1.
a)
![x\ \textless \ 30](https://tex.z-dn.net/?f=x%5C+%5Ctextless+%5C+30)
б)
![x \geq \frac{1}{3}](https://tex.z-dn.net/?f=x+%5Cgeq++%5Cfrac%7B1%7D%7B3%7D+)
в)
![y\ \textgreater \ 5,8](https://tex.z-dn.net/?f=y%5C+%5Ctextgreater+%5C+5%2C8)
2.
![a\ \textless \ 4,8](https://tex.z-dn.net/?f=a%5C+%5Ctextless+%5C+4%2C8+)
Ответ: при a<4,8
3.
![\left \{ {{2x-3\ \textgreater \ 0} \atop {7x+4\ \textgreater \ 0}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2x-3%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7B7x%2B4%5C+%5Ctextgreater+%5C+0%7D%7D+%5Cright.+)
![\left \{ {{2x\ \textgreater \ 3} \atop {7x\ \textgreater \ -4}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2x%5C+%5Ctextgreater+%5C+3%7D+%5Catop+%7B7x%5C+%5Ctextgreater+%5C+-4%7D%7D+%5Cright.+)
![\left \{ {{x\ \textgreater \ 1,5} \atop {x\ \textgreater \ - \frac{4}{7} }}\right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+1%2C5%7D+%5Catop+%7Bx%5C+%5Ctextgreater+%5C+-+%5Cfrac%7B4%7D%7B7%7D+%7D%7D%5Cright.+)
x∈(1,5;+∞)
![\left \{ {{3-2x\ \textless \ 1} \atop {1,6+x\ \textless \ 2,9}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B3-2x%5C+%5Ctextless+%5C+1%7D+%5Catop+%7B1%2C6%2Bx%5C+%5Ctextless+%5C+2%2C9%7D%7D+%5Cright.+)
![\left \{ {{-2x\ \textless \ 1-3} \atop {x\ \textless \ 2,9-1,6}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B-2x%5C+%5Ctextless+%5C+1-3%7D+%5Catop+%7Bx%5C+%5Ctextless+%5C+2%2C9-1%2C6%7D%7D+%5Cright.+)
<span>
![\left \{ {{x\ \textgreater \ 1} \atop {x\ \textless \ 1,5}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+1%7D+%5Catop+%7Bx%5C+%5Ctextless+%5C+1%2C5%7D%7D+%5Cright.+)
</span>x∈(1;1,5)
4.
![\left \{ {{6-2x\ \textless \ 3(x-1)} \atop {6- \frac{x}{2} \geq 2 }} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B6-2x%5C+%5Ctextless+%5C+3%28x-1%29%7D+%5Catop+%7B6-+%5Cfrac%7Bx%7D%7B2%7D+%5Cgeq+2+%7D%7D+%5Cright.+)
![\left \{ {{-2x-3x\ \textless \ -3-6} \atop {- \frac{x}{2} \geq 2-6 }} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B-2x-3x%5C+%5Ctextless+%5C+-3-6%7D+%5Catop+%7B-+%5Cfrac%7Bx%7D%7B2%7D+%5Cgeq+2-6+%7D%7D+%5Cright.+)
![\left \{ {{-5x\ \textless \ -9} \atop {- \frac{x}{2} \geq -4 }} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B-5x%5C+%5Ctextless+%5C+-9%7D+%5Catop+%7B-+%5Cfrac%7Bx%7D%7B2%7D+%5Cgeq+-4+%7D%7D+%5Cright.+)
![\left \{ {{x\ \textgreater \ 1,8} \atop {x \leq 8}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+1%2C8%7D+%5Catop+%7Bx+%5Cleq+8%7D%7D+%5Cright.+)
x∈(1,8;8]
Считаем целые на этом промежутке 2, 3, 4, 5, 6, 7, 8
5. Подкоренное выражение не может быт меньше 0. Решаем систему
![\left \{ {{3x-2\ \textgreater \ 0} \atop {6-x\ \textgreater \ 0}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B3x-2%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7B6-x%5C+%5Ctextgreater+%5C+0%7D%7D+%5Cright.+)
![\left \{ {{3x\ \textgreater \ 2} \atop {-x\ \textgreater \ -6}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B3x%5C+%5Ctextgreater+%5C+2%7D+%5Catop+%7B-x%5C+%5Ctextgreater+%5C+-6%7D%7D+%5Cright.+)
![\left \{ {{x\ \textgreater \ \frac{2}{3} } \atop {x\ \textless \ 6}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C++%5Cfrac%7B2%7D%7B3%7D+%7D+%5Catop+%7Bx%5C+%5Ctextless+%5C+6%7D%7D+%5Cright.+)
Выражение имеет смысл при
![\frac{2}{3}\ \textless \ x\ \textless \ 6](https://tex.z-dn.net/?f=+%5Cfrac%7B2%7D%7B3%7D%5C+%5Ctextless+%5C+x%5C+%5Ctextless+%5C+6)
1) 750 гр, 700 гр, 1600 гр, 2050 гр, 3080 гр
2) 4 см, 3 см, 35 см, 44 см, 190 см
3) 24 с, 15 с, 54 с, 1 с, 1800 с
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