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RoseWind [281]
3 years ago
15

Accidents on highways are one of the main causes of death or injury in developing countries and the weather conditions have an i

mpact on the rates of death and injury. 25% of accidents in foggy conditions result in death, 12.5% of accidents in rainy conditions result in death, and 5% of accidents in sunny conditions result in death. Sunny conditions occur 60% of the time, while rainy and foggy conditions each occur 20% of the time. What is the probability that and accident results in a death?
Mathematics
1 answer:
pashok25 [27]3 years ago
6 0

Answer:

0.105 = 10.5% probability that an accident results in a death.

Step-by-step explanation:

What is the probability that an accident results in a death?

5% of 60%(sunny)

25% of 20%(foggy)

12.5% of 20%(rainy)

So

p = 0.05*0.6 + 0.25*0.2 + 0.125*0.2 = 0.105

0.105 = 10.5% probability that an accident results in a death.

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Answer:

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Step-by-step explanation:

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3 years ago
Find all possible values of α+
const2013 [10]

Answer:

\rm\displaystyle  0,\pm\pi

Step-by-step explanation:

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===========================

we want to find all possible values of α+β+γ when <u>tanα+tanβ+tanγ = tanαtanβtanγ</u><u> </u>to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

\rm\displaystyle  \tan( \alpha )  +  \tan( \beta ) =  \tan( \alpha )  \tan( \beta )  \tan( \gamma )  -  \tan( \gamma )

factor out tanγ:

\rm\displaystyle  \tan( \alpha )  +  \tan( \beta ) =   \tan( \gamma ) (\tan( \alpha )  \tan( \beta ) -  1)

divide both sides by tanαtanβ-1 and that yields:

\rm\displaystyle   \tan( \gamma ) =  \frac{ \tan( \alpha )  +  \tan( \beta ) }{ \tan( \alpha )  \tan( \beta )    - 1}

multiply both numerator and denominator by-1 which yields:

\rm\displaystyle   \tan( \gamma ) =   -  \bigg(\frac{ \tan( \alpha )  +  \tan( \beta ) }{ 1 - \tan( \alpha )  \tan( \beta )   } \bigg)

recall angle sum indentity of tan:

\rm\displaystyle   \tan( \gamma ) =   -  \tan( \alpha  +  \beta )

let α+β be t and transform:

\rm\displaystyle   \tan( \gamma ) =   -  \tan( t)

remember that tan(t)=tan(t±kπ) so

\rm\displaystyle   \tan( \gamma ) =    -\tan(   \alpha   +\beta\pm k\pi )

therefore <u>when</u><u> </u><u>k </u><u>is </u><u>1</u> we obtain:

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remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

\rm\displaystyle   \tan( \gamma ) =    \tan(   -\alpha  -\beta\pm \pi )

recall that if we have common trigonometric function in both sides then the angle must equal which yields:

\rm\displaystyle  \gamma  =      -   \alpha   -  \beta \pm \pi

isolate -α-β to left hand side and change its sign:

\rm\displaystyle \alpha  +  \beta  +   \gamma  =  \boxed{ \pm \pi  }

<u>when</u><u> </u><u>i</u><u>s</u><u> </u><u>0</u>:

\rm\displaystyle   \tan( \gamma ) =    -\tan(   \alpha   +\beta \pm 0 )

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\rm\displaystyle   \tan( \gamma ) =    \tan(   -\alpha   -\beta\pm 0 )

recall that if we have common trigonometric function in both sides then the angle must equal therefore:

\rm\displaystyle  \gamma  =      -   \alpha   -  \beta \pm 0

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\rm\displaystyle \alpha  +  \beta  +   \gamma  =  \boxed{ 0  }

and we're done!

8 0
3 years ago
Read 2 more answers
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slava [35]

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

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CAH: Cos(Ф)= Adj / Hyp

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5)

Adj = 14

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∠X

so use

CAH

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7)

∠X

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use TOA

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X = arcTan( 29 /24)

X = 50.389

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8)

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use TOA agian

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:)

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attashe74 [19]

Answer:

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Step-by-step explanation:

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4 0
3 years ago
In ΔMNO, the measure of ∠O=90°, the measure of ∠N=70°, and OM = 3.3 feet. Find the length of MN to the nearest tenth of a foot.
Aleks04 [339]

Answer:

Side MN = 3.5

Step-by-step explanation:

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Angle ∠N = 70° = 1.22173 rad = 7/18π

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4 0
3 years ago
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