An air traffic controller has noted that it clears an average of seven planes per hour for landing. What is the probability that
during the next two hours exactly 15 planes will be cleared for landing?a. 0.0989 b. Not enough information is given to answer the problem. c. 0.0033 d. 0.0651
1 answer:
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Answer:
A. System C simplifies to 2x - 3y = 4 and 4x - y = 54 by dividing the second equation by three (3).
B. Systems A and C have the same solutions.
C. Systems A and B have different solutions.
Step-by-step explanation:
Given the following system of equations;
<em><u>System A</u></em>
2x - 3y = 4 .....equation 1
4x - y = 18 .......equation 2
We would solve the above equations using the elimination method;
Multiplying eqn 1 by 2;
2*(2x) - 2*(3y) = 4*2
4x - 6y = 8 ...... equation 3
Subtracting eqn 2 from eqn 3;
(4x - 4x) + (-6y - (-y)) = 8 - 18
0 + (-6y + y) = -10
-5y = -10
5y = 10
y = 2
To find the value of x;
2x - 3y = 4
2x - 3(2) = 4
2x - 6 = 4
2x = 4 + 6
2x = 10
x = 5
<em><u>Solutions (x, y) = (5, 2)</u></em>
<u><em>System B</em></u>
3x - 4y = 5 ..... equation 1
y = 5x + 3 ..... equation 2
We would solve the equations using substitution method;
Substituting eqn 2 into eqn 1, we have;
3x - 4(5x + 3) = 5
3x - 20x - 12 = 5
-17x - 12 = 5
-17x = 12 + 5
-17x = 17
x = -1
To find the value of y;
y = 5x + 3
y = 5(-1) + 3
y = -5 + 3
y = -2
<u><em>Solutions (x, y) = (-1, -2)</em></u>
<u><em>System C</em></u>
2x - 3y = 4 ..... equation 1
12x - 3y = 54 ...... equation 2
We would solve the above equations using the elimination method;
Subtracting eqn 2 from eqn 1;
(2x - 12x) + (-3y -(-3y)) = 4 - 54
-10x + (-3y + 3y) = -50
-10x + 0 = -50
-10x = -50
10x = 50
x = 5
To find the value of y;
2x - 3y = 4
2(5) - 3y = 4
10 - 3y = 4
3y = 10 - 4
3y = 6
y = 2
<u><em>Solutions (x, y) = (5, 2)</em></u>