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Tanya [424]
3 years ago
13

Among the 7th graders in a middle school, three quarters of them play at least one sport. Among the 7th graders who play sports,

half of them play more than one sport. Among the 7th graders who play more than one sport, one third of them play more than two sports. Among the 7th graders who play more than two sports, one quarter of them play more than three sports. Sixteen 7th graders play more than three sports at the school. How many 7th graders are in the school
Mathematics
1 answer:
kifflom [539]3 years ago
4 0

Answer:

512

Step-by-step explanation:

Let the number of 7th graders in the school is x.

As three-quarters of them play at least one sport, so, the number of 7th graders who play sport = \frac 3 4 x.

Among the 7th graders who play sports, half of them play more than one sport. So, the number of 7th graders who play more than one sport = \frac 1 2\times \frac 3 4 x=\frac 3 8 x.

Among the 7th graders who play more than one sport, one-third of them play more than two sports. So, the number of 7th graders who play more than two sport = \frac 1 3\times \frac 3 8 x=\frac 1 8 x.

Among the 7th graders who play more than two sports, one-quarter of them play more than three sports.

So, the number of 7th graders who play more than three sport = \frac 1 4\times \frac 1 8 x=\frac{1}{32} x.

7th graders play more than three sports at the school= 16

\Rightarrow \frac{1}{32} x=16

\Rightarrow x =16 \times 32

\Rightarrow x = 512

Hence, the total numbers of 7th graders in the school are 512.

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A small regional carrier accepted 23 reservations for a particular flight with 20 seats. 14 reservations went to regular custome
MrRissso [65]

Answer:

- The probability that overbooking occurs means that all 8 non-regular customers arrived for the flight. Each of them has a 56% probability of arriving and they arrive independently so we get that  

P(8 arrive) = (0.56)^8 = 0.00967

- Let's do part c before part b. For this, we want an exact booking, which means that exactly 7 of the 8 non-regular customers arrive for the flight. Suppose we align these 8 people in a row. Take the scenario that the 1st person didn't arrive and the remaining 7 did. That odds of that happening would be (1-.56)*(.56)^7.

Now take the scenario that the second person didn't arrive and the remaining 7 did. The odds would be  

(0.56)(1-0.56)(0.56)^6 = (1-.56)*(.56)^7. You can run through every scenario that way and see that each time the odds are the same. There are a total of 8 different scenarios since we can choose 1 person (the non-arriver) from 8 people in eight different ways (combination).  

So the overall probability of an exact booking would be [(1-.56)*(.56)^7] * 8 = 0.06079

- The probability that the flight has one or more empty seats is the same as the probability that the flight is NOT exactly booked NOR is it overbooked. Formally,  

P(at least 1 empty seat) = 1 - P(-1 or 0 empty seats)  

= 1 - P(overbooked) - P(exactly booked)

= 1 - 0.00967 - 0.06079  

= 0.9295.

Note that, the chance of being both overbooked and exactly booked is zero, so we don't have to worry about that.

Hope that helps!

Have a great day :P

7 0
3 years ago
There are 360 mins for a monthly cell phone minutes for 4 people in the family, can each person get the same number of minutes o
telo118 [61]

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Answer:

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3 years ago
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3 years ago
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