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snow_lady [41]
3 years ago
7

Answer to the problem 3/8r=15/16

Mathematics
1 answer:
Slav-nsk [51]3 years ago
5 0
Your answer would be r=5/2

If you want me to explain how i got that then tell me on my profile
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The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x
natulia [17]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

       P(a < X < b) =  \int_{a}^{b} \frac{2}{x^{3}} dx = 2\int_{a}^{b} x^{-3} dx

                            = 2[ \frac{x^{-3+1} }{-3+1}]^{b}_a   dx    { Because \int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a }

                            = 2[ \frac{x^{-2} }{-2}]^{b}_a = \frac{2}{-2} [ x^{-2} ]^{b}_a

                            = -1 [ b^{-2} - a^{-2}  ] = \frac{1}{a^{2} } - \frac{1}{b^{2} }

a) Now P(X < 5) = P(1 < X < 5)  {because x > 1 }

     Comparing with general probability we get,

     P(1 < X < 5) = \frac{1}{1^{2} } - \frac{1}{5^{2} } = 1 - \frac{1}{25} = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/8^{2} - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = \frac{1}{6^{2} } - \frac{1}{10^{2} } = \frac{1}{36} - \frac{1}{100 } = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

                                = (\frac{1}{1^{2} } - \frac{1}{6^{2} }) + (1/10^{2} - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

               ⇒  P(1 < X < x) = 0.75

               ⇒  \frac{1}{1^{2} } - \frac{1}{x^{2} } = 0.75

               ⇒  \frac{1} {x^{2} } = 1 - 0.75 = 0.25

               ⇒  x^{2} = \frac{1}{0.25}   ⇒ x^{2} = 4 ⇒ x = 2  

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0
3 years ago
Perform the indicated operation and write the answer in the form a + bi. (–1 + 5i) + (3 + 7i)
pashok25 [27]

Answer:

12i + 2

Step-by-step explanation:

Combine like terms.

-1 + 3 = 2

5i + 7i = 12i

12i + 2 is your answer.

~

5 0
3 years ago
What is the common factors of 20,25,40?
Marina CMI [18]
The common factors for 20 is 1,5
25 is 1,5
40 is 1,5
GCF:5
3 0
3 years ago
What happens to the value of the expression 5/x+5 as x decreases from a large positive number to a small positive number?
Tresset [83]

option 2. it increases

because as x decrease 5/x will increase which will overall increase the expression value

6 0
3 years ago
Explain why 0.32 is greater than 0.102
lyudmila [28]

Answer:0.32 is closer the the number one then 0.102 is

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
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