In a group of 60 workers, the average salary is $80 a day per worker. if some of the workers earn $75 a day and all the rest ear
1 answer:
The total number of workers that earn $75 per day is 48
<h3>What is average salary?</h3>The average salary is calculated based on reported salaries of respondents. The average salary definition is to add the salaries in the sample together, then divide by the number of respondents.
Given that:
In a group of 60 workers, the average salary is $80 a day per worker.
If some of the workers earn $75 a day and all the rest earn $100 a day.
Let 'x' be the total number of workers that earn $75 per day.
So, the total number of workers that earn $100 per day is (60 - x).
As the average salary of 60 workers is $80.
Then,
or, 75 x + 6000- 100x = 80*68
or, -25x= -1200
x= 48
So, the total number of workers earn $75 per day is 48.
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Answer:
The solutions are x = -9 , x = -5
Step-by-step explanation:
* Lets find the vertex of the parabola
- In the quadratic equation y = ax² + bx + c, the vertex of the parabola
is (h , k), where h = -b/2a and k = f(h)
∵ The equation is y = x² + 14x + 45
∴ a = 1 , b = 14 , c = 45
∵ h = -b/2a
∴ h = -14/2(1) = -14/2 = -7
∴ The x-coordinate of the vertex of the parabola is -7
- Lets find k
∵ k = f(h)
∵ h = -7
- Substitute x by -7 in the equation
∴ k = (-7)² + 14(-7) + 45 = 49 - 98 + 45 = -4
∴ The y-coordinate of the vertex point is -4
∴ The vertex of the parabola is (-7 , -4)
- Plot the point on the graph and then find two points before it and
another two points after it
- Let x = -9 , -8 and -6 , -5
∵ x = -9
∴ y = (-9)² + 14(-9) + 45 = 81 - 126 + 45 = 0
- Plot the point (-9 , 0)
∵ x = -8
∴ y = (-8)² + 14(-8) + 45 = 64 - 112 + 45 = -3
- Plot the point (-8 , -3)
∵ x = -6
∴ y = (-6)² + 14(-6) + 45 = 36 - 84 + 45 = -3
- Plot the point (-6 , -3)
∵ x = -5
∴ y = (-5)² + 14(-5) + 45 = 25 - 70 + 45 = 0
- Plot the point (-5 , 0)
* To solve the equation x² + 14x + 45 = 0 means find the value of
x when y = 0
- The solution of the equation x² + 14x + 45 = 0 are the x-coordinates
of the intersection points of the parabola with the x-axis
∵ The parabola intersects the x-axis at points (-9 , 0) and (-5 , 0)
∴ The solutions of the equation are x = -9 and x = -5
* The solutions are x = -9 , x = -5
