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Verdich [7]
4 years ago
8

Whats the answer and why

Mathematics
1 answer:
IRISSAK [1]4 years ago
4 0
Apply the Pythagorean Theorem here.  

Square the lengths of the 2 shorter sides:  (20 mi)^2 and (40 mi)^2.  Correct results are 400 and 1600.  Combine these:  obtain 2000.

Then the length of the diagonal (which is the distance between the 2 cities) is
sqrt(2000) = sqrt(400)*sqrt(5) = 20 sqrt(5)    (answer)
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What is 5/20 as in a percent
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A certain restaurant always overbooks. If possible. At 7:00 pm the restaurant can seat 50 parties, but takes reservations for 53
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The probability that the restaurant can accommodate all the customers who do show up is 0.3564.

Step-by-step explanation:

The information provided are:

  • At 7:00 pm the restaurant can seat 50 parties, but takes reservations for 53.
  • If the probability of a party not showing up is 0.04.
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Let <em>X</em> denote the number of parties that showed up.

The random variable X follows a Binomial distribution with parameters <em>n</em> = 53 and <em>p</em> = 0.96.

As there are only 50 sets available, the restaurant can accommodate all the customers who do show up if and only if 50 or less customers showed up.

Compute the probability that the restaurant can accommodate all the customers who do show up as follows:

P(X\leq 50)=1-P(X>50)\\=1-P(X=51)-P(X=52)-P(X=53)\\=1-[{53\choose 51}(0.96)^{51}(0.04)^{53-51}]-[{53\choose 52}(0.96)^{52}(0.04)^{53-52}]\\-[{53\choose 53}(0.96)^{53}(0.04)^{53-53}]\\=1-0.27492-0.25377-0.11491\\=0.3564

Thus, the probability that the restaurant can accommodate all the customers who do show up is 0.3564.

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