds%5E2~~%5Cbegin%7Bcases%7Ds%3Dside%5C%5C%5B-0.5em%5D%5Chrulefill%5C%5CA%3D12%5Cend%7Bcases%7D%5Cimplies%2012%3Ds%5E2%5Cimplies%20%5Csqrt%7B12%7D%3Ds%5Cimplies%20%5Cstackrel%7Byes%7D%7B3.464%5Capprox%20s%7D%20)
Answer:
0.99865
Step-by-step explanation:
The question above is modelled by gaussian distribution. Gaussian distribution is also known as Normal distribution.
To solve the above question, we would be using the z score formula
The formula for calculating a z-score
z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
In the above question,
x is 115 liters
μ is 100
σ is the population standard deviation is unknown. But we were given variance in the question.
Standard deviation = √Variance
Variance = 9
Hence, Standard deviation = √9 = 3
We go ahead to calculate our z score
z = (x-μ)/σ
z = (115 - 100) / 3
z = 15/ 3
z score = 5
Using the z score table of normal distribution to find the Probability of having a z score of 5
P(x = 115) = P(z = 5) =
0.99865
Therefore the probability that this year it will produce 115 liters of wine = 0.99865
