Answer:
x=3
Step-by-step explanation:
Right triangle so you can use pythagorean theorem
a squared + b squared = c squared
b=x
14^2 + b^2= 17^2
14+b=17
b=3
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)
When two fractions have the same denominator, you can compare which fraction is greater by just comparing the numerators.
For example, if you have 2/5 and 3/5, the denominators are the same. So you can just look at the numerators. 3 is greater than 5, so 3/5 is greater than 2/5.
The reasoning to this is that the two numbers are divided by the same number (5), so you can compare the original numbers (numerators).
-16F temperature change divided by 4 hour difference from 8 to 12/noon.
-16 divided by 4 = -4
The answer is -4 degrees Fahrenheit.
Answer:
(-2, 5)
Step-by-step explanation:
I will assume that your system is
y = -4x - 3
y = -2x + 1
Multiplying the second equation by -2 results in
y = -4x - 3
-2y = 4x - 2
combining these two equations eliminates x temporarily:
-y = -5, so that y must be 5.
Substituting 5 for y in the second equation, we get:
5 = -2x + 1, or
4 = -2x, which results in x = -2
and so the solution is (-2, 5)
