To control the traffic during Ramadan month, a Police Sergeant is assigned to control the traffic
1 answer:
To complete the table it is necessary to know the possibilities that the sergeant has to change or remain in an intersection. The probabilities (depending on the box) are:
- 0
- 0.2
- 0.25
- 0.33
<h3>How to calculate the probability of intersection change? </h3>
To know the probability of intersection change, it is necessary to locate the police officer at one of the intersections. Subsequently, count how many possibilities of change you have, for example: 3 possibilities and finally add the possibility of remaining in the intersection as shown below:
- Intersection 3 has 3 possibilities of changing towards intersections 2, 8 and 4. Additionally, it has the possibility of staying at intersection 3, that is, it has 4 possible decisions.
To know the probability we divide the number 1 (because it is only a decision that we have to make) and divide it by the number of possibilities (4).
- 1 ÷ 4 = 0.25
According to the image we can infer that in some intersections they only have 3, 4 and 5 possibilities, so the probability of change will be different as shown below:
- 1 ÷ 3 = 0.33
- 1 ÷ 4 = 0.25
- 1 ÷ 5 = 0.2
Learn more about probabilities in: brainly.com/question/8069952
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Using it's vertex, the maximum value of the quadratic function is -3.19.
<h3>What is the vertex of a quadratic equation?</h3>A quadratic equation is modeled by:
The vertex is given by:
In which:
Considering the coefficient a, we have that:
- If a < 0, the vertex is a maximum point.
- If a > 0, the vertex is a minimum point.
In this problem, the equation is:
y + 4 = -x² + 1.8x
In standard format:
y = -x² + 1.8x - 4.
The coefficients are a = -1 < 0, b = 1.8, c = -4, hence the maximum value is:
More can be learned about the vertex of a quadratic function at brainly.com/question/24737967
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1- Solution using graphs:
Take a look at the attached images.
The red graph represents the first given function while the blue graph represents the second given function.
We can note that the two graphs are the same line (they overlap).
This means that any chosen point on one of them will satisfy the other.
This means that there are infinite number of solutions to these two equations.
2- Solution using substitution:
The first given equation is:
y = -5x + 3 ...........> equation I
The second given equation is:
2y + 10x = 6 ...........> equation II
Substitute with I in II and solve as follows:
2(-5x+3) + 10x = 6
-10x + 6 + 10x = 6
0 = 0
This means that there are infinitely many solutions to the given system of equations.
Hope this helps :)
Take a look at the attached images.
The red graph represents the first given function while the blue graph represents the second given function.
We can note that the two graphs are the same line (they overlap).
This means that any chosen point on one of them will satisfy the other.
This means that there are infinite number of solutions to these two equations.
2- Solution using substitution:
The first given equation is:
y = -5x + 3 ...........> equation I
The second given equation is:
2y + 10x = 6 ...........> equation II
Substitute with I in II and solve as follows:
2(-5x+3) + 10x = 6
-10x + 6 + 10x = 6
0 = 0
This means that there are infinitely many solutions to the given system of equations.
Hope this helps :)