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OLga [1]
3 years ago
12

The end points of wx are w (-5,-1) and x (2,6) What is the length of wx

Mathematics
1 answer:
sammy [17]3 years ago
4 0

Answer:

9.90 units (3 s.f.)

Step-by-step explanation:

distance formula

=  \sqrt{(x1 - x2)^{2}  + (y1 - y2)^{2} }

Length of WX

=  \sqrt{(2 - ( - 5))^{2}  + (6 - ( - 1)^{2} }  \\  =  \sqrt{(2 + 5)^{2}  + (6 + 1)^{2} }  \\  =  \sqrt{7 ^{2}  + 7^{2} }  \\  =  \sqrt{98}  \\  = 9.90 \: units \: (3 \: s.f.)

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Maksim231197 [3]

Answer:

10.38% probability that a randomly chosen book is more than 20.2 mm thick

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of n elements, the mean is n\mu and the standard deviation is s = \sqrt{n}\sigma

In this problem, we have that:

\mu = 250*0.08 = 20, \sigma = \sqrt{250}*0.01 = 0.1581

What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)

This is 1 subtracted by the pvalue of Z when X = 20.2. So

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

By the Central Limit Theorem

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

Z = \frac{20.2 - 20}{0.1581}

Z = 1.26

Z = 1.26 has a pvalue of 0.8962

1 - 0.8962 = 0.1038

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2 years ago
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Step-by-step explanation:

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