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tresset_1 [31]
3 years ago
6

A train leaves L.A. at 2pm and heads north at 50mph. If the next train leaves the station 3 hours later and heads north at 60 mp

h, what time will the second train catch up with the first?
Mathematics
1 answer:
yaroslaw [1]3 years ago
8 0

Answer:

  • 8 AM

Step-by-step explanation:

  • Start time = 2 PM
  • Speed of the first train = 50 mph
  • Speed of the second train = 60 mph
  • Trains head same direction
  • The second train spends 3 hour less time than the first but both take same distance

<u>Let the time in travel for the first train be x, then we have equation for distance:</u>

  • 50x = 60(x - 3)
  • 50x = 60x - 180
  • 60x - 50x = 180
  • 10x = 180
  • x = 18 hours

<u>Time when the second train caches up the first one:</u>

  • 2 PM + 18 hours = 8 AM next day
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Four cards are dealt from a standard fifty-two-card poker deck. What is the probability that all four are aces given that at lea
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Answer:

The probability is 0.0052

Step-by-step explanation:

Let's call A the event that the four cards are aces, B the event that at least three are aces. So, the probability P(A/B) that all four are aces given that at least three are aces is calculated as:

P(A/B) =  P(A∩B)/P(B)

The probability P(B) that at least three are aces is the sum of the following probabilities:

  • The four card are aces: This is one hand from the 270,725 differents sets of four cards, so the probability is 1/270,725
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So, the number of ways to select exactly 3 aces is:

4C3*48C1=\frac{4!}{3!(4-3)!}*\frac{48!}{1!(48-1)!}=192

Because we are going to select 3 aces from the 4 in the poker deck and we are going to select 1 card from the 48 that aren't aces. So the probability in this case is 192/270,725

Then, the probability P(B) that at least three are aces is:

P(B)=\frac{1}{270,725} +\frac{192}{270,725} =\frac{193}{270,725}

On the other hand the probability P(A∩B) that the four cards are aces and at least three are aces is equal to the probability that the four card are aces, so:

P(A∩B) = 1/270,725

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P=\frac{1/270,725}{193/270,725} =\frac{1}{193}=0.0052

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The equation for the relationship is y = \frac{7}{2}\cdot x.

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Given that point (x,y) = (6, 21) is part of a direct relationship. That is:

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