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bekas [8.4K]
3 years ago
15

UHHHHHHHHHHHH THIS IS EASY MATH WORK BUT I ONLY HAVE 2 BRAINCELLS THAT ARE SLOW SO JSJSJJSJJSJ HELP.

Mathematics
2 answers:
stealth61 [152]3 years ago
6 0
1708 is than answer
lesya692 [45]3 years ago
4 0

Answer:

1,708

My browser has a tool for solving the area of trapezoids that I used. Hope this helps!

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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
2 years ago
Easy question and easy point <br><br><br> what is 2+2-2+6*8
oksian1 [2.3K]
The answer is 46 thank you
7 0
2 years ago
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A leaking pond loses 20 gallons of water in 35 hours. How many gallons of water will it lose in 47 hours?
Mama L [17]
20/35 gallons per hour
(20/35) * 47 = around 27 gallons in 47 hours
6 0
2 years ago
Classify ∠1 and ∠2 using all names that apply
Vinvika [58]

Step-by-step explanation:

complementry

since the angle 1 and 2 both measures 90⁰

6 0
2 years ago
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An angle equal to its supplement is _____ degree.
bonufazy [111]

Answer:

90 Degrees.

The angle which is equal to its supplement is 90 degrees.

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