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lisov135 [29]
4 years ago
10

Segment LM is the midsegment of trapezoid ABCD. AB= x + 8, LM = 4x + 3, and DC = 187. What is the value of x?

Mathematics
1 answer:
kykrilka [37]4 years ago
4 0
Hello,
If we draw the line AM intercept DC in F,
using the theorem of Thales:

LM/DF=1/2
==>
(4x+3)/(187+x+8à=1/2
==>8x+6=195+x
==> 7x=189
==>x=27

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Step-by-step explanation:

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vekshin1

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A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Success with
Vikentia [17]

Answer:

(a) The PMF of <em>X</em> is: P(X=k)=(1-0.20)^{k-1}0.20;\  k=0, 1, 2, 3....

(b) The probability that a player defeats at least two opponents in a game is 0.64.

(c) The expected number of opponents contested in a game is 5.

(d) The probability that a player contests four or more opponents in a game is 0.512.

(e) The expected number of game plays until a player contests four or more opponents is 2.

Step-by-step explanation:

Let <em>X</em> = number of games played.

It is provided that the player continues to contest opponents until defeated.

(a)

The random variable <em>X</em> follows a Geometric distribution.

The probability mass function of <em>X</em> is:

P(X=k)=(1-p)^{k-1}p;\ p>0, k=0, 1, 2, 3....

It is provided that the player has a probability of 0.80 to defeat each opponent. This implies that there is 0.20 probability that the player will be defeated by each opponent.

Then the PMF of <em>X</em> is:

P(X=k)=(1-0.20)^{k-1}0.20;\  k=0, 1, 2, 3....

(b)

Compute the probability that a player defeats at least two opponents in a game as follows:

P (X ≥ 2) = 1 - P (X ≤ 2)

              = 1 - P (X = 1) - P (X = 2)

              =1-(1-0.20)^{1-1}0.20-(1-0.20)^{2-1}0.20\\=1-0.20-0.16\\=0.64

Thus, the probability that a player defeats at least two opponents in a game is 0.64.

(c)

The expected value of a Geometric distribution is given by,

E(X)=\frac{1}{p}

Compute the expected number of opponents contested in a game as follows:

E(X)=\frac{1}{p}=\frac{1}{0.20}=5

Thus, the expected number of opponents contested in a game is 5.

(d)

Compute the probability that a player contests four or more opponents in a game as follows:

P (X ≥ 4) = 1 - P (X ≤ 3)

              = 1 - P (X = 1) - P (X = 2) - P (X = 3)

              =1-(1-0.20)^{1-1}0.20-(1-0.20)^{2-1}0.20-(1-0.20)^{3-1}0.20\\=1-0.20-0.16-0.128\\=0.512

Thus, the probability that a player contests four or more opponents in a game is 0.512.

(e)

Compute the expected number of game plays until a player contests four or more opponents as follows:

E(X\geq 4)=\frac{1}{P(X\geq 4)}=\frac{1}{0.512}=1.953125\approx 2

Thus, the expected number of game plays until a player contests four or more opponents is 2.

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