You are playing the duck pond game at the carnival! there are 20 ducks in the pond. five of the ducks have blue dots on their bellies. you win if you pick up a duck that has a blue dot. you can play one round for $1 or four rounds for $3. in each round you will pick a duck out of the pond and see if it has a blue dot on its belly. if you win you get a prize. after that you place the duck back in the pond, close your eyes, and the worker moves all of the ducks around. if you play the duck pond game four times, what is the probability that you will win three of the times? (hint: how many possible outcomes are there for this experiment? )

Pt= 3/256

Step-by-step explanation:

For each round the probability of winning is:

Pw = number of blue dotted ducks/ total number of ducks

Pw= 5/20 ( since the duck is being replaced)

The probability of losing is:

Pl= number of ducks without blue dotted belly/ total number of ducks

Pl = 15/20

Therefore the probability of winning 3 times out of 4 is:

Pt= Pw× Pw×Pw×Pl

Pt= (5×5×5×15)/(20×20×20×20)

Pt= 1875/160000

Pt= 3/256

Goodluck...

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

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.