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SOVA2 [1]
3 years ago
8

HELP ASAP! I REALLY NEED IT!

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
4 0

Answer:

46 \frac{7}{8}  \: cubic \: feet

Step-by-step explanation:

\boxed{volume \: of \: prism = base \: area \:  \times height}

Base area= length ×width

Let's convert all the mixed numbers into improper fraction for easier calculation.

Width

= 7½

=  \frac{7(2)}{2}  +  \frac{1}{2}

=  \frac{14}{2}  +  \frac{1}{2}

=  \frac{15}{2} ft

Height

= 1¼

=  \frac{4}{4}  +  \frac{1}{4}

=  \frac{5}{4} ft

Volume of prism

= 5 \times  \frac{15}{2}  \times  \frac{5}{4}

=  \frac{375}{8}

= 46 \frac{7}{8}  \: ft {}^{3}

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he life of light bulbs is distributed normally. The variance of the lifetime is 625 and the mean lifetime of a bulb is 540 hours
almond37 [142]

Using the normal distribution, it is found that there is a 0.877 = 87.7% probability of a bulb lasting for at most 569 hours.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

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

  • The z-score measures how many standard deviations the measure is above or below the mean.
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The mean and the standard deviation are given, respectively, by:

\mu = 540, \sigma = \sqrt{625} = 25

The probability of a bulb lasting for at most 569 hours is the <u>p-value of Z when X = 569</u>, hence:

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

Z = \frac{569 - 540}{25}

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Z = 1.16 has a p-value of 0.877.

0.877 = 87.7% probability of a bulb lasting for at most 569 hours.

More can be learned about the normal distribution at brainly.com/question/24663213

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