9.) Answer: B. f(x) = 4 - x
Explanation/Proof:
If we substitute, the answers are correct.
f(x) = 4 - (1)
f(x) = 3 ✅
f(x) = 4 - (2)
f(x) = 2 ✅
And so on and so forth.
Answer:
The System of equation is
.
Step-by-step explanation:
Given:
Let 'x' be the number of questions worth 5 points.
Let 'y' be the number of questions worth 2 points
Total Number of Problems = 29
So the Total Number of Problems is equal to sum of the number of questions worth 5 points and the number of questions worth 2 points.
Framing in equation form we get;
.
Also Given:
Test is of Total Points = 100
Now Total points in test is equal to sum of the number of questions worth 5 points multiplied by and the number of questions worth 2 points multiplied by 2.
Framing in equation form we get;

Hence The System of Equations are
.
Answer:
x = -34
, y = 31
Step-by-step explanation suing Gaussian elimination:
Solve the following system:
{2 x + 3 y = 25
3 x + 4 y = 22
Express the system in matrix form:
(2 | 3
3 | 4)(x
y) = (25
22)
Write the system in augmented matrix form and use Gaussian elimination:
(2 | 3 | 25
3 | 4 | 22)
Swap row 1 with row 2:
(3 | 4 | 22
2 | 3 | 25)
Subtract 2/3 × (row 1) from row 2:
(3 | 4 | 22
0 | 1/3 | 31/3)
Multiply row 2 by 3:
(3 | 4 | 22
0 | 1 | 31)
Subtract 4 × (row 2) from row 1:
(3 | 0 | -102
0 | 1 | 31)
Divide row 1 by 3:
(1 | 0 | -34
0 | 1 | 31)
Collect results:
Answer: {x = -34
, y = 31
Answer:-1>p
Step-by-step explanation:
6>3p+9
-9 -9
-3>3p
Divide by 3 on each side
-1>p

Recall that the PDF is given by the derivative of the CDF:

The mean is given by
![\mathbb E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\int_0^2\left(x-\dfrac{x^2}2\right)\,\mathrm dx=\frac23](https://tex.z-dn.net/?f=%5Cmathbb%20E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cint_0%5E2%5Cleft%28x-%5Cdfrac%7Bx%5E2%7D2%5Cright%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac23)
The median is the number

such that

. We have

but both roots can't be medians. As a matter of fact, the median must satisfy

, so we take the solution with the negative root. So

is the median.