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timurjin [86]
3 years ago
15

Suppose you are taking the bus home, and can take either the 51 or the 82. you know that the 82 will arrive in exactly 10 minute

s, but because the 51 is unreliable, you suspect that the amount of time until it arrives is uniformly distributed between 0 and 30 minutes. you take the first bus that arrives. let t be the number of minutes you wait until you board a bus. find e[t].
Mathematics
1 answer:
elena55 [62]3 years ago
8 0
We are dealing here with a uniform distribution ranging from 0 to 30 minutes.  We need to calculate the probability that the unreliable bus will arrive before the reliable one.  This probability is the area under the uniform distribution "curve" from 0 to 10 minutes.  This constitutes 1/3 of the entire unform distr. curve.  So the probability that the unreliable bus will arrive before the reliable one is 1/3, or 0.33.  The probability that it will arrive AFTER the reliable bus is 2/3, or 0.67.
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Ramiro earns $20 per hour during the week and $30 per hour for overtime on the weekends. One week Ramiro earned a total of $650.
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Answer:

Week=25 Hours

Weekend= 5 Hours

Step-by-step explanation:

So we need to use the info they gave us and create two equations. Firstly we know how much he gets paid per hour during the week (x) and how much he gets paid on the weekend (y).

$20x+$30y=$650

We get this because we know the combined rates he is paid times the hours should add up to the amount he earned.

The next equation will be made off of the information that he worked 5 times as many hours during the week as on the weekend. This tells us that we will take the weekend hours (y) and multiply them by 5 in order to get the week hours (x).

x=5y      Now, since we have one variable by itself, we can plug it in for x in the first equation.

20(5y)+30y=650    Our first step here is to distribute the 20 to the 5y in order to eliminate the parenthesis.

100y+30y=650    Next add the like terms together (100y+30y).

Now all we have to do to find y is divide by 130 on both sides to get y alone.

130y=650  

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130     130

y=5             Now to solve for x we just plug our y value into one of the equations above. I'm going to use the second equation.

x=5(5)

x=25      

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