Sagal works as a DJ at a local radio station.On occasion, she chooses some of the songs she will play based on the phone-in requests received by the switchboard the previous day. Sagal's list of 200 possible selections includes
a)100 songs in the top 100
b)134 hard-rock songs
c)50 phone-in requests
d)45 hard-rock songs in the top 100
e)20 phone-in requests in the top 100
f)24 phone-in requests for hard-rock songs
use a venn diagram to determine
a)How many phone-in requests were for hard-rock songs in the top 100
b)How many of the songs in the top 100 were neither phone-in requests nor hard-rock selections.
To answer these questions using a Venn diagram, we need to draw a diagram with three intersecting circles: one for the top 100 songs, one for the phone-in requests, and one for the hard-rock songs. We can then use the given information to fill in the circles and find the answers.
Let's start by labeling the circles:
- Circle A represents the top 100 songs.
- Circle B represents the phone-in requests.
- Circle C represents the hard-rock songs.
Using the given information, we can fill in the diagram:
- The total number of songs in the top 100 is 100, so we can put this number in circle A.
- The total number of phone-in requests is 50, so we put this number in circle B.
- The total number of hard-rock songs is 134, so we put this number in circle C.
Now, let's consider the overlapping regions and the given information:
- There are 45 hard-rock songs in the top 100, so we fill in the overlapping region between circles A and C with this number.
- There are 20 phone-in requests in the top 100, so we fill in the overlapping region between circles A and B with this number.
- There are 24 phone-in requests for hard-rock songs, so we fill in the overlapping region between circles B and C with this number.
Now we can calculate the answers:
a) To find the number of phone-in requests for hard-rock songs in the top 100, we look at the overlapping region between circles A, B, and C. In this case, we can see that the number is 24.
b) To find the number of songs in the top 100 that were neither phone-in requests nor hard-rock selections, we look at the portion of circle A that is outside of both circles B and C. In this case, we can see that the number is 100 - (20 + 45) = 35.
By analyzing the Venn diagram, we can determine that there were 24 phone-in requests for hard-rock songs in the top 100, and 35 songs in the top 100 that were neither phone-in requests nor hard-rock selections.