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BARSIC [14]
3 years ago
14

Two objects are moving along separate linear paths where each path is described by postion, d, and time, t. The variable d is me

asured in meters and the variable t is measured in seconds. The equation describing the graph of the postion of the first object with respect to time is d=2.5t+2.2. The graph of the the position of the second object is a parallel line passing through (t=0,d=1). What is the equation of the second graph.
d=2.5t+1
d=-0.4t+1
d=2.5t+3.2
Mathematics
1 answer:
weqwewe [10]3 years ago
7 0
The first equation is:
d = 2.5 t + 2.2
For the parallel line :
m = 2.5.
It is passing through: t = 0, d = 1
d = m t + b
1 = 2.5 * 0 + b
b = 1
Answer:
A ) d = 2.5 t + 1
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Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X > 10) b. P(X > 20) c
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Answer:

(a) The value of P (X > 10) is 0.3679.

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(d) The value of x is 30.

Step-by-step explanation:

The probability density function of an exponential distribution is:

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The value of E (X) is 10.

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.

7 0
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elena-14-01-66 [18.8K]
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