Answer:
The frequency by which the equipment should receive periodic maintenance is
Step-by-step explanation:
A Wellbull distribution is mathematically represented as
![f(x,\alpha, \beta ) = \left \{ { {\frac{\alpha }{\beta^{\alpha } }x^{\alpha -1} e^{-[\frac{x}{\beta } ]^\alpha} \ \ \ \ \ \ \\ \\ , x \ge0} \atop {0 \ \ \ \ \ \ \ \ Otherwise }} \right.](https://tex.z-dn.net/?f=f%28x%2C%5Calpha%2C%20%5Cbeta%20%20%29%20%3D%20%5Cleft%20%5C%7B%20%7B%20%7B%5Cfrac%7B%5Calpha%20%7D%7B%5Cbeta%5E%7B%5Calpha%20%7D%20%7Dx%5E%7B%5Calpha%20-1%7D%20e%5E%7B-%5B%5Cfrac%7Bx%7D%7B%5Cbeta%20%7D%20%5D%5E%5Calpha%7D%20%5C%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%5C%5C%20%5C%5C%20%2C%20x%20%5Cge0%7D%20%5Catop%20%7B0%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20Otherwise%20%7D%7D%20%5Cright.)
Where x is the frequency that the equipment should receive periodic maintenance
probability of a breakdown before the next scheduled maintenance is mathematically represented as
![P(x) = \int\limits^x_0 {\frac{\alpha }{\beta^{\alpha } } x^{\alpha -1 } e^{-[\frac{x}{\beta } ]^{\alpha }} } \, dx](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%5Cint%5Climits%5Ex_0%20%7B%5Cfrac%7B%5Calpha%20%7D%7B%5Cbeta%5E%7B%5Calpha%20%7D%20%7D%20x%5E%7B%5Calpha%20-1%20%7D%20e%5E%7B-%5B%5Cfrac%7Bx%7D%7B%5Cbeta%20%7D%20%5D%5E%7B%5Calpha%20%7D%7D%20%7D%20%5C%2C%20dx)
Substituting 2 for
and 60 for
0.05 for P(x)
![0.05 = \int\limits^x_0 {\frac{2}{60^2} x^{2-1} e^{-[\frac{x}{60}]^2 } \, dx](https://tex.z-dn.net/?f=0.05%20%3D%20%5Cint%5Climits%5Ex_0%20%7B%5Cfrac%7B2%7D%7B60%5E2%7D%20x%5E%7B2-1%7D%20e%5E%7B-%5B%5Cfrac%7Bx%7D%7B60%7D%5D%5E2%20%20%7D%20%5C%2C%20dx)
![0.05 = \frac{2}{3600}\int\limits^x_0 {xe^{[-\frac{x^2}{3600} ]}} \, dx](https://tex.z-dn.net/?f=0.05%20%3D%20%5Cfrac%7B2%7D%7B3600%7D%5Cint%5Climits%5Ex_0%20%7Bxe%5E%7B%5B-%5Cfrac%7Bx%5E2%7D%7B3600%7D%20%5D%7D%7D%20%5C%2C%20dx)
Let 
=> 
=> 
Multiply both sides by minus
=> 
Substituting this into the equation

Integrating and substituting back for x
![0.05 = -\frac{1800}{1800} [e^{[-\frac{x^2}{3600} ]}]\left {{x} \atop {0}} \right.](https://tex.z-dn.net/?f=0.05%20%3D%20-%5Cfrac%7B1800%7D%7B1800%7D%20%5Be%5E%7B%5B-%5Cfrac%7Bx%5E2%7D%7B3600%7D%20%5D%7D%5D%5Cleft%20%7B%7Bx%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
substituting for the range of x and 0
![0.05 = - [e^{-[\frac{x^2}{3600}] } -1]](https://tex.z-dn.net/?f=0.05%20%3D%20-%20%20%5Be%5E%7B-%5B%5Cfrac%7Bx%5E2%7D%7B3600%7D%5D%20%20%7D%20-1%5D)
![0.05 = -e^{[-\frac{x^2}{3600} ]} +1](https://tex.z-dn.net/?f=0.05%20%3D%20-e%5E%7B%5B-%5Cfrac%7Bx%5E2%7D%7B3600%7D%20%5D%7D%20%2B1)

![-0.95 = -e^{[-\frac{x^2}{3600} ]}](https://tex.z-dn.net/?f=-0.95%20%3D%20-e%5E%7B%5B-%5Cfrac%7Bx%5E2%7D%7B3600%7D%20%5D%7D)
![0.95 = e^{[-\frac{x^2}{3600} ]}](https://tex.z-dn.net/?f=0.95%20%3D%20e%5E%7B%5B-%5Cfrac%7Bx%5E2%7D%7B3600%7D%20%5D%7D)
Taking ln of both sides

making x the subject of the formula


Answer:
A. 20t² + 9t - 20
Step-by-step explanation:
(5t × 4t) + (5t × 5) - (4 × 4t) - (4 × 5)
= 20t² + (25t - 16t) - 20
= <u>20t² + 9t - 20</u> (A)
<em>Hope </em><em>this </em><em>is </em><em>h</em><em>e</em><em>l</em><em>p</em><em>ful </em><em>and </em><em>useful </em><em>:</em><em>)</em>
<h3>
Answer: 4900 (choice D)</h3>
===================================================
Work Shown:
1 km = 1000 m
3.5 km = 3500 m ............. multiplying both sides by 3.5
(70 paces)/(50 m) = (x paces)/(3500 m)
70/50 = x/3500
7/5 = x/3500
7*3500 = 5x .............. cross multiply
5x = 7*3500
x = (7*3500)/5
x = (7*5*700)/5
x = 7*700
x = 4900
Ann takes 4900 paces to walk 3.5 km
Answer:
18xy-2x-5y-8
Step-by-step explanation:
Просто умножьте,то что было в скобках
Answer:
45
Step-by-step explanation:
Set up ratios for 2 similar triangles:
20/28=x/x+18
Cross multiply
28x=20x+360
8x=360
x=45