Answer:
1= 0
2= 0.5
3= 1.5
4= 3
5= 5
6= 7.5
7= 10.5
8= 14
explanation: This is the edmentum answer
Answer:
(15, 12)
Step-by-step explanation:
Let's generate two systems of equations that fit this scenario.
Number of trips to the airport = x
Number of trips from the airport = y
Total number of trips to and from the airport = 27
Thus:
=> equation 1.
Total price for trips to the Airport = 14*x = 14x
Total price of trips from the airport = 7*y = 7y
Total collected for the day = $294
Thus:
=> equation 2.
Multiply equation 1 by 7, and multiply equation 2 by 1 to make both equations equivalent.
7 × 
1 × 
Thus:
=> equation 3
=> equation 4
Subtract equation 4 from equation 3
-7x = -105
Divide both sides by -7
x = 15
Substitute x = 15 in equation 1


Subtract both sides by 15


The ordered pair would be (15, 12)
Answer:
Vanessa would draw about 70 quarters
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.

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

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)
We are given a coordinate (4,16).
Where first coordinate is the value of x and second coordinate is the value of y for the function y=f(x).
We need to find the value of given point (4,16) for function y= 0.5f(x).
Here function f(x) is being multiplied by 0.5.
On multiplying 0.5 by y, it will effect the value of y only. It does not effect value of x . Because x value is still x. Only function f(x) is being multiplied by 0.5.
Therefore, y= 0.5f(4) = 0.5 * 16 = 8.
So, (4,8) is the point on the graph of y = 0.5f(x) corresponds to (4, 16).