Asurvey was conducted among 100 students of age groups 7−12 years and 13−18 years to find their favorite book genre. the students had to select any one genre out of detective, adventure, and biography. out of the 50 students in the age group 7−12 years who participated in the survey, 23 liked adventure or biography. the total number of students of both age groups who liked detective books was 28.

using a two-way table, compute the total number of students in the age group 13−18 years who liked adventure or biography.

23
27
49
51

49

Step-by-step explanation:

Total number of students =100

Out of the 50 students in the age group 7−12 years who participated in the survey, 23 liked adventure or biography.

So, 50-23 = 27 Out of the 50 students in the age group 7−12 years who participated in the survey liked detective

Now we are given that The total number of students of both age groups who liked detective books was 28.

No. of students of age group 13-17 who like detective books = Students of both age group like detective - No.of students of 7−12 years who liked detective = 28-27 =1

So ,The total number of students of both age groups who liked adventure or biography was 100-28 = 72

Since the age group 7−12 years who participated in the survey, 23 liked adventure or biography.

So,  the age group 13-17 years who participated in the survey liked adventure or biography = 72-23=49

Age group          Adventure or Biography       Detective     Total

 7-12                              23                                    27               50  

 13-18                            49                                     1                  50

Total                             72                                    28               100

So, Option C is true.

The total number of students in the age group 13−18 years who liked adventure or biography. is 49

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2