Question

select all the correct answers.
researchers for a textile company carried out an experiment comparing the longevity of two new fabric blends. they carried out a series of usage tests, known as double rubs, on 100 pieces of each type of material. these scales are used for this type of testing.

fabric grade	number of double rubs (in thousands)
medium duty	9 – 15
light duty	3 – 9
delicate duty	< 3

after performing the tests on each fabric, researchers found that on average, fabric a lasted through 7,900 double rubs and fabric b lasted through 9,200 double rubs.
the marketing department wants to advertise that both fabrics are tested and approved for medium - duty use. which statements are true about this situation?

• the sales department can refer to fabric a as a medium - duty fabric.
• fabric b is a more durable fabric because it has a higher double rub rating than fabric a.
• neither fabric meets the requirements of a medium - duty fabric.
• fabric a is a more durable fabric because it has a lower double rub rating than fabric b.
• the sales department can refer to fabric b as a medium - duty fabric.

Explanation:

Step1: Analyze Fabric A's rating

Fabric A: 7,900 double rubs. Medium - duty range is 9 - 15 (thousand). 7.9 < 9, so Fabric A is in Light - duty (3 - 9) range? Wait, no, 7.9 is between 3 and 9 (thousand), but medium - duty is 9 - 15. Wait, the problem says "medium - duty use" approval. Wait, the marketing wants to advertise for medium - duty use. Let's check each statement:

1. "The sales department can refer to fabric A as a medium - duty fabric." Fabric A: 7,900 = 7.9 thousand. Medium - duty is 9 - 15 thousand. 7.9 < 9, so no. Wait, maybe I misread. Wait the table: Fabric Grade: Heavy duty (15+), Medium duty (9 - 15), Light duty (3 - 9), Delicate duty (<3). So Fabric A: 7.9 thousand (7900) is in Light duty (3 - 9) range. Fabric B: 9,200 = 9.2 thousand, which is in Medium duty (9 - 15) range.

2. "Fabric B is a more durable fabric because it has a higher double rub rating than fabric A." Fabric B: 9200, Fabric A: 7900. 9200>7900, so more durable. Correct.

3. "Neither fabric meets the requirements of a medium - duty fabric." Fabric B: 9200 is in 9 - 15 (medium - duty), so Fabric B meets. So this is wrong.

4. "Fabric A is a more durable fabric because it has a lower double rub rating than fabric B." Lower rating means less durable. So wrong.

5. "The sales department can refer to fabric B as a medium - duty fabric." Fabric B: 9200 is in 9 - 15 (medium - duty), so correct.

Wait, maybe I made a mistake earlier. Let's re - evaluate:

- Medium - duty range: 9 - 15 thousand double rubs.

Fabric A: 7,900 (7.9 thousand) → Light duty (3 - 9).

Fabric B: 9,200 (9.2 thousand) → Medium duty (9 - 15).

Now check each statement:

1. "The sales department can refer to fabric A as a medium - duty fabric." Fabric A is 7.9k, medium - duty starts at 9k. So no.

2. "Fabric B is a more durable fabric because it has a higher double rub rating than fabric A." 9200>7900, so more durable. Correct.

3. "Neither fabric meets the requirements of a medium - duty fabric." Fabric B is 9.2k, which is in medium - duty (9 - 15k). So this is wrong.

4. "Fabric A is a more durable fabric because it has a lower double rub rating than fabric B." Lower rating means less durable. Wrong.

5. "The sales department can refer to fabric B as a medium - duty fabric." Fabric B is 9.2k, which is in 9 - 15k (medium - duty). Correct.

Wait, but the problem says "select all correct answers". Wait maybe I misread the fabric A and B's ratings. The problem says: "fabric A lasted through 7,900 double rubs and fabric B lasted through 9,200 double rubs."

So Fabric A: 7900 (7.9k), Fabric B: 9200 (9.2k).

Medium - duty: 9 - 15k. So Fabric B is in medium - duty (9.2 is between 9 and 15), Fabric A is in light - duty (7.9 is between 3 and 9).

Now check each statement:

- Statement 1: Fabric A as medium - duty? No, 7.9 < 9. So wrong.

- Statement 2: Fabric B more durable (9200>7900). Correct.

- Statement 3: Neither meets medium - duty? Fabric B meets (9.2 is in 9 - 15), so wrong.

- Statement 4: Fabric A more durable? No, lower rating. Wrong.

- Statement 5: Fabric B as medium - duty? Yes, 9.2 is in 9 - 15. Correct.

Wait, but maybe the "medium - duty use" approval is different. Wait the marketing wants to advertise that both are tested and approved for medium - duty use. Wait, maybe the approval is based on passing the test for medium - duty, not the range. Wait, the problem says "tested on each fabric, researchers found that... Fabric A lasted through 7,900... Fabric B through 9,200... marketing wants to advertise that both are tested and approved for medium - duty use."

Wait, maybe the approval is not based on the range but on passing the test. Wait, maybe I misinterpreted the table. The table is the fabric grade (number of double rubs), and the test is to see if they can be approved for medium - duty use.

So to be approved for medium - duty use, maybe they need to meet or exceed a certain number. Wait, the problem says "tested and approved for medium - duty use". So maybe the minimum for medium - duty use approval is, say, 9,000? Fabric A: 7900 < 9000, Fabric B: 9200>9000. But the statements:

Wait, let's re - check each option:

1. "The sales department can refer to fabric A as a medium - duty fabric." If medium - duty fabric is defined as per the grade (9 - 15k), Fabric A is 7.9k (light duty), so no. But if "medium - duty use" approval is different, maybe the company's standard is different. Wait, the problem is a bit unclear, but let's go with the table.

