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3 years ago

Look at the data.

Mathematics

1 answer:

andriy [413]3 years ago

4 0

Answer:

2 cm

Step-by-step explanation:

Data

Time (min) Depth (cm)

2 8

4 15

6 29

8 37

10 39

12 49

14 55

The line of best fit to find the amount of water is:

y = 3.9107x + 1.8571

(I used Excel to get it, you can use a calculator or similar programs if you want to)

In the equation, y represents depth (in cm) and x represents time (in min).

The amount of water, in cm, present initially in the bathtub is found at time equal to zero. Replacing x = 0 in the equation, we get:

y = 3.9107(0) + 1.8571

y = 1.8571 ≈ 2 cm

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3 years ago

What is the completely factored form of this polynomial? 18x^3– 120x^2-42x

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Answer:

6×(3×+1)(×-7)

Step-by-step explanation:

18×^3-120×^2-42×

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3 years ago

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The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to agi

Tresset [83]

Answer:

P(X \le 250 ) = 0.7564 [/tex] , $P(X < 250 ) = 0.7564$ ,

$P(X < 300 ) = 0.09922$

$P(100 < X < 250 ) =0.644$

$x = 192.1$

Step-by-step explanation:

From the question we are told that

The value for $\alpha = 2.6$

The value for $\beta = 220$

Generally the Weibull distribution function is mathematically represented as

$F( x , \alpha , \beta ) = \left \{ 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x < 0} \atop { 1- e^{-(\frac{x}{\beta } )^{\alpha } }}\ \ \ \ \ \ x \ge 0} \right$

Generally the probability that a specimen's lifetime is at most 250 is mathematically represented as

$P(X \le 250 ) = F(250, 2.7 , 220 )$

$P(X \le 250 )=1 - e^{- (\frac{250}{220} )^{2.7}}$

$P(X \le 250 ) = 1 - 0.2436$

$P(X \le 250 ) = 0.7564$

Generally the probability that a specimen's lifetime is less than 250

$P(X < 250 ) = F(250, 2.7 , 220 )$

[texP(X < 250 ) =1 - e^{- (\frac{250}{220} )^{2.7}}[/tex]

$P(X < 250 ) = 1 - 0.2436$

$P(X < 250 ) = 0.7564$

Generally the probability that a specimen's lifetime is more than 300

$P(X > 300 ) = 1- p(X \le 300 )$

$P(X > 300 ) = 1- F(300, 2.7 , 220 )$

[texP(X < 300) =1- [1 - e^{- (\frac{300}{220} )^{2.7}}][/tex]

$P(X < 300 ) = 0.09922$

Generally the probability that a specimen's lifetime is between 100 and 250 is

$P(100 < X < 250 ) = P(X < 250) - P(X < 100)$

=> $P(100 < X < 250 ) =F(250 , 2.7 , 220 ) - F(100 , 2.7 , 220 )$

=> $P(100 < X < 250 ) =(1 - e^{-(\frac{250}{220})^{2.7}}) - (1 - e^{-(\frac{100}{220})^{2.7}})$

=> $P(100 < X < 250 ) = (1 - 0.244 ) - (1- 0.888)$

=> $P(100 < X < 250 ) =0.644$

Generally the value such that exactly 50% of all specimens

$P(X > x) = 1-P(X < x) = 0.50$

=> $P(X > x) = 1- (1 - e^{- (\frac{x}{220}) ^{2.7}}) = 0.50$

=> $P(X> x ) = e^(- \frac{x}{20})^{2.7} = 0.50$

=> $P(X> x ) = (- \frac{x}{20})^{2.7} = ln0.50$

=> $P(X> x ) = \frac{x}{20} =[ -ln0.50 ] ^{frac{1}{2.7}}$

=> $x = 220[ -ln0.50 ] ^{frac{1}{2.7}}$

=> $x = 192.1$

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kherson [118]

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Answer:

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