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Tju [1.3M]
1 year ago
5

Hello I really need help with this

Mathematics
2 answers:
Harman [31]1 year ago
5 0

Answer:

<u>7</u>

Step-by-step explanation:

The sides are in proportion.

  • \frac{AC}{DF} = \frac{AB}{DE}
  • 35/? = 20/4
  • 35/? = 5
  • ? = 35/5
  • ? = <u>7</u>
Talja [164]1 year ago
5 0

Answer:

7

Step-by-step explanation:

Given,

△ABC ~ △DEF

( ~ means similar )

To find : missing side length

Similar triangle rule : -

If two triangles are similar, their corresponding sides are similar.

So,

AB ~ DE

BC ~ EF

AC ~ DF

Let the missing side length ( DF ) be " x ".

Note : -

When the corresponding sides are divided, their ratios will be same.

That is,

AB / DE

= 20 / 4

= 5 / 1

= 5 : 1

BC / EF

= 40 / 8

= 5 / 1

= 5 : 1

AC / DF should also be equal to 5 : 1.

AC / DF = 5 : 1

35 / x = 5 / 1

Cross multiply,

x * 5 = 35 * 1

5x = 35

Divide 5 on both sides,

x = 35 / 5

x = 7

Therefore,

the missing side length is 7.

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A large manufacturing plant uses lightbulbs with lifetimes that are normally distributed with a mean of 1200 hours and a standar
a_sh-v [17]

Answer:

The bulbs should be replaced each 1060.5 days.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 1200, \sigma = 60

How often should the bulbs be replaced so that no more than 1% burn out between replacement periods?

This is the first percentile, that is, the value of X when Z has a pvalue of 0.01. So X when Z = -2.325.

Z = \frac{X - \mu}{\sigma}

-2.325 = \frac{X - 1200}{60}

X - 1200 = -2.325*60

X = 1060.5

The bulbs should be replaced each 1060.5 days.

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Answer:

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Step-by-step explanation:

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