A because everything after the verb is a preposition
Go to mathpapa.com for your answer
Answer:
pages
Step-by-step explanation:
Variable:
x = number of pages he has to read on a weekday
x + 30 = The number of pages read on Saturday and Sunday
![5x+2(x+30) = 473](https://tex.z-dn.net/?f=5x%2B2%28x%2B30%29%20%3D%20473)
![==> 5x + 2x + 60 = 473](https://tex.z-dn.net/?f=%3D%3D%3E%205x%20%2B%202x%20%2B%2060%20%3D%20473)
![==> 7x =413](https://tex.z-dn.net/?f=%3D%3D%3E%207x%20%3D413)
![==> x = 59](https://tex.z-dn.net/?f=%3D%3D%3E%20x%20%3D%2059)
Meaning that Raoul has to read 59 pages on Wednesday
Answer:
Coef=6
Step-by-step explanation:
Answer:
51/4
Step-by-step explanation:
To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.
X~ Uniform(0,100)
Then the probability mass function is given as follows.
![f(x) = P(X=x) = 1/100 \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0 \,\,\,\, \text{otherwise}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20P%28X%3Dx%29%20%3D%201%2F100%20%20%5C%2C%5C%2C%5C%2C%5C%2C%20%5Ctext%7Bif%7D%20%5C%2C%5C%2C%5C%2C%5C%2C%200%20%5Cleq%20x%20%5Cleq%20100%5C%5Cf%28x%29%20%3D%20P%28X%3Dx%29%20%3D%200%20%20%5C%2C%5C%2C%5C%2C%5C%2C%20%5Ctext%7Botherwise%7D)
Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located 70 meters away from city A then the mid point between 20 and 70 is (70+20)/2 = 45 then we can represent D as follows
![D(x) =\left\{ \begin{array}{ll} x & \mbox{if } 0\leq x \leq 20 \\ x-20 & \mbox{if } 20\leq x < 45\\ 70-x & \mbox{if } 45 \leq x \leq 70\\ x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.](https://tex.z-dn.net/?f=D%28x%29%20%3D%5Cleft%5C%7B%09%5Cbegin%7Barray%7D%7Bll%7D%09%09x%20%20%26%20%5Cmbox%7Bif%20%7D%200%5Cleq%20x%20%5Cleq%2020%20%5C%5C%09%09x-20%20%26%20%5Cmbox%7Bif%20%7D%2020%5Cleq%20x%20%3C%2045%5C%5C%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%2070-x%20%26%20%5Cmbox%7Bif%20%7D%2045%20%5Cleq%20x%20%5Cleq%2070%5C%5C%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20x-70%20%26%20%5Cmbox%7Bif%20%7D%2070%20%5Cleq%20x%20%5Cleq%20100%5C%5C%09%5Cend%7Barray%7D%5Cright.)
Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable
,
is a random variable as well, remember that there is a theorem that says that
![E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx](https://tex.z-dn.net/?f=E%5BY%5D%20%3D%20E%5BD%28X%29%5D%20%3D%20%5Cint%5Climits_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20D%28x%29%20f%28x%29%20%5C%2C%5C%2C%20dx)
Where
is the probability mass function of X. Using the information of our problem
![E[Y] = \int\limits_{-\infty}^{\infty} D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx \bigg]\\= \frac{51}{4} = 12.75](https://tex.z-dn.net/?f=E%5BY%5D%20%3D%20%5Cint%5Climits_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20%20D%28x%29f%28x%29%20dx%20%5C%5C%3D%20%5Cfrac%7B1%7D%7B100%7D%20%5Cbigg%5B%20%5Cint%5Climits_%7B0%7D%5E%7B20%7D%20x%20dx%20%2B%5Cint%5Climits_%7B20%7D%5E%7B45%7D%20%28x-20%29%20dx%20%2B%5Cint%5Climits_%7B45%7D%5E%7B70%7D%20%2870-x%29%20dx%20%2B%5Cint%5Climits_%7B70%7D%5E%7B100%7D%20%28x-70%29%20dx%20%20%5Cbigg%5D%5C%5C%3D%20%5Cfrac%7B51%7D%7B4%7D%20%3D%2012.75)