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Umnica [9.8K]
2 years ago
11

Factorise and divide 3^ 2 (2 ^2 − 14 + 24) ÷ 6 ( x − 4)​

Mathematics
1 answer:
Fiesta28 [93]2 years ago
3 0

Answer:

i think its 21/x-4

Step-by-step explanation:

sorry if im wrong

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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
RoseWind [281]

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
PLEASE HELP!!! Show your work too, please!
dimulka [17.4K]

Step-by-step explanation:

first fish tank: 95-4x

second fish tank: 40+5x

1. Define variable

The variable x represents the number of days.

2. Write the inequality

<em>95-4x=40+5x</em>

<em />

3. You probably don't need the answer but I am just going to solve.

The first fish tank will have less water than the second fish tank after 7 days.

<em>95-4x=40+5x </em>

<em>95-4(7)=40+5(7)</em>

<em>95-28=40+35</em>

<em>67=75</em>

<em>Since the first equation (95-4x) represents the first fish tank, and the second equation (40+5x) represents the second fish tank, the solution shows how the amount of water in the first fish tank is less than the amount of water un the second fish tank after 7 days.</em>

8 0
3 years ago
Read 2 more answers
Two cars simultaneously left Points A and B and headed towards each other, and met after 2 hours and 45 minutes. The distance be
rjkz [21]

Answer:

Its 41 mph and 55 mph

Step-by-step explanation:

8 0
2 years ago
How would u do this and can u explain
Amanda [17]


M=2-(-6)/(-1)-(-2)=8
Y=8x+b
-6=8*(-2)+b
-6=-16+b
B=16-6=10
Y=8x+10

I hope my answer is help to you
4 0
2 years ago
Compare the value of 30 and 3
GarryVolchara [31]
30 is greater than 3. So 30 > 3
4 0
3 years ago
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