Answer:
18 weeks
Step-by-step explanation:
In this question, we are asked to use an equation to show the number of weeks it took Hugo who received a certain amount in his birthday and continually saved a certain amount before he could gather a certain amount of money.
In this question, we understand that Hugo wants to buy a printer that costs $460. Fortunately, he had his birthday and he received $100 bucks. Now, let’s say the number of weeks he had to save for is w and he saves 20 per week. This means the total amount he hit from his savings would be 20w
Mathematically, we can use the equation below to model this scenario;
100 + 20(w) = 460
20w = 460 - 100
20w = 360
w = 360/20
w = 18 weeks
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)
Answer:
C = (2, 6)
Step-by-step explanation:
The coordinates of point C can be found as the weighted average of the endpoint coordinates. The weights are the reverse of the relative segment lengths.
For AC : CB = 3 : 1, we have ...
C = (A +3B)/(1+3) = ((-1, 0) +3(3, 8))/4 = (-1+9, 0+24)/4
C = (2, 6)
Answer: 30 buttons
Step-by-step explanation:
If there were 8 kids, and 7 more joined, then there were 15 kids making snowmen (8+7 = 15). Each child used 2 buttons for the eyes, so 30 buttons were used (15 x2 = 30). This is assuming no other buttons were used on the snowmen for anything else
Answer: Choice A. {-3,-1,0,1,2}
Explanation:
The range is the list of y coordinates of each point.