Guessing you meant by a factor of 3... not 13 since none of the solutions are anywhere close to that.
to compress is to smoosh.
It's the equation of a line. If you smoosh it vertically the line becomes flatter and the slope smaller.
Essentially g(x) = 3f(x)
3y = 12x + 6
y = (12/3)x + 6/3
y = 4x + 2
Step-by-step explanation:
5/8 x 3/11 = answer
Keep change flip
They are essentially asking us to solve:
![357=900e^{-0.01155x} \implies\\ \frac{357}{900}=e^{-0.01155x} \implies\\ \ln{\frac{357}{900}}=-0.01155x \implies \\ x\approx 80.1](https://tex.z-dn.net/?f=%20357%3D900e%5E%7B-0.01155x%7D%20%5Cimplies%5C%5C%20%5Cfrac%7B357%7D%7B900%7D%3De%5E%7B-0.01155x%7D%20%5Cimplies%5C%5C%20%5Cln%7B%5Cfrac%7B357%7D%7B900%7D%7D%3D-0.01155x%20%5Cimplies%20%5C%5C%20x%5Capprox%2080.1%20)
Solving this equation for x tells us that it will take around 80.1 years for the materials in the vault to reduce to 357 pounds.
![- 8x + 5 = - 8x + 4 \\ - 8x = - 8x + 4 - 5 \\ - 8x = - 8x - 1 \\ 0 = - 1(false)](https://tex.z-dn.net/?f=-%208x%20%2B%205%20%3D%20%20-%208x%20%2B%204%20%5C%5C%20%20%20-%208x%20%3D%20%20-%208x%20%2B%204%20-%205%20%5C%5C%20%20-%208x%20%3D%20%20-%208x%20-%201%20%5C%5C%20%200%20%3D%20%20-%201%28false%29)
we don't have solutions !!
Answer:
the probability of no defects in 10 feet of steel = 0.1353
Step-by-step explanation:
GIven that:
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.
Let consider β to be the average value for defecting
So;
β = 2
Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.
Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2
i.e
![Y \sim P( \beta = 2)](https://tex.z-dn.net/?f=Y%20%5Csim%20P%28%20%5Cbeta%20%3D%202%29)
the probability mass function can be represented as follows:
![\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28y%29%20%3D%20%5Cdfrac%7Be%5E%7B-%20%5Cbeta%7D%20%5C%20%5Cbeta%5E%20%5C%20y%7D%7By%21%7D%7D)
where;
y = 0,1,2,3 ...
Hence, the probability of no defects in 10 feet of steel
y = 0
![\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28y%20%3D0%29%20%3D%20%5Cdfrac%7Be%5E%7B-%202%7D%20%5C%202%5E%20%5C%200%7D%7B0%21%7D%7D)
![\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}](https://tex.z-dn.net/?f=%5Cmathtt%7BP%28y%20%3D0%29%20%3D%20%5Cdfrac%7B0.1353%20%20%5Ctimes%201%7D%7B1%7D%7D)
P(y =0) = 0.1353