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Answer:
If k = −1 then the system has no solutions.
If k = 2 then the system has infinitely many solutions.
The system cannot have unique solution.
Step-by-step explanation:
We have the following system of equations
The augmented matrix is
The reduction of this matrix to row-echelon form is outlined below.
The last row determines, if there are solutions or not. To be consistent, we must have k such that
Case k = −1:
If k = −1 then the last equation becomes 0 = −2 which is impossible.Therefore, the system has no solutions.
Case k = 2:
This gives the infinite many solution.
Answer:
Colour | Probability
YELLOW | 0.20
WHITE | 0.18
GREEN | 0.12
RED | 0.18
BLUE | 0.32
Step-by-step explanation:
The complete question is presented on the attached image to this solution.
From the image of the spinner and the given probabilities, the combination of YELLOW, WHITE and GREEN make up exactly half of the total space on the spinner.
0.2 + 0.18 + 0.12 = 0.50
Then, BLUE and RED make up the other half of the spinner.
Probability of landing on either BLUE or RED = 1 - 0.50 = 0.50
Let P(BLUE) = x and P(RED) = y
x + y = 0.50
Two of the lines shown on the diagram are diameters of the circle.
The first line that is a diameter splits the circle into two parts; (WHITE, YELLOW, GREEN) and (RED, BLUE).
From here, we have established that x + y = 0.50
The other line that is a diameter splits The circle into two part; (WHITE, BLUE) and (YELLOW, GREEN, RED)
From this other information,
P(WHITE) + P(BLUE) = 0.50
0.18 + x = 0.50
x = 0.50 - 0.18 = 0.32
P(YELLOW) + P(GREEN) + P(RED) = 0.50
0.20 + 0.12 + y = 0.50
y = 0.50 - 0.32 = 0.18
To check, x + y = 0.32 + 0.18 = 0.50 (Correct!!)
Hope this Helps!!!
