This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Okay selorm, let's solve problem 5. Let W be the set of people who use WhatsApp, I for Instagram, and T for TikTok. Given: Total people = 120 |W| = 70 |I| = 65 |T| = 50 |W I| = 35 |W T| = 28 |I T| = 22 |W I T| = 15 1. How many use only one app? This is the sum of people who use only WhatsApp, only Instagram, and only TikTok. Step 1: Calculate the number of people using only each app. Only WhatsApp: |W only| = |W| - (|W I| + |W T|) + |W I T| |W only| = 70 - (35 + 28) + 15 = 70 - 63 + 15 = 22 Only Instagram: |I only| = |I| - (|W I| + |I T|) + |W I T| |I only| = 65 - (35 + 22) + 15 = 65 - 57 + 15 = 23 Only TikTok: |T only| = |T| - (|W T| + |I T|) + |W I T| |T only| = 50 - (28 + 22) + 15 = 50 - 50 + 15 = 15 Step 2: Sum these values to find the total number using only one app. Only one app = 22 + 23 + 15 Only one app = 60 The number of people who use only one app is 60. 2. How many use exactly two apps? This is the sum of people who use (WhatsApp and Instagram only), (WhatsApp and TikTok only), and (Instagram and TikTok only). Step 1: Calculate the number of people using exactly two apps for each pair. WhatsApp and Instagram only: |W I| - |W I T| = 35 - 15 = 20 WhatsApp and TikTok only: |W T| - |W I T| = 28 - 15 = 13 Instagram and TikTok only: |I T| - |W I T| = 22 - 15 = 7 Step 2: Sum these values to find the total number using exactly two apps. Exactly two apps = 20 + 13 + 7 Exactly two apps = 40 The number of people who use exactly two apps is 40. 3. How many use none? First, we find the number of people who use at least one app using the Principle of Inclusion-Exclusion. Step 1: Apply the Principle of Inclusion-Exclusion formula to find |W I T|. |W I T| = |W| + |I| + |T| - (|W I| + |W T| + |I T|) + |W I T| Step 2: Substitute the given values. |W I T| = 70 + 65 + 50 - (35 + 28 + 22) + 15 Step 3: Perform the calculations. |W I T| = 185 - 85 + 15 |W I T| = 100 + 15 |W I T| = 115 Step 4: Subtract the number of people using at least one app from the total number of people. Number who use none = Total people - |W I T| Number who use none = 120 - 115 Number who use none = 5 The number of people who use none is 5. 3 done, 2 left today. You're making progress.