Question

1. technology depot received 2 boxes of wireless headphones. each box has 10 headphones. the store owner noticed that out of all the headphones 5 were damaged. based on these results, what can the store owner predict about the next shipment of headphones? a. a shipment of 4 boxes will contain 2 more damaged headphones than a shipment of 2 boxes. b. a shipment of 6 boxes will contain 10 more damaged headphones than a shipment of 2 boxes. c. a shipment of 8 boxes will contain 12 more damaged headphones than a shipment of 2 boxes. d. a shipment of 10 boxes will contain 5 more damaged headphones than a shipment of 2 boxes.

Explanation:

Step1: Find the damage rate

First, find the number of damaged headphones per box. In 2 boxes (each with 10 headphones, so total \(2\times10 = 20\) headphones), 5 are damaged. So the damage rate per box is \(\frac{5}{2}\) damaged headphones per box.

Step2: Analyze each option

• Option A: Shipment of 2 boxes has 5 damaged. Shipment of 4 boxes: total headphones \(4\times10 = 40\). Damaged should be \(\frac{5}{2}\times4 = 10\). Difference from 2 - box shipment: \(10 - 5 = 5\), not 2. So A is wrong.
• Option B: Shipment of 6 boxes: damaged headphones \(\frac{5}{2}\times6 = 15\). Difference from 2 - box (5 damaged): \(15 - 5 = 10\). This matches. Let's check others.
• Option C: Shipment of 8 boxes: damaged \(\frac{5}{2}\times8 = 20\). Difference from 5: \(20 - 5 = 15\), not 12. So C is wrong.
• Option D: Shipment of 10 boxes: damaged \(\frac{5}{2}\times10 = 25\). Difference from 5: \(25 - 5 = 20\), not 5. So D is wrong.

Answer:

B. A shipment of 6 boxes will contain 10 more damaged headphones than a shipment of 2 boxes.