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Sagot :
Mr Reisman have some data available of his class frm past. This data described the number of left handed students in a math class.
We will first define/assign variables to each of the numbers i.e ( number of left handed students ) and ( number of students in the class ).
[tex]\begin{gathered} x\text{ = number of left handed students} \\ y\text{ = number of students in math class} \end{gathered}[/tex]Now we will go ahead and define the relationship between these two variables ( x and y ) defined above.
We see that if i increase the size of math class i.e ( value of variable y ) then the likelyhood of left-handed students increases i.e ( value of x increaes ). We can associate such relationships with propotions. To classify this type we can categorize as " direct proportions ".
We will go ahead and express our proportionality ( direct ) relation of two vairbales ( x and y ) in a mathematical form as follows:
[tex]y\text{ = k}\cdot x[/tex]Where,
[tex]\text{ k = constant of proportionality}[/tex]The general equation that can be used for forecasting or evaluating values for different class size and number of left handed students can be expressed in the form as follows:
[tex]\frac{y_0}{x_0}\text{ = }\frac{y_1}{x_1}[/tex]The above equation is a basic manipulation of equating the limit of proportionality for two class different math class sizes where,
[tex]\begin{gathered} y_{o\text{ }}=25,orignal\text{ math class size ( as per past data )} \\ x_o\text{ = 3, original number of left handed students ( as per data )} \\ y_{1\text{ }}=\text{ 125 , the new class size} \\ x_1\text{ = The expected number of left handed students in the new class} \end{gathered}[/tex]So, we are have three known quantities and one unknown ( x1 ). We can plug in the above quantities in the generalized equation above and solve for ( x1 ) as follows:
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