Answer: c. 0.40396
Step-by-step explanation:
The total number of flaws is given by:
![{\left({0}\times{4}\right)}+{\left({1}\times{3}\right)}(0\times4)+(1\times3) +{\left({2}\times{5}\right)}+{\left({3}\times{2}\right)}+(2\times5)+(3\times2) +{\left({4}\times{4}\right)}+{\left({5}\times{1}\right)}+(4\times4)+(5\times1) +{\left({6}\times{1}\right)}+(6\times1)={46}=46](https://tex.z-dn.net/?f=%7B%5Cleft%28%7B0%7D%5Ctimes%7B4%7D%5Cright%29%7D%2B%7B%5Cleft%28%7B1%7D%5Ctimes%7B3%7D%5Cright%29%7D%280%5Ctimes4%29%2B%281%5Ctimes3%29%20%2B%7B%5Cleft%28%7B2%7D%5Ctimes%7B5%7D%5Cright%29%7D%2B%7B%5Cleft%28%7B3%7D%5Ctimes%7B2%7D%5Cright%29%7D%2B%282%5Ctimes5%29%2B%283%5Ctimes2%29%20%2B%7B%5Cleft%28%7B4%7D%5Ctimes%7B4%7D%5Cright%29%7D%2B%7B%5Cleft%28%7B5%7D%5Ctimes%7B1%7D%5Cright%29%7D%2B%284%5Ctimes4%29%2B%285%5Ctimes1%29%20%2B%7B%5Cleft%28%7B6%7D%5Ctimes%7B1%7D%5Cright%29%7D%2B%286%5Ctimes1%29%3D%7B46%7D%3D46)
Average number of flaws for the 20 sheets : ![\displaystyle\mu=\frac{46}{{20}}={2.3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cmu%3D%5Cfrac%7B46%7D%7B%7B20%7D%7D%3D%7B2.3%7D)
Required probability : ![=P(X\geq3)=1-P(X](https://tex.z-dn.net/?f=%3DP%28X%5Cgeq3%29%3D1-P%28X%3C3%29)
![=1-[P(X=0)+P(X=1)+P(X=2)]](https://tex.z-dn.net/?f=%3D1-%5BP%28X%3D0%29%2BP%28X%3D1%29%2BP%28X%3D2%29%5D)
![=1-(\dfrac{e^{-2.3}2.3^0}{0!}+\dfrac{e^{-2.3}2.3^1}{1!}+\dfrac{e^{-2.3}2.3^2}{2!})\ \ \ [\text{Poisson distribution formula: }P(X=x)=\dfrac{e^{-\mu}\mu^x}{x!}]\\\\=1-0.596038825932=0.403961174068\approx0.40396](https://tex.z-dn.net/?f=%3D1-%28%5Cdfrac%7Be%5E%7B-2.3%7D2.3%5E0%7D%7B0%21%7D%2B%5Cdfrac%7Be%5E%7B-2.3%7D2.3%5E1%7D%7B1%21%7D%2B%5Cdfrac%7Be%5E%7B-2.3%7D2.3%5E2%7D%7B2%21%7D%29%5C%20%5C%20%5C%20%5B%5Ctext%7BPoisson%20distribution%20formula%3A%20%7DP%28X%3Dx%29%3D%5Cdfrac%7Be%5E%7B-%5Cmu%7D%5Cmu%5Ex%7D%7Bx%21%7D%5D%5C%5C%5C%5C%3D1-0.596038825932%3D0.403961174068%5Capprox0.40396)
Hence, c. is the correct option.
I think it will be the fourth picture because:
40 * 7/10 = 280/10 = 28
Hope this helps :)
Answer:
The number of units that must be sold in order to have the greatest revenue is 50,000 units
Step-by-step explanation:
Given;
y = -0.0002x² + 20x
where;
y is the revenue
x is the units of the product
The equation above is a quadratic equation, to obtain the value of x (units) that will give maximum value of y (revenue), we differentiate the equation.
dy/dx = -0.0004x + 20
Now, equate the differential value to zero, in order to get the value of x that will make the equation maximum.
-0.0004x + 20 = 0
-0.0004x = -20
x = (-20) / (-0.0004)
x = 50,000 units
Therefore, the number of units that must be sold in order to have the greatest revenue is 50,000 units
Answer:
9,000 is the answer
Step-by-step explanation:
log -4x-log4=1
when subtracting logs of the same base, you divide)
log (-4x/4)=1
log (-x) = 1
inverse of log is take it to the power of 10
-x = 10^1
-x = 10
divide by -1
x =-10