Answer:
512
Step-by-step explanation: area of triangle= 1/2*base*height
Purple = 1/5 of the colors
5 colors per tray, 20 trays = 5 * 20 = 100 colors
1/5 * 100 = 100/5 = 20
20 colors are purple
20/100 = 1/5
1/5
Answer:
<h2>x = -347 1/2</h2>
Step-by-step explanation:
When solving algebra, it is important the we follow the steps in correct order and check our answer at the end.
Step 1: Simplify by combining like terms
y = -x/2 + 5/4 + 8y = -25
Step 2: Substitute
y = -25
-25 = -x/2 + 5/4 + 8(-25)
-25 = -x/2 + 5/4 + -200
-25 = -x/2 - 198 3/4
Step 3: Answer
x = -347 1/2
Step 4: Check
y = 3/2x + 5/4 −2x + 8y = −25
-25 = 3/2(-347 1/2) + 5/4 −2(-347 1/2) + 8(-25)
-25 = -25✔️
Step 5: Verified Answer
x = -347 1/2
I'm always happy to help :)
Answer:
Step-by-step explanation:
1/7+1/13=1/t
multiply both sides by 7*13*t
13t+7t=7*13
21t=91
t=91/19
it will take 4 hours and 8 minutes
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)
