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8_murik_8 [283]
3 years ago
12

7a to the 2 power - a to the 2 power + 16 = what

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
8 0

Answer:

48a^2 + 16

Step-by-step explanation:

7a to the 2 power - a to the 2 power + 16 = (7a)^2 - a^2 + 16.

This latter result can be rewritten as 49a^2 - a^2 + 16, or 48a^2 + 16

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Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X &gt; 10) b. P(X &gt; 20) c
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(b) The value of P (X > 20) is 0.1353.

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Step-by-step explanation:

The probability density function of an exponential distribution is:

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The parameter λ is:

\lambda=\frac{1}{E(X)}=\frac{1}{10}=0.10

(a)

Compute the value of P (X > 10) as follows:

P(X>10)=\int\limits^{\infty}_{10} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{10} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{10}\\=|e^{-0.10 x} |^{\infty}_{10}\\=e^{-0.10\times10}\\=0.3679

Thus, the value of P (X > 10) is 0.3679.

(b)

Compute the value of P (X > 20) as follows:

P(X>20)=\int\limits^{\infty}_{20} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{20} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{20}\\=|e^{-0.10 x} |^{\infty}_{20}\\=e^{-0.10\times20}\\=0.1353

Thus, the value of P (X > 20) is 0.1353.

(c)

Compute the value of P (X < 30) as follows:

P(X

Thus, the value of P (X < 30) is 0.9502.

(d)

It is given that, P (X < x) = 0.95.

Compute the value of <em>x</em> as follows:

P(X

Take natural log on both sides.

ln(e^{-0.10x})=ln(0.05)\\-0.10x=-2.996\\x=\frac{2.996}{0.10}\\ =29.96\\\approx30

Thus, the value of x is 30.

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