In 2005, there were 74,250 car accidents. In 20,187 of them, the driver was a

Mathematics

1 answer:

zhuklara [117]3 years ago

6 0

Answer:

27.19% probability that a female driver was involved in an accident

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

74,250 car accidents. Of those, in 20,187, the driver was a female.

Based on this, what is the probability that a female driver was involved in an accident?

p = 20187/74250 = 0.2719

27.19% probability that a female driver was involved in an accident

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Find the vertex, focus, directrix, and focal width of the parabola. (5 points)

Anarel [89]

$\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf -\cfrac{1}{20}x^2=y\implies \cfrac{x^2}{-20}=y\implies x^2=-20y\implies (x-0)^2=-20(y-0) \\\\\\ (x-\stackrel{h}{0})^2=4(\stackrel{p}{-5})(y-\stackrel{k}{0})$

something noteworthy is that the squared variable is the "x", thus the parabola is a vertical one, the "p" value is negative, so is opening downwards, and the h,k is pretty much the origin,

vertex is at (0,0)

the focus point is "p" or 5 units down from there, namely at (0, -5)

the directrix is "p" units on the opposite direction, up, namely at y = 5

the focal width, well, |4p| is pretty much the focal width, in this case, is simply yeap, you guessed it, 20.

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balandron [24]

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