Answer:
slope = 2
y intercept = ( 0 , -1 )
equation:
y = 2x - 1
Step-by-step explanation:
By "density" I assume you mean "probability density function". For this to be the case for
![f(x)](https://tex.z-dn.net/?f=f%28x%29)
, we require
![\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20f%28x%29%5C%2C%5Cmathrm%20dx%3D1)
Since
![f(x)=\begin{cases}cx^{1/2}&\text{for }0](https://tex.z-dn.net/?f=f%28x%29%3D%5Cbegin%7Bcases%7Dcx%5E%7B1%2F2%7D%26%5Ctext%7Bfor%20%7D0%3Cx%3C2%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
you have
![\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=\int_0^2cx^{1/2}\,\mathrm dx=\dfrac{2c}3x^{3/2}\bigg|_{x=0}^{x=2}=\dfrac{2^{5/2}c}3=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20f%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cint_0%5E2cx%5E%7B1%2F2%7D%5C%2C%5Cmathrm%20dx%3D%5Cdfrac%7B2c%7D3x%5E%7B3%2F2%7D%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%3D2%7D%3D%5Cdfrac%7B2%5E%7B5%2F2%7Dc%7D3%3D1)
which means
I believe the answer is C
Answer:
Step-by-step explanation:
<u>Given</u>
- Total 17 marbles
- 4 - blue marbles
- 6 - green marbles
- 2 - red marbles
- The rest - yellow marbles
<u>Probability of drawing red first:</u>
- P(red) = number of red / total number = 2/17
<u>Probability of drawing green second, without replacement:</u>
- P(green) = number of green / number left in the bag = 6/16 = 3/8
<u>Probability of red and green in order:</u>
- P = P(red)*P(green) = 2/17*3/8 = 3/68
Answer:
The least common multiple of 30, 25, 4 is 150.
Step-by-step explanation:
The given numbers are 30, 25 and 4.
The factors of given numbers are
![30=2\times 3\times 5](https://tex.z-dn.net/?f=30%3D2%5Ctimes%203%5Ctimes%205)
![30=5\times 5](https://tex.z-dn.net/?f=30%3D5%5Ctimes%205)
![4=2\times 2](https://tex.z-dn.net/?f=4%3D2%5Ctimes%202)
The L.C.M of given numbers is a smallest number that divides the given numbers completely.
![L.C.M.=\frac{2\times 3\times 5\times 5\times 5\times 2\times 2}{5\times 2}](https://tex.z-dn.net/?f=L.C.M.%3D%5Cfrac%7B2%5Ctimes%203%5Ctimes%205%5Ctimes%205%5Ctimes%205%5Ctimes%202%5Ctimes%202%7D%7B5%5Ctimes%202%7D)
![L.C.M.=2\times 3\times 5\times 5\times 2=150](https://tex.z-dn.net/?f=L.C.M.%3D2%5Ctimes%203%5Ctimes%205%5Ctimes%205%5Ctimes%202%3D150)
Therefore the least common multiple of 30, 25, 4 is 150.