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3 years ago

6

A^2−8ab+16b^2=81, find a–4b

1 answer:

neonofarm [45]3 years ago

4 0

Answer:

-9, 9

Step-by-step explanation:

a² − 8ab + 16b² = 81

(a - 4b)² = 81 Wrote the left-hand side as a square

a - 4b = ±9 Took the square root of each side

All values of a - 4b are -9 and +9.

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a) $P(X\leq 4)=0.0183+0.0733+ 0.1465+0.1954+0.1954=0.6288$

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Let X the random variable that represent the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. We know that $X \sim Poisson(\lambda=4)$

The probability mass function for the random variable is given by:

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And f(x)=0 for other case.

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$P(X\leq 4)=P(X=0)+P(X=1)+ P(X=2)+P(X=3)+P(X=4)$

Using the pmf we can find the individual probabilities like this:

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$P(X=2)=\frac{e^{-4} 4^2}{2!}=0.1465$

$P(X=3)=\frac{e^{-4} 4^3}{3!}=0.1954$

$P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954$

$P(X\leq 4)=0.0183+0.0733+ 0.1465+0.1954+0.1954=0.9646$

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$P(4\leq X\leq 8)=P(X=4)+P(X=5)+ P(X=6)+P(X=7)+P(X=8)$

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$P(X \geq 8) = 1-P(X$

$P(X \geq 8) = 1-P(X$

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The mean is 4 and the deviation is 2, so we want this probability

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$P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954$

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$P(X=6)=\frac{e^{-4} 4^6}{6!}=0.1042$

$P(4\leq X \leq 6)=0.1954+0.1563+0.1042=0.4559$

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