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...

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9