Answer:gjoifglkfmglflddmlgkm;dllgmdflgmlkdmglkfdmglkfmglfmklgdlkmldmlglfmhlkgmgflbmglkhm
dfjbdjkfkdndvlkdlfnvfldfgvglfkmvlfdkmglfmglkfmjgkfdgjmfd
Step-by-step
explanation:gvyugugiuihuihiuhuvyvyuhubhbjbjkxcxjfnifdgjkfdkfdjfdkgfjvfdjigifbnjifvbvdffbndvjvnfjvfcjnvifdjifjb
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Answer: 0.083
Step-by-step explanation:
Numbers on cube=6
faces on coin=2
Therefore, the total outcomes=![6\times2=12](https://tex.z-dn.net/?f=6%5Ctimes2%3D12)
Now, the favorable outcome that he rolls a 4 and flips a head=1
The probability that he rolls a 4 and flips a head=![\frac{\text{favorable outcome}}{\text{total outcome}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7Bfavorable%20outcome%7D%7D%7B%5Ctext%7Btotal%20outcome%7D%7D)
⇒The probability that he rolls a 4 and flips a head=
=0.083333\approx0.83.
Therefore, The probability that he rolls a 4 and flips a head=0.083
Answer:
Step-by-step explanation:
Given is a system of equations as
![x1-4x2 - x4 = -7\\ \\x2 - 2x4 = 3 \\\\x4 + 2x5 = 3](https://tex.z-dn.net/?f=x1-4x2%20-%20x4%20%3D%20-7%5C%5C%20%5C%5Cx2%20-%202x4%20%3D%203%20%5C%5C%5C%5Cx4%20%2B%202x5%20%3D%203)
We have 5 variables and 3 equations
a) coefficient matrix of this system is
1 -4 0 -1 0\\
0 1 0 -2 0\\
0 0 0 1 2\\
We find that x3 has no coefficient in any of the equations so we can omit x3 and write as equations for 4 variables as
1 -4 -1 0\\
0 1 -2 0\\
0 0 1 2\\
b) Augmented matrix is
1 -4 -1 0\\ 7
0 1 -2 0\\
3
0 0 1 2\\3
c) For row operations to ehelon form
we can do R1+4R2 = R1
We get
1 0 -9 0 \\ 19
0 1 -2 0 \\ 3
0 0 1 2 \\ 3
Now let us do R1 = R1+9R3 and R2 = R2+2R3
1 0 0 0 \\ 46
0 1 0 0 \\ 9
0 0 1 2 \\ 3
d) We find that there are infinite solutions to the system in parametric form, since x4 and x5 are linked with only one equation
e) x1 = 46, x2 = 9, x4+2x5 =3
Or x1 =46, x2 =9, x4 = 3-2x5, x5 = x5 is the parametric solution