Question

algebra i b-cr
a group of 120 people were asked whether their income level is above or below $25,000 and whether they subscribe to a movie channel. the data from the survey is shown in the venn diagram. use the venn diagram to find the missing values in the frequency table.
income and subscriptions
which shows the correct values for the variables in the table?
○ $a = 18, b = 34, c = 65$
○ $a = 34, b = 18, c = 68$
○ $a = 34, b = 68, c = 47$
○ $a = 47, b = 18, c = 68$

Explanation:

Step1: Define the frequency table structure

We assume the frequency table has rows: Below $25k*, *Above $25k and columns: Subscriber, Non-Subscriber, Total.

• $a$ = People with income above $25k$ AND are subscribers
• $b$ = People with income above $25k$ AND are non-subscribers
• $c$ = Total people with income below $25k$

Step2: Calculate $c$ (total below $25k$)

Add the two segments of the "Below $25,000$" circle:
$c = 55 + 18 = 73$
Wait, correction: $c$ is total non-subscribers? No, re-align with options:
Total people = 120. Total subscribers: $18 + 34 = 52$. Total non-subscribers: $120 - 52 = 68$.
People above $25k$ and subscriber: $a = 34$ (only orange non-overlap)
People above $25k$ and non-subscriber: $b = 18$? No, non-overlap outside both circles is 13 (above $25k$, non-subscriber). Wait, total below $25k$: $55+18=73$, so above $25k$ total: $120-73=47$. Above $25k$ subscriber is 34, so above $25k$ non-subscriber: $47-34=13$. No, match options:
Option 2: $a=34, b=18, c=68$.
Wait, $c$ = total non-subscribers: $55 + 13 = 68$.
$a$ = above $25k$ subscriber = 34.
$b$ = below $25k$ subscriber = 18.

Step3: Verify totals

Total subscribers: $18 + 34 = 52$. Total non-subscribers: $55 + 13 = 68$. $52 + 68 = 120$, which matches total people.

Answer:

a = 34, b = 18, c = 68