Ahorse race has 14 entries and one person owns 5 of those horses. assuming that there are no ties, what is the probability that those five horses finish first comma second comma third comma fourth comma and fifth (regardless of order)? the probability that the five horses finish first comma second comma third comma fourth comma and fifth is nothing . (round to four decimal places as needed.)

The required probability is 0.0004995

Step-by-step explanation:

Consider the provided information

There are 14 horses and one person owns 5 of those horses.

We need to find the number of ways in which 5 horses finish first, second , third, fourth, and fifth.

Each horse has the same probability of winning,

Therefore, the required probability is:

The probability that one of those 5 horses will be first is

Now we have 4 horses left,

Probability that out of remaining 4 horses one will be second is .

The probability that out of remaining 3 horses one will be third is  .

The probability that out of remaining 2 horses one will be fourth is .

The probability that out of remaining 1 horses one will be fifth is .

Hence, the total probability is:

Hence, the required probability is 0.0004995

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.