We have
(a + b)² = a² + 2ab + b²
so that with a = x² and b = 5, we have
x⁴ + 10x² + 25 = (x² + 5)²
Next, we have
a² - b² = (a - b) (a + b)
so that with a = x and b = √5 i,
x² + 5 = x² - (-5) = (x - √5 i) (x + √5 i)
So, the complete factorization over the complexes is
(x - √5 i)² (x + √5 i)²
Let X = the 29% alloy and Y = the 60% alloy.
They want a total of 80kg, so you have X +Y = 80
Rewrite that to get X = 80-Y
You also want 0.20X + 0.60Y = 0.52(80)
Replace X with 80-y:
0.20(80-y) + 0.60y = 0.52(80)
Simplify:
16 - 0.20y + 0.60y = 41.6
Combine like terms:
16 +0.40y = 41.6
Subtract 16 from each side:
0.40y = 25.6
Divide both sides by 0.40
y = 25.6 / 0.40
y = 64
Now you have Y replace y with 80 in X = 80-Y
X = 80 - 64
X = 16
They need 64 Kg of the 60% alloy and 16 Kg of the 20% alloy.
Answer:
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Step-by-step explanation:
Answer: 
Step-by-step explanation:
Given : To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin tablets that are similar in appearance.
Proportion of success : 
Sample size taken by customs official : n= 3
Let x be a binomial variable that represents the tablets in the bottle.
Using Binomial probability formula :-
The probability that the traveler will be arrested for illegal possession of narcotics =
![1-^3C_0(\dfrac{2}{3})^0(1-\dfrac{2}{3})^3\\\\=1-(1)(1)(\dfrac{1}{3})^3\ [\becuase ^nC_0=1]\\\\=1-\dfrac{1}{27}=\dfrac{26}{27}](https://tex.z-dn.net/?f=1-%5E3C_0%28%5Cdfrac%7B2%7D%7B3%7D%29%5E0%281-%5Cdfrac%7B2%7D%7B3%7D%29%5E3%5C%5C%5C%5C%3D1-%281%29%281%29%28%5Cdfrac%7B1%7D%7B3%7D%29%5E3%5C%20%5B%5Cbecuase%20%5EnC_0%3D1%5D%5C%5C%5C%5C%3D1-%5Cdfrac%7B1%7D%7B27%7D%3D%5Cdfrac%7B26%7D%7B27%7D)
Hence, the probability that the traveler will be arrested for illegal possession of narcotics =
