If four points are collinear are they coplanar

Mathematics

1 answer:

kap26 [50]3 years ago

6 0

It is False , because they could be in a common plane but they do not form a single line

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The set of life spans of an appliance is normally distributed with a mean mu = 48 months and a standard deviation sigma = 8 mont

navik [9.2K]

Using the normal distribution, it is found that the life span of an appliance that has a z-score of –3 is of 24 months.

<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.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, the parameters are given as follows:

$\mu = 48, \sigma = 8, Z = -3$ .

Hence:

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

$-3 = \frac{X - 48}{8}$

X - 48 = -24

X = 24.

The life span of an appliance that has a z-score of –3 is of 24 months.

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

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6 0

2 years ago

Establish the identity.<br> (2 cos 0-6 sin 0)² + (6 cos 0+2 sin 0)2 = 40

kogti [31]

Rewriting the left-hand side as follows,

$(2\cos\theta-6\sin \theta)^2 +(6\cos \theta+2\sin \theta)^2\\\\=4\cos^2 \theta-24\cos \theta \sin \theta+36 \sin^2 \theta+36 \cos^2 \theta+24 \cos \theta \sin \theta+4 \sin^2 \theta\\\\=40\cos^2 \theta+40 \sin^2 \theta\\\\=40(\cos^2 \theta+\sin^2 \theta)\\\\=40$