3. Write an equation of the line that passes through (-2, 8) and (4,4).

Mathematics

1 answer:

gtnhenbr [62]3 years ago

4 0

$y = - \frac{2}{3} x + \frac{20}{3}$

Step-by-step explanation:

y=mx+c

label your points

(-2;8). pnt2

(4;4). pnt1

$m = \frac{y2 - y1}{x2 - x1}$

$m = \frac{8 - 4}{ - 2 - 4}$

$m = \frac{ 4}{ - 6}$

$m = - \frac{2}{3}$

substitute gradient and 1 point into equation to get c

$8 = ( - \frac{2}{3} )( - 2) + c$

$8 = \frac{4}{3} + c$

$c = 8 - \frac{4}{3}$

$c = \frac{20}{3}$

Therefore the equation is

$y = - \frac{2}{3} x + \frac{20}{3}$

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The lengths of nails produced in a factory are normally distributed with a mean of 4.84 centimeters and a standard deviation of

Helga [31]

Answer:

Top 3%: 4.934 cm

Bottom 3%: 4.746 cm

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:

$\mu = 4.84, \sigma = 0.05$