The panel for a political forum consists of four Democrats, 5 republicans, 3 independents in how many orders can they be seated
2 answers:
I'm assuming we can say each Democrat, Republican, and Independent are the same element.
Since there are 12 seats, we can seat them in 12! different ways, assuming straight line.
However, the four democrats are the same element, since we only care about the different parties. Using this same logic, the 5 Republicans can swap without us knowing and the 3 Independents, as well.
Thus, we've overcounted by a factor of 4! 5! 3!, because each element are identical.
To counter this, we divide by the number of elements repeated:
Since there are 12 seats, we can seat them in 12! different ways, assuming straight line.
However, the four democrats are the same element, since we only care about the different parties. Using this same logic, the 5 Republicans can swap without us knowing and the 3 Independents, as well.
Thus, we've overcounted by a factor of 4! 5! 3!, because each element are identical.
To counter this, we divide by the number of elements repeated:
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<h2>Answers / Step-by-step explanation:</h2><h3>a. What is the length of one side of the square.</h3>
<em>Looking at the image, the radius (r) of the circle appears to cover half of the length of a side of the square. Hence, the side of the square has a length of </em><em>2r</em><em>.</em>
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<h3>b. The formula A= πr² is used to find the area of a circle. The formula A=4r² can be used to find the area of the square. Write the ratio of the area of the circle to the area of the square in the simplest form.</h3><em />.
<em>Notice that the value "r²" disappears from the expression because is being multiplied and divided by it at the same time.</em>
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c. Complete the table.
<em>To complete each cell of the table, simply take the equation of the asked parameter and substitute the value of r by the number indicated in the title of the column. For example, column 3 should be filled out like this:</em>
Area of Circle (units²): π(3)²or 9π.
Length of 1 Side of the Square: 2r= 2(3)= 6.
Area of Square (units²)= 4r²= 4(3)²= 36.
Ratio: .
<em>Do the same for all the other columns. </em>
<em>The answers to the table are presented on the attached image</em><em>.</em>
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d. What can you conclude about the relationship between the area of the circle and the square?
<em>They will always have the same value, π/4, regardless of the size of the square and circle. As long as the circle borders meet the square's at the middle of each side of the square, the relationship will be the same</em><em>.</em>
Answer:
-2
Step-by-step explanation:
4x:3=6:5.
4x/3=6/5
4x × 5=6×3
20 X=18
X=18-20
X=-2
