Identify whether the following variables are numerical or categorical. If numerical, state whether the variable is discrete or continuous. If categorical, state whether the categories have a natural order (ordinal) or not (nominal). (10 pts) (a) Fraction (or percentage) of birds in a large sample infected with avian flu virus (b) Number of crimes committed by a randomly sampled individual (c) Gender (d) Logarithm of body mass (e) Stage of fruit ripeness (e. g., underripe, ripe, or overripe) (f) Tree species (g) Petal area of rose flowers

Solution :

Variables are of two types --- Numerical variable and Categorical variable.

The numerical variable includes measurement and numbers that can be counted. It is also known as quantitative variable. It is of two types --- Discrete and continuous variables.

The categorical variable includes the description of the groups or the things like the type of clothes, color of eyes, etc. that cannot be counted. It is also called qualitative variable. It is of two types -- Nominal variable and Ordinal Variable.

In the context,

a). The percentage or fraction of birds that are infected by a flu is numerical continuous variable.

b). The number of the crimes committed by an individual can be a whole number only and is countable. So it is a Numerical discrete variable.

c). Gender of a person is categorized as male or female. Therefore it is a categorical nominal variable.

d). The logarithm of the body mass is not countable and the body mass can be in decimal form also. So it is a Numerical continuous variable.

e). The different stages of a fruit ripeness can be categorized as fully ripe or unripe i.e. it ranges from unripe fruits to overripe fruits. So it is Categorical ordinal variables.

f). Tree species can be named for the different types of species of the trees. So it is Categorical nominal variable.

g). The petal area of a rose flower cannot be count as the numbers of he petals are not fixed, so it is a Numerical continuous variable.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c