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slava [35]
3 years ago
10

Lola takes the train from Paris to Nice. The distance between the two cities is about 920 , 000 meters. If the train travels at

a speed of 230 kilometers per hour, how long will it take Lola to travel from Paris to Nice?
Mathematics
2 answers:
Zielflug [23.3K]3 years ago
8 0
We can first use the formula:
Time = Distance/speed

One thing we need to notice is that we need to change the unit of the distance:
920000÷1000
=920km

In this case,it will take:
920÷230
=4hrs

Therefore,4 hours is the answer.

Hope it helps!



nika2105 [10]3 years ago
5 0

First of all we must use the same unit measure for all data, otherwise it wouldn't make sense to compare meters and kilometers.

Since one kilometer is the same as 1000 meters, we have that 920000 meters are 920 kilometers.

Now, the train travels at 230 kilometers per hour. It means that it travels 230 kilometers with each passing hour

So, after 1 hour, the train travels 230 km. After two hours, the train travels 2x230 = 460km, and so on

In general, the distance traveled after k hours is 230k.

We want that distance to be 920, so the equation is

230k = 920 \iff k = \cfrac{920}{230} = \cfrac{92}{23} = 4

So, the train travels 920 kilometers (i.e. 920000 meters) in 4 hours.

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For the second estimator we have this:

E(\theta_2) = \frac{1}{2} [2E(X_1) -E(X_3) +E(X_5)]=\frac{1}{2} [2\mu -\mu +\mu] = \frac{1}{2} [2\mu]= \mu

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Step-by-step explanation:

For this case we assume that we have a random sample given by: X_1, X_2,....,X_7 and each X_i \sim N (\mu, \sigma)

Part a

In order to check if an estimator is unbiased we need to check this condition:

E(\theta) = \mu

And we can find the expected value of each estimator like this:

E(\theta_1 ) = \frac{1}{7} E(X_1 +X_2 +... +X_7) = \frac{1}{7} [E(X_1) +E(X_2) +....+E(X_7)]= \frac{1}{7} 7\mu= \mu

So then we conclude that \theta_1 is unbiased.

For the second estimator we have this:

E(\theta_2) = \frac{1}{2} [2E(X_1) -E(X_3) +E(X_5)]=\frac{1}{2} [2\mu -\mu +\mu] = \frac{1}{2} [2\mu]= \mu

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Part b

For this case first we need to find the variance of each estimator:

Var(\theta_1) = \frac{1}{49} (Var(X_1) +...+Var(X_7))= \frac{1}{49} (7\sigma^2) = \frac{\sigma^2}{7}

And for the second estimator we have this:

Var(\theta_2) = \frac{1}{4} (4\sigma^2 -\sigma^2 +\sigma^2)= \frac{1}{4} (4\sigma^2)= \sigma^2

And the relative efficiency is given by:

RE= \frac{Var(\theta_1)}{Var(\theta_2)}=\frac{\frac{\sigma^2}{7}}{\sigma^2}= \frac{1}{7}

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brainly.com/question/21605027

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