Answer:
42.4
Step-by-step explanation:
1) use this formula of Area of the triangle:
2) using the formula described above:
A=0.5*14*11*0.55≈42.4 (mm²)
Answer:
a) 7.79%
b) 67.03%
c) Cumulative Distribution Function
Step-by-step explanation:
We are given the following in the question:
where x is the duration of a call, in minutes.
a) P( calls last between 2 and 3 minutes)
![=\displaystyle\int^3_2 p(x)~ dx\\\\= \displaystyle\int^3_20.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^3_2\\\\=-\Big[e^{-0.3}-e^{-0.2}\Big]\\\\= 0.0779\\=7.79\%](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint%5E3_2%20p%28x%29~%20dx%5C%5C%5C%5C%3D%20%5Cdisplaystyle%5Cint%5E3_20.1e%5E%7B-0.1x%7D~dx%5C%5C%5C%5C%3D%5CBig%5B-e%5E%7B-0.1x%7D%5CBig%5D%5E3_2%5C%5C%5C%5C%3D-%5CBig%5Be%5E%7B-0.3%7D-e%5E%7B-0.2%7D%5CBig%5D%5C%5C%5C%5C%3D%200.0779%5C%5C%3D7.79%5C%25)
b) P(calls last 4 minutes or more)
![=\displaystyle\int^{\infty}_4 p(x)~ dx\\\\= \displaystyle\int^{\infty}_40.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^{\infty}_4\\\\=-\Big[e^{\infty}-e^{-0.4}\Big]\\\\=-(0- 0.6703)\\= 0.6703\\=67.03\%](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_4%20p%28x%29~%20dx%5C%5C%5C%5C%3D%20%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_40.1e%5E%7B-0.1x%7D~dx%5C%5C%5C%5C%3D%5CBig%5B-e%5E%7B-0.1x%7D%5CBig%5D%5E%7B%5Cinfty%7D_4%5C%5C%5C%5C%3D-%5CBig%5Be%5E%7B%5Cinfty%7D-e%5E%7B-0.4%7D%5CBig%5D%5C%5C%5C%5C%3D-%280-%090.6703%29%5C%5C%3D%200.6703%5C%5C%3D67.03%5C%25)
c) cumulative distribution function
(2x^2 + 4x + 6) - (-3x - 5x^2 + 4)
The negative sign separating the expressions is just multiplying the rightmost expression by -1.
(2x^2 + 4x + 6) + (3x + 5x^2 - 4)
Now, let's add together terms that share the same variable.
2x^2 + 5x^2 = 7x^2
4x + 3x = 7x
6 + (-4) = 2
Let's combine each of these terms into one expression.
7x^2 + 7x + 2 is the final answer.
Answer:
12
Step-by-step explanation:
f(x)=x^+4x+2 First, let's evaluate when x=3, x=4 and x=5.
f(3) = 3²+4(3)+2 = 9 + 12 + 2 = 23
f(4) = 4²+4(4)+2 = 16 + 16 + 2 = 34
f(5) = 5²+4(5)+2 = 25 + 20 + 2 = 47
Now, let's find the rate of change.
34 - 23 = 11
47 - 34 = 13
Finally, the average rate of change.
(11 + 13) / 2 = 12
Answer:
Horizontal axis
Step-by-step explanation:
By convention, the independent variables is arrayed along the Horizontal axis (abscissa) in a scattergram.
The stcattergram has two dimensions
- The X (independent) variable is arrayed along the horizontal axis.
- The Y(dependent) variable is arrayed along the vertical axis.
- Each dot scattergram is case in data set.
- The dot is placed at the intersection cases scores on X and Y.
