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3 years ago

Find the length of the given segments and determine if they are congruent Simplify DE and RS

Mathematics

1 answer:

SOVA2 [1]3 years ago

6 0

Answer:

The answer is below

Step-by-step explanation:

The complete question is contained in the image.

The distance between points $A(x_1,y_1)$ and $B(x_2,y_2)$ in the coordinate plane is given as:

$|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Point D is at (7, 0) and E at (0, -2) hence the distance between the two points is:

$|DE|=\sqrt{(0-7)^2+(-2-0)^2}=\sqrt{49+4}=\sqrt{53}=7.28$

Point R is at (-7, -7) and S at (3, -3) hence the distance between the two points is:

$|RS|=\sqrt{(3-(-7))^2+(-3-(-7))^2}=\sqrt{100+16}=\sqrt{116}=10.77$

Since |RS| ≠ |DE|, therefore they are not congruent

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The length of time that an auditor spends reviewing an invoice is approximately normally distributed with a mean of 600 seconds

Bumek [7]

Answer: 11.5%

Explanation:

Since 1 minute = 60 seconds, we multiply 12 minutes by 60 so that 12 minutes = 720 seconds. Thus, we're looking for a probability that the auditor will spend more than 720 seconds.

Now, we get the z-score for 720 seconds by the following formula:

$\text{z-score} = \frac{x - \mu}{\sigma}$

where

$t = \text{time for the auditor to finish his work } = 720 \text{ seconds}
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\\ \sigma = \text{standard deviation } = 100 \text{ seconds}$

So, the z-score of 720 seconds is given by:

$\text{z-score} = \frac{x - \mu}{\sigma}
\\
\\ \text{z-score} = \frac{720 - 600}{100}
\\
\\ \boxed{\text{z-score} = 1.2}$

Let

t = time for the auditor to finish his work
z = z-score of time t

Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:

$P(t \ \textgreater \ 720) 
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Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice.

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SIZIF [17.4K]

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If $b$ the graph moves vertically down

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lisov135 [29]

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