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3 years ago

Please help me solve number 15

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

6 0

Through (2, 5); perpendicular to y = (-2/7)x - 3

first, you should know that the slopes of parallel lines are the same. the slopes of perpendicular lines are opposite reciprocals of one another. in this case, because you need to find a perpendicular line, you'll want to find the opposite reciprocal of (-2/7)

change the sign and flip the fraction: your new slope is 7/2

from there, you just plug it into point-slope form:

y - y1 = m(x - x1)
y - 5 = (7/2)(x - 2)

then you can solve it further to bring it into slope-intercept (y = mx + b):

y - 5 = (7/2)(x - 2)
y - 5 = (7/2)x - 7
y = (7/2)x - 2 is your answer.

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C) 20 hours

Step-by-step explanation:

x = number of hours

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3 years ago

A manufacturer makes chocolate squares that have a target weight of 8 g. Quality control engineers sample 30 chocolate squares t

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Using the normal distribution and the central limit theorem, it is found that the power of the test is of 0.9992 = 99.92%.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem:

The mean is $\mu = 8.5$ .

The standard deviation is $\sigma = 0.87$ .

A sample of 30 is taken, hence $n = 30, s = \frac{0.87}{\sqrt{30}} = 0.1588$ .

The power of the test is given by the probability of a sample mean above 8, which is 1 subtracted by the p-value of Z when X = 8, so:

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

By the Central Limit Theorem:

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

$Z = \frac{8 - 8.5}{0.1588}$

$Z = -3.15$

$Z = -3.15$ has a p-value of 0.0008.

1 - 0.0008 = 0.9992.

The power of the test is of 0.9992 = 99.92%.

To learn more about the normal distribution and the central limit theorem, you can check brainly.com/question/24663213

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3 years ago

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Answer:

Solution of the equation 2|x +7|-3=5 is :

x1 = - 11 and x2 = - 3

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