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GalinKa [24]
3 years ago
5

Toby's Trucking Company determined that on an annual basis, the distance traveled per truck is normally distributed, with a mean

of 50,000 miles and a standard deviation of 12,000 miles How many miles will be traveled by at least (equal to and more than) 72% of the trucks?
Physics
1 answer:
Reptile [31]3 years ago
6 0

Answer: 56994 miles

Explanation:

Given : Toby's Trucking Company determined that on an annual basis, the distance traveled per truck is normally distributed with

\mu=50,000\text{ miles}

Standard deviation : \sigma=12,000\text{ miles}

Let a be the distance traveled by at least 72% of the trucks.

Let X be the random variable that represents the distance traveled by a truck

Then P(x\geq a)=0.72

The critical value corresponds to p-value 0.72 :z=0.5828415

Also, z=\dfrac{x-\mu}{\sigma}

\Rightarrow\ 0.5828415=\dfrac{a-50000}{12000}\\\\\Rightarrow\ a=12000(0.5828415)+50000=56994.098\approx56994

Hence, 56994 miles will be traveled by at least (equal to and more than) 72% of the trucks .

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Answer:

the correct result is r = 3.71 10⁸ m

Explanation:

For this exercise we will use the law of universal gravitation

          F = - \frac{m_{1} m_{2} }{r^2}

We call the masses of the Earth M, the masses of the moon m and the masses of the rocket m ', let's set a reference system in the center of the Earth, the distance from the Earth to the moon is d = 3.84 108 m

rocket force -Earth

          F₁ = - \frac{m' M }{r^2}

rocket force - Moon

          F₂ = - \frac{m' m }{(d-r)^2}

in the problem ask for what point the force has the relation

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let's substitute

          2 2 \frac{M}{r^2} = \frac{m}{(d-r)^2}

          (d-r) ² = \frac{m}{2M} r²

           d² - 2rd + r² = \frac{m}{2M} r²

           r² (1 -\frac{m}{2M}) - 2rd + d² = 0

Let's solve this quadratic equation to find the distance r, let's call

           a = 1 - \frac{m}{2M}

           a = 1 - \frac{7.36 10^{22} }{2 \  5398 10^{24}} = 1 - 6.15 10⁻³

           a = 0.99385

         

            a r² - 2d r + d² = 0

           r =  \frac  {2d \frac{+}{-}   \sqrt{4d^2 - 4 a d^2}} {2a}

           r = [2d ± 2d \sqrt{1-a}] / 2a

           r = \frac{d}{a}   (1 ± √ (1.65 10⁻³)) =  \frac{d}{a} (1 ± 0.04)

           r₁ = \frac{d}{a} 1.04

           r₂ = \frac{d}{a} 0.96

let's calculate

           r₁ = \frac{3.84 10^8}{0.99385} 1.04

           r₁ = 401.8 10⁸ m

          r₂ = \frac{3.84 10^8}{0.99385} 0.96

          r₂ = 3.71 10⁸ m

therefore the correct result is r = 3.71 10⁸ m

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Answer:

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Answer:

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Explanation:

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We have the final answer as

<h3>0.67 m/s²</h3>

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