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Marysya12 [62]
2 years ago
6

For a parallel structure of identical​ components, the system can succeed if at least one of the components succeeds. Assume tha

t components fail independently of each other and that each component has a 0.21 probability of failure. Complete parts​ (a) through​ (c) below.
Would it be unusual to observe one component​ fail? Two​ components?
It
▼
would not
would
be unusual to observe one component​ fail, since the probability that one component​ fails,

enter your response here​, is
▼
less
greater
than 0.05. It
▼
would not
would
be unusual to observe two components​ fail, since the probability that two components​ fail,

enter your response here​, is
▼
greater
less
than 0.05.
Mathematics
1 answer:
Dennis_Churaev [7]2 years ago
5 0

Using the probability concept, we have that:

a) It would not be unusual to observe one component​ fail, since the probability that one component​ fails is greater than 0.05.

b) It would be unusual to observe two components​ fail, since the probability that two components​ fail is less than 0.05.

<h3>What is a probability?</h3>

A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>. If a probability is less than 0.05, the event is considered unusual.

In this problem, the probabilities are given as follows:

  • 0.21 probability that one component fails, hence not unusual.
  • (0.21)² = 0.0441 probability that two components fail, hence unusual.

More can be learned about probabilities at brainly.com/question/14398287

#SPJ1

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Distance = \sqrt{(7-4)^{2}+(4+1)^{2}  } = 5.830951894845

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What is 65/8 as a proper fraction?
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Use the long division solution to convert the original fraction (658) ( 65 8 ) to a mixed number . The whole number portion of the mixed number.
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The vertex form of the equation of
Ivan

Answer:

The standard form of the equation is y = 2x^2 + 16x + 25

Step-by-step explanation:

To find the standard form, first square the parenthesis.

y = 2(x + 4)^2 - 7

y = 2(x^2 + -8x + 16) - 7

Now distribute the 2

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Now combine like terms

y = 2x^2 + 16x + 32 - 7

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4 0
3 years ago
A classic rock radio station claims to play an average of 50 minutes of music every hour. However, it seems that every time you
tia_tia [17]

Answer:

a) 47.917-1.796\frac{2.811}{\sqrt{12}}=46.460    

47.917+1.796\frac{2.811}{\sqrt{12}}=49.374    

b) Null hypothesis: \mu =50

Alternative hypothesis: \mu \neq 50

And after analyze the interval obtained the upper limit not contains the value of 50, so then we can conclude that the claim is not satisfied for this case, and the population mean seems to be lower than 50 at 10% of significance.

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

We have the following data: 44 49 45 51 49 53 49 44 47 50 46 48

And we can calculate the sample mean and deviation with the following formulas:

\bar X= \frac{\sum_{i=1}^n X_i}{n}

s= \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}

And replacing we got:

\bar X= 47.917, s= 2.811

\mu population mean (variable of interest)  

n=12 represent the sample size  

Part a: Calculate the confidence interval

The confidence interval for the mean is given by the following formula:  

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)  

The degrees of freedom are given:

df= n-1= 12-1=11

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,11)".And we see that t_{\alpha/2}=1.796

Now we have everything in order to replace into formula (1):

47.917-1.796\frac{2.811}{\sqrt{12}}=46.460    

47.917+1.796\frac{2.811}{\sqrt{12}}=49.374    

Part b

For this case the system of hypothesis are:

Null hypothesis: \mu =50

Alternative hypothesis: \mu \neq 50

And after analyze the interval obtained the upper limit not contains the value of 50, so then we can conclude that the claim is not satisfied for this case, and the population mean seems to be lower than 50 at 10% of significance.

6 0
3 years ago
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Fudgin [204]

check the picture below.

namely, which of those intervals has the steepest slope, recall slope = average rate of change.

now, from the picture, notice, those two there are the steepest, the other three are leaning too much to the "ground".

so, from those two, which is the steepest anyway?  let's check their slope.


\bf \stackrel{\textit{from the 6th to the 8th hour}}{(\stackrel{x_1}{6}~,~\stackrel{y_1}{104})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{146})} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{146-104}{8-2}\implies \cfrac{42}{2}\implies 21~~\bigotimes \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \stackrel{\textit{from the 1st to the 2nd hour}}{(\stackrel{x_1}{1}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{34})} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{34-12}{2-1}\implies \cfrac{22}{1}\implies 22~~\checkmark

4 0
3 years ago
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