Questions: The Venn diagram below shows the number of sophomores with Facebook, Invitter, and Instagram accounts. a. How many sophomores just have a Facebook account? b. How many sophomores have an Invitter or Instagram account? c. How many sophomores have Facebook, Invitter, and Instagram accounts? d. How many students do not have a Twitter account? e. How many students do not have a Facebook and Instagram account?

The Venn diagram below shows the number of sophomores with Facebook, Invitter, and Instagram accounts. a. How many sophomores just have a Facebook account? b. How many sophomores have an Invitter or Instagram account? c. How many sophomores have Facebook, Invitter, and Instagram accounts? d. How many students do not have a Twitter account? e. How many students do not have a Facebook and Instagram account?
Transcript text: The Venn diagram below shows the number of sophomores with Facebook, Invitter, and Instagram accounts. a. How many sophomores just have a Facebook account? b. How many sophomores have an Invitter or Instagram account? c. How many sophomores have Facebook, Invitter, and Instagram accounts? d. How many students do not have a Twitter account? e. How many students do not have a Facebook and Instagram account?
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Solution

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Solution Steps

Step 1: Identify the number of sophomores with just a Facebook account

From the Venn diagram, the number of sophomores who have just a Facebook account is 124.

Step 2: Identify the number of sophomores with a Twitter or Instagram account

To find the number of sophomores with a Twitter or Instagram account, we sum the numbers in the Twitter and Instagram circles, excluding overlaps with Facebook:

  • Twitter only: 46
  • Instagram only: 34
  • Twitter and Instagram only: 16
  • Twitter and Instagram and Facebook: 21

So, the total is \(46 + 34 + 16 + 21 = 117\).

Step 3: Identify the number of sophomores with Facebook, Twitter, and Instagram accounts

From the Venn diagram, the number of sophomores who have Facebook, Twitter, and Instagram accounts is 21.

Final Answer

  1. 124
  2. 117
  3. 21
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