(a) As dry air moves upward, it expands and cools. If the ground temperature is 30°C and the temperature at a height of 1 km is 10°C, express the temperature T (in °C) as a function of the height h (in kilometers), assuming that a linear model is appropriate. (b) Draw the graph of the function in part (a). What does the slope represent? (c) What is the temperature at a height of 1.5 km? Solution (a) Because we are assuming that Tis a linear function of h, we can write T= mh + b. We are given that T = 30 when h = 0, so 30 = m· + b In other words, the y-intercept is b = 30 We are also given that T = 10 when h = 1, so 1 v ) + (30 10 = m. The slope of the line is therefore m = 10 – and the required linear function is T = (b) The graph is sketched in the figure below. 20 3 4 -20 - 40 The slope ism = °C/km, and this represents the rate of change of ---Select--- v with respect to ---Select--- v (c) At a height of h = 1.5 km, the temperature is

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.