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Here d varies directly with cube of w, and inversely with p. So w cube have to be in the numerator and p have to be in the denominator. And we need to use k for constant of proportionality. Therefore the required equation is
In direct proportionality, the relatioship is linear that is as w increases, d increases and as w decreases d decreases and for inverse, it is opposite .
Answer:
First Part;
As the temperature in the city increases, the number of cups of hot chocolate sold decreases
Second Part;
The approximate value of the slope in number of cups sold per change in temperature is -0.12222
The approximate value of the y-intercept is 20.944 degrees temperature
Step-by-step explanation:
<em>Question;</em>
<em>First Part</em>
<em>What is the relationship between temperature in the city and the number of cups of hot chocolate sold, using your own words</em>
<em>Second Part</em>
<em>How can the line of best fit be made. Give the approximate values of the slope and the y-intercept of the line of best fit</em>
Explanation
The data points are presented in the following table;
A scatter plot is formed from the given data using MS Excel
First part;
From the values of the number of cups sold, <em>y</em>, and the temperature at which they are sold, <em>x</em>, there is correlation between the <em>x</em> and <em>y</em> values, such that as the temperature increases, the number of cups sold decreases, the becomes more rapid as the temperature increases past 50, such that the reason for taking the hot chocolate decreases with increasing temperature
Second Part;
The line of best fit can be found using the least squares regression formula to draw a straight line from the regression equation as follows;
y = a + b·x
a = - b·
Where;
b = The slope
a = The y-intercept
From MS Excel, we have;
= 15,
= 48.63636
Therefore;
The approximate value of the slope, b = -0.12222 (number of cups sold per unit change in temperature)
a = 15 - (-0.12222)×48.63636 ≈ 20.944
The approximate value of the y-intercept, a = 20.944 (in degrees of temperature).