Using the following table, what is the term that best describes the entry of 0.31?

do you prefer dancing or playing sports?
playing sports dancing row totals
male students 0.25 0.27 0.52
female students 0.17 0.31 0.48
column totals 0.42 0.58 1
joint frequency
joint relative frequency
marginal frequency
marginal relative frequency

option B. Joint relative frequency

Step-by-step explanation:

The given table is

                                Playing sports          Dancing row            Total (Row)

Male students              0.25                         0.27                         0.52

Female students          0.17                          0.31                         0.48

Total (Column)             0.42                         0.58                         1.00

If we see last row and last column total is 1.00.

In any table if total of last row or column is 1.00 then the given data in the table is of "Joint relative frequency".

Therefore, option B. Joint relative frequency is correct answer.

b. astronomers

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!