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washington high school's head tennis coach, ms. racket, runs a tennis camp for middle school students every summer. the students bring their own lunches, but ms. racket provides them with snacks.there is a proportional relationship between the number of students who enroll in ms. racket's tennis camp, x, and the total number of snacks she buys, y.what is the constant of proportionality? write your answer as a whole number or decimal.snacks per student

Sagot :

The constant of proportionality is comes out to be 3.

What is constant of proportionality?

When two variables are proportional to one another, their relationship can be expressed as y = kx or y = k/x, where k defines how the 2 factors are related to one another. The above k is recognized as the proportionality constant.

  • The proportionality constant is the constant value of the ratio of two proportional quantities.
  • When the ratio or product of two varying quantities yields a constant, they are said to be in a proportional relationship.
  • The proportionality constant's value is determined by the type of proportion between both the two given quantities: direct variation or inverse variation.

Now according to the question.

The proportionality constant denotes the ratio of the words x and y.

It is found by dividing Δy by Δx.

Δy/Δx = (y₂ - y₁)/(x₂ - x₁)

Consider two values from the table;

y₂ = 39 ; x₂ = 13

y₁ = 30 ; x₁ = 10

Substituting the values in the formula;

Δy/Δx = (39 - 30)/(13 - 10)

Δy/Δx = 9/3

Δy/Δx = 3

Therefore, the value of constant of proportionality is 3.

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The complete question is -

Washington high school's head tennis coach, Ms. racket, runs a tennis camp for middle school students every summer. the students bring their own lunches, but Ms. racket provides them with snacks. there is a proportional relationship between the number of students who enroll in Ms. racket's tennis camp, x, and the total number of snacks she buys, y. what is the constant of proportionality? write your answer as a whole number or decimal. snacks per student.

X      Y

10     30

13     39

14     42

21     63

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