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3 years ago

6

How to solve this problem I don’t get it at all

1 answer:

Zarrin [17]3 years ago

8 0

Use a calculator to help u and u will get your answer

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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

GrogVix [38]

Answer:

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

(b) The value of P (X > 20) is 0.1353.

(c) The value of P (X < 30) is 0.9502.

(d) The value of x is 30.

Step-by-step explanation:

The probability density function of an exponential distribution is:

$f(x)=\lambda e^{-\lambda x};\ x>0, \lambda>0$

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

3 years ago

What is the answer for<br> -4x+4y=12<br> 3x-4y=-18

Liula [17]

Use elimination.

-x = -6
X = 6

-4 (6) + 4y = 12
Y = 9

(X,y)

(6,9) is the solution

6 0

3 years ago

In triangle PQR, PR = 23mm, QR = 39mm, and m<R = 163 degrees. Find the area of the triangle to the nearest tenth.

Schach [20]

Answer: 131.1287 square mm (approx)

Step-by-step explanation:

The area of a triangle,

$A=\frac{1}{2} \times s_1\times s_2\times sin \theta$

Where $s_1$ and $s_2$ are adjacent sides and $\theta$ is the include angle of these sides,

Here PR and QR are adjacent sides and ∠R is the included angle of these sides,

Thus, we can write,

$s_1 = PR= 23\text{ mm}$ , $s_2=QR=39\text{ mm}$ and $\theta = 163^{\circ}$ ,

Thus, the area of the triangle PQR,

$A=\frac{1}{2} \times 23\times 39\times sin163^{\circ}$

$A=\frac{262.257419136}{2} = 131.128709568\approx 131.1287\text{ square mm}$

5 0

3 years ago

If 1 card is drawn at random from a standard 52-card deck, what is the probability that the card drawn is a black nine?

Korolek [52]

I think it's 2/52 or 1/26

5 0

3 years ago

15) Find the value of x in the given square<br> Area = 34 in

lyudmila [28]

Answer:

Area of a square is given by:

A = a2

where a = length of side

6 0

2 years ago