Ответ №1.................................................
Основное свойство пропорции: Произведение крайних членов пропорции равно произведению ее средних членов.
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![\displaystyle \tt a). \ \ \frac{4x-32}{12}=\frac{4}{5}\\\\{} \ \ \ \ \ \ 5\cdot(4x-32)=4\cdot12\\\\{} \ \ \ \ \ \ 20x-160=48\\\\{} \ \ \ \ \ \ x=208:20\\\\{} \ \ \ \ \ \ x=10,4\\\\\\b). \ \ \frac{6x+3}{27}=\frac{5}{9}\\\\{} \ \ \ \ \ \ 9\cdot(6x+3)=27\cdot5\\\\{} \ \ \ \ \ \ 54x+27=135\\\\{} \ \ \ \ \ \ x=108:54\\\\{} \ \ \ \ \ \ x=2](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Ctt+a%29.+%5C+%5C+%5Cfrac%7B4x-32%7D%7B12%7D%3D%5Cfrac%7B4%7D%7B5%7D%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+5%5Ccdot%284x-32%29%3D4%5Ccdot12%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+20x-160%3D48%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+x%3D208%3A20%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+x%3D10%2C4%5C%5C%5C%5C%5C%5Cb%29.+%5C+%5C+%5Cfrac%7B6x%2B3%7D%7B27%7D%3D%5Cfrac%7B5%7D%7B9%7D%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+9%5Ccdot%286x%2B3%29%3D27%5Ccdot5%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+54x%2B27%3D135%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+x%3D108%3A54%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+x%3D2)
![\displaystyle \tt c). \ \ \frac{4x-24}{60}=\frac{4}{15}\\\\{} \ \ \ \ \ \ 15\cdot(4x-24)=60\cdot4\\\\{} \ \ \ \ \ \ 60x-360=240\\\\{} \ \ \ \ \ \ x=600:60\\\\{} \ \ \ \ \ \ x=10\\\\\\d), \ \ \frac{3}{4}=\frac{7x+9}{40}\\\\{} \ \ \ \ \ \ 4\cdot(7x+9)=3\cdot40\\\\{} \ \ \ \ \ \ 28x+36=120\\\\{} \ \ \ \ \ \ x=84:28\\\\{} \ \ \ \ \ \ x=3](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Ctt+c%29.+%5C+%5C+%5Cfrac%7B4x-24%7D%7B60%7D%3D%5Cfrac%7B4%7D%7B15%7D%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+15%5Ccdot%284x-24%29%3D60%5Ccdot4%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+60x-360%3D240%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+x%3D600%3A60%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+x%3D10%5C%5C%5C%5C%5C%5Cd%29%2C+%5C+%5C+%5Cfrac%7B3%7D%7B4%7D%3D%5Cfrac%7B7x%2B9%7D%7B40%7D%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+4%5Ccdot%287x%2B9%29%3D3%5Ccdot40%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+28x%2B36%3D120%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+x%3D84%3A28%5C%5C%5C%5C%7B%7D+%5C+%5C+%5C+%5C+%5C+%5C+x%3D3)
2 детали из 30 с дефектами, а 28 без дефектов.
Вер-сть дефекта p=0,04; q=1-p=0,96.
По теореме Бернулли
P = C(2,30)*p^2*q^28 = 30*29/2*(0,04)^2*(0,96)^28 ~ 0,222
№1
Каждый бизнесмен раздаст визитки 4-ём остальным.
5 * 4 = 20 (виз.) - всего.
Ответ: 20 визиток.
№2
У 1-ого человека есть 5 способов;
у 2-ого - 4 способа;
у 3-ого - 3 способа;
у 4-ого - 2 способа.
5 * 4 * 3 * 2 = 120 - способов.
или
5!/(5 - 4)! = 5!/1! = 5! = 120
Ответ: 120 спосбов.
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6=3*2
15=3*5
НОК(6,15)=3*2*5=30
5/6=25/30
2/15=4/30
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2=2*2
12=2*2*3
18=2*3*3
НОК(4,12,18)=2*2*3*3=36
1/4=9/36
5/12=15/36
13/18=26/36