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juin [17]
3 years ago
12

Ten weight lifters are competing in a team weight-lifting contest. Of the lifters, 3 are from the United States, 4 are from Russ

ia, 2 are from China, and 1 is from Canada. If the scoring takes account of the countries that the lifters represent, but not their individual identities, how many different outcomes are possible from the point of view of scores? How many different outcomes correspond to results in which the United States has 1 competitor in the top three and 2 in the bottom three?
Mathematics
1 answer:
ruslelena [56]3 years ago
5 0

Answer:

(a) 65536 - the basic principle of counting

(b) 2520 - use the multinomials.  

Step-by-step explanation:

Divide 8 people among 4 schools

The teachers are different among themselves, and so are the schools.  

(a)

Every teacher can choose a school. By the basic principle of counting: 4.4.4.4.4.4.4.4 = 4^8 = 65536

different divisions of the teachers

Note: this does not ensure that every school gets a teacher  

(b) - <u>Every school gets precisely 2 teachers:</u>

to divide 8 different objects into four groups of fixed sizes 2, 2, 2 and 2, use the multinomial coefficient  

( 8   2, 2, 2, 2) = (8!)/(2!2!2!2!) ==> 2520

different divisions of the teachers

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35.5 feet

Step-by-step explanation:

x + x + 3 + x + 5 = 99.5

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3x = 91.5

x = 30.5

Largest side = (x+5)

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3 0
3 years ago
58. 122. 61. None of the choices are correct
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Answer:

C. 61

Step-by-step explanation:

Two sides are equal, so the triangle is an isosceles triangle.

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58 + x + x = 180

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3 years ago
Glenn needs to cut pieces of a lanyard that are each 1 meter long to make lanyard key chains. If he has 3 pieces of lanyard that
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Step-by-step explanation:

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3 0
3 years ago
​Triangle A′B′C′​ is a dilation of ​triangle ABC​ .
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Answer:

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Step-by-step explanation:

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6 0
2 years ago
The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches.
Mama L [17]

Answer:

a) P(Y > 76) = 0.0122

b) i) P(both of them will be more than 76 inches tall) = 0.00015

   ii) P(Y > 76) = 0.0007

Step-by-step explanation:

Given - The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches.

To find - (a) If a man is chosen at random from the population, find

                    the probability that he will be more than 76 inches tall.

              (b) If two men are chosen at random from the population, find

                    the probability that

                    (i) both of them will be more than 76 inches tall;

                    (ii) their mean height will be more than 76 inches.

Proof -

a)

P(Y > 76) = P(Y - mean > 76 - mean)

                 = P( \frac{( Y- mean)}{S.D}) > \frac{( 76- mean)}{S.D})

                 = P(Z >  \frac{( 76- mean)}{S.D})

                 = P(Z > \frac{76 - 69.7}{2.8})

                 = P(Z > 2.25)

                 = 1 - P(Z  ≤ 2.25)

                 = 0.0122

⇒P(Y > 76) = 0.0122

b)

(i)

P(both of them will be more than 76 inches tall) = (0.0122)²

                                                                           = 0.00015

⇒P(both of them will be more than 76 inches tall) = 0.00015

(ii)

Given that,

Mean = 69.7,

\frac{S.D}{\sqrt{N} } = 1.979899,

Now,

P(Y > 76) = P(Y - mean > 76 - mean)

                 = P( \frac{( Y- mean)}{\frac{S.D}{\sqrt{N} } })) > \frac{( 76- mean)}{\frac{S.D}{\sqrt{N} } })

                 = P(Z > \frac{( 76- mean)}{\frac{S.D}{\sqrt{N} } })

                 = P(Z > \frac{( 76- 69.7)}{1.979899 }))

                 = P(Z > 3.182)

                 = 1 - P(Z ≤ 3.182)

                 = 0.0007

⇒P(Y > 76) = 0.0007

6 0
3 years ago
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