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hectictar
Apr 15, 2018

#6**0 **

https://web2.0calc.com/img/upload/9dc0601484f88e63c19f0354/ugh3.jpg

Pretend that we just got all the people that liked the movie in a room together. The question is what is the probability that a randomly selected person in that room is aged 18-34 ?

probability = number of people aged 18-34 in the room / number of people in the room

probability = num of people aged 18-34 that liked the movie / num of people that liked the movie

probability = 12 / (12 + 5 + 9)

probability = 12 / 26

probability ≈ 0.46

hectictarOct 23, 2018

#1**+1 **

m∠ABE = m∠CBE | __ | because parallelogram ABEF ≅ parallelogram CBED . |

m∠ABC = m∠ABE + m∠CBE | by the angle addition postulate. | |

30° = m∠ABE + m∠ABE | by substitution. | |

30° = 2m∠ABE | ||

15° = m∠ABE |

Let's draw a height of parallelogram ABEF so that BE and AF are the bases, and call it h .

sin( m∠ABE ) = h / AB

sin( 15° ) = h / x

x sin 15° = h

sin( m∠PBE ) = h / BP

sin( m∠PBE ) = x sin 15° / 10

m∠PBE = arcsin( x sin 15° / 10 )

And m∠PBE = (m∠PBQ)/2

(m∠PBQ)/2 = arcsin( x sin 15° / 10 ) | __ | |

m∠PBQ = 2 arcsin( x sin 15° / 10 ) |
| |

cos( m∠PBQ ) = cos( 2 arcsin( x sin 15° / 10 ) ) |
| |

cos( m∠PBQ ) = 1 - 2[ x sin 15° / 10 ] | By the double angle formula for cosine: cos(2u) = 1 - 2 sin | |

cos( m∠PBQ ) = 1 - 2 x |
| |

cos( m∠PBQ ) = 1 - 2 x^{2} sin^{2}(30/2°) / 100 |
| |

cos( m∠PBQ ) = 1 - 2 x^{2} ( (1 - cos 30°) / 2 ) / 100 | By the half-angle formula for sine: sin | |

cos( m∠PBQ ) = 1 - x |
| |

cos( m∠PBQ ) = 1 - x^{2} (1 - √3 / 2) / 100 |
| |

cos( m∠PBQ ) = 1 - x^{2} (2 - √3) / 200 |

hectictarOct 14, 2018