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3 years ago

Could someone please help me figure this out...

Mathematics

2 answers:

Oduvanchick [21]3 years ago

6 0

<h3>Answer: 29</h3>

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Work Shown:

The two angles shown are a linear pair. They are adjacent and supplementary. Supplementary angles add to 180 degrees.

(4x-5)+(x+40) = 180

5x+35 = 180

5x = 180-35

5x = 145

x = 145/5

x = 29

--------

As a check, if x = 29, then

4x-5 = 4*29-5 = 116-5 = 111

x+40 = 29+40 = 69

The two angles are 69 and 111 degrees which add to 69+111 = 180, which helps confirm the answer.

navik [9.2K]3 years ago

4 0

Answer:

x = 29

Step-by-step explanation:

The two angles with measures are a linear pair.

Angles in a linear pair are supplementary, so their measures add to 180 deg.

4x - 5 + x + 40 = 180

Combine like terms on left side.

5x + 35 = 180

Subtract 35 from both sides.

5x = 145

Divide both sides by 5.

x = 29

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3 years ago

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Step-by-step explanation:

Definitions and concepts

The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:

$P(X=x) =\lambda^x \frac{e^{-\lambda}}{x!}$

And the parameter $\lambda=1.4$ represent the average ocurrence rate per unit of time.

Solution to the problem

For this case the batch would be rejected if we found more than 3 defects, so then the probability of accept the batch would be given by:

$P(X\leq 3)= P(X=0) +P(X=1)+P(X=2) +P(X=3)$

And we can find the individual probabilities like this:

$P(X=0) =1.4^0 \frac{e^{-1.4}}{0!}= 0.2466$

$P(X=1) =1.4^1 \frac{e^{-1.4}}{1!}= 0.3452$

$P(X=2) =1.4^2 \frac{e^{-1.4}}{2!}= 0.2417$

$P(X=3) =1.4^3 \frac{e^{-1.4}}{3!}= 0.1128$

And replacing we got:

$P(X\leq 3)= P(X=0) +P(X=1)+P(X=2) +P(X=3)=0.2466+ 0.3452+0.2417+0.1128=0.9463$

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