Answer: 13,333 snowflakes
Step-by-step explanation:
For this exercise let be "x" represents the number of snowflakes that will be in the fort.
According to the information given in the exercise, the weight of one block is 1 kilogram. Knowing that the fort must have 40 blocks, the total weight is:
![total\ weight=(1\ g)(40)\\\\total\ weight=40\ g](https://tex.z-dn.net/?f=total%5C%20weight%3D%281%5C%20g%29%2840%29%5C%5C%5C%5Ctotal%5C%20weight%3D40%5C%20g)
Since each snowflake weighs
grams, need to divide the total weight calculated above by the weight of a snowfake.
Therefore, through this procedure you get the following result:
![x=\frac{40\ grams}{3 * 10 ^{-3}\ grams}\\\\x\approx13,333](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B40%5C%20grams%7D%7B3%20%2A%2010%20%5E%7B-3%7D%5C%20grams%7D%5C%5C%5C%5Cx%5Capprox13%2C333)
Therefore, the there will be 13,333 snowflakes in the fort.
Answer:
![Mean = 0.36](https://tex.z-dn.net/?f=Mean%20%3D%200.36)
![SD = 0.5817](https://tex.z-dn.net/?f=SD%20%3D%200.5817)
![P(x=3) = 0.003588](https://tex.z-dn.net/?f=P%28x%3D3%29%20%3D%200.003588)
Step-by-step explanation:
Given
Let
A = Event of being a universal donor.
So:
![P(A) = 0.06](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.06)
![n = 6](https://tex.z-dn.net/?f=n%20%3D%206)
Solving (a): Mean and Standard deviation.
The mean is:
![Mean = np](https://tex.z-dn.net/?f=Mean%20%3D%20np)
![Mean = 6 * 0.06](https://tex.z-dn.net/?f=Mean%20%3D%206%20%2A%200.06)
![Mean = 0.36](https://tex.z-dn.net/?f=Mean%20%3D%200.36)
The standard deviation is:
![SD = \sqrt{np(1-p)}](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7Bnp%281-p%29%7D)
![SD = \sqrt{6*0.06*(1-0.06)}](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B6%2A0.06%2A%281-0.06%29%7D)
![SD = \sqrt{0.3384}](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B0.3384%7D)
![SD = 0.5817](https://tex.z-dn.net/?f=SD%20%3D%200.5817)
Solving (b): P(x = 3)
The event is a binomial event an dthe probability is calculated as:
![P(x) = ^nC_x * p^x * (1-p)^{n-x}](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%5EnC_x%20%2A%20p%5Ex%20%2A%20%281-p%29%5E%7Bn-x%7D)
So, we have:
![P(x=3) = ^6C_3 * 0.06^3 * (1-0.06)^{6-3}](https://tex.z-dn.net/?f=P%28x%3D3%29%20%3D%20%5E6C_3%20%2A%200.06%5E3%20%2A%20%281-0.06%29%5E%7B6-3%7D)
![P(x=3) = ^6C_3 * 0.06^3 * (1-0.06)^3](https://tex.z-dn.net/?f=P%28x%3D3%29%20%3D%20%5E6C_3%20%2A%200.06%5E3%20%2A%20%281-0.06%29%5E3)
![P(x=3) = 20 * 0.06^3 * (1-0.06)^3](https://tex.z-dn.net/?f=P%28x%3D3%29%20%3D%2020%20%2A%200.06%5E3%20%2A%20%281-0.06%29%5E3)
![P(x=3) = 0.003588](https://tex.z-dn.net/?f=P%28x%3D3%29%20%3D%200.003588)
If 80% are women, then 20% are men
20% of what equals 880
0.20x = 880
x = 880/.20
x = 4400
check..
men : 20% of 4400 = 0.20(400) = 880
women : 80% of 4400 = 0.80(4400) = 3520
totaling : 3520 + 880 = 4400
so there are a total of 4400 workers
Answer:
only -2 is in the domain
Step-by-step explanation:
For negative values under the sqrt, there is no real answer, hence
-2x ≥ 0
only for x=-2 this is the case.
The domain represents all the valid input values for x.
The base. Hope this helps!