A survey of 347 high school students asked students to describe their politics as Liberal,

Moderate or Conservative. The results are summarized by gender with 27 out of 95

Liberals are males, out of 128 Moderates, 91 are female and there are 93 Conservative females.

A. (i) 68

   (ii) Moderate : 128

B. the percent of female high school students surveyed that gave a response.

Step-by-step explanation:

Use the data given to fill and complete a two-way frequency table as shown

Form a two-way frequency table as shown;

               Liberal          Moderate    Conservative        Total

Boys           27                 37                      31                   95

Girls            68                 91                      93                 252

Total           95                128                    124                 347  

Entries in the "Total" row and "Total" column give the marginal frequencies

The entries that are shaded are the joint frequencies

The entries that are underlined/ marginal frequencies add up to the lower right corner cell both for last column and for the last cell row.

A.

The joint frequency for liberal female is :

check the column for liberal and the row for girls = 68

The largest marginal frequency for political  preference is :

Check the underlined entries : the political preference with the largest marginal frequency is Moderate : 128

B. To get relative frequency every entry is divided by the total at the right bottom corner cell. i.e 347

252/347 represents the percent of female surveyed for the high school students that gave a response.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.