suppose y varies directly with x, and y = 8 when x = -6. what direct variation equation relates x and y? what is the value of y

when x = -2?

Mathematics

1 answer:

Kisachek [45]3 years ago

8 0

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{we also know that }
\begin{cases}
y=8\\
x=-6
\end{cases}\implies 8=k(-6)\implies \cfrac{8}{-6}=k
\\\\\\
-\cfrac{4}{3}=k\qquad therefore\qquad \boxed{y=-\cfrac{4}{3}x}
\\\\\\
\textit{when x = -2, what is \underline{y}?}\qquad y=-\cfrac{4}{3}(-2)$

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Answer:

z = -0.4.

Step-by-step explanation:

Here's the formula for finding the z-score (a.k.a. standardized normal variable) of one measurement $x$ of a normal random variable $X \sim N(\mu,\; \sigma^{2})$ :

$\displaystyle z = \frac{x-\mu}{\sigma}$ ,

where

$z$ is the z-score of this measurement,
$x$ is the value of this measurement,
$\mu$ is the mean of the random normal variable, and
$\sigma$ is the standard deviation (the square root of variance) of the random normal variable.