2. "Fabric B is a more durable fabric because it has a higher double rub rating than fabric A." 9200>7900, so more durable. Correct.

3. "Neither fabric meets the requirements of a medium - duty fabric." Fabric B: 9200 is in 9 - 15k (medium - duty grade), so it meets. So wrong.

4. "Fabric A is a more durable fabric because it has a lower double rub rating than fabric B." Lower rating means less durable. Wrong.

5. "The sales department can refer to fabric B as a medium - duty fabric." Fabric B is 9.2k, which is in medium - duty (9 - 15k) grade. Correct.

Also, maybe "The sales department can refer to fabric A as a medium - duty fabric" is wrong, "Fabric B is more durable" is correct, "Neither..." is wrong, "Fabric A more durable" is wrong, "The sales department can refer to fabric B as a medium - duty fabric" is correct. Also, maybe "Neither fabric meets the requirements..." is wrong, and "The sales department can refer to fabric B as a medium - duty fabric" and "Fabric B is a more durable fabric..." are correct. Also, maybe "The sales department can refer to fabric A as a medium - duty fabric" is wrong, but wait, maybe the company's medium - duty fabric is defined differently. Wait, maybe the light - duty is 3 - 9k, medium - duty is 9 - 15k, so Fabric A is light - duty, Fabric B is medium - duty. But the marketing wants to advertise both as medium - duty approved. Maybe the approval is not the same as the grade.

Alternatively, maybe the question is about which statements are true about the situation (the test results and the marketing's plan).

So:

- Statement 1: Fabric A as medium - duty fabric. Fabric A's grade is light - duty (7.9k), so sales can't refer to it as medium - duty. Wrong.

- Statement 2: Fabric B more durable (9200>7900). Correct.

- Statement 3: Neither meets medium - duty requirements. Fabric B's grade is medium - duty (9.2k), so it meets. Wrong.

- Statement 4: Fabric A more durable (lower rating). Wrong, lower rating means less durable.

- Statement 5: Fabric B as medium - duty fabric. Fabric B's grade is medium - duty (9.2k), so sales can refer to it as medium - duty. Correct.

Also, maybe "The sales department can refer to fabric A as a medium - duty fabric" is wrong, but wait, maybe the company is mis - representing, but the statement is about whether it's true. So the true statements are "Fabric B is a more durable fabric because it has a higher double rub rating than fabric A" and "The sales department can refer to fabric B as a medium - duty fabric" and maybe "Neither fabric meets the requirements..." is wrong, "Fabric A more durable" is wrong, "The sales department can refer to fabric A as a medium - duty fabric" is wrong. Wait, but maybe I made a mistake with Fabric A's range. 7900 is 7.9 thousand, which is in Light duty (3 - 9 thousand) range. Fabric B is 9.2 thousand, in Medium duty (9 - 15 thousand) range.

So the correct statements are:

- Fabric B is a more durable fabric because it has a higher double rub rating than fabric A.

- The sales department can refer to fabric B as a medium - duty fabric.

Wait, but let's check the first statement again: "The sales department can refer to fabric A as a medium - duty fabric." If the marketing wants to advertise for medium - duty use, maybe the approval is based on passing the test, not the grade. Maybe the test for medium - duty use is to last through at least, say, 9,000 double rubs. Fabric A: 7900 < 9000, so not approved. Fabric B: 9200>9000, approved. But the marketing wants to advertise both as approved. So maybe the statements are about the situation (test results and marketing's claim).

But according to the grade (number of double rubs), Fabric B is medium - duty, Fabric A is light - duty. So:

- Statement 1: False (Fabric A is light - duty, not medium - duty).

- Statement 2: True (9200>7900, so more durable).

- Statement 3: False (Fabric B is medium - duty, so it meets).

- Statement 4: False (lower rating = less durable).

- Statement 5: True (Fabric B is medium - duty, so sales can refer to it as such).

So the correct statements are the second and fifth? Wait, but the options are checkboxes. Let's confirm:

Fabric A: 7900 double rubs (7.9k), Fabric B: 9200 (9.2k).

Medium - duty fabric grade: 9 - 15k double rubs. So Fabric B is in medium - duty grade, Fabric A in light - duty.

So:

- "Fabric B is a more durable fabric because it has a higher double rub rating than fabric A." True, since 9200>7900.

- "The sales department can refer to fabric B as a medium - duty fabric." True, since 9.2k is in 9 - 15k (medium - duty) range.

- "The sales department can refer to fabric A as a medium - duty fabric." False, 7.9k is in light - duty.

- "Neither fabric meets the requirements of a medium - duty fabric." False, Fabric B meets.

- "Fabric A is a more durable fabric because it has a lower double rub rating than fabric B." False, lower rating means less durable.

So the correct statements are the second and fifth (and maybe the first? No, first is wrong). Wait, maybe I misread the first statement: "The sales department can refer to fabric A as a medium - duty fabric." If the marketing is lying, but the statement is about whether it's true. So no. So the correct answers are "Fabric B is a more durable fabric because it has a higher double rub rating than fabric A" and "The sales department can refer to fabric B as a medium - duty fabric" and maybe "Neither..." is wrong, "Fabric A more durable" is wrong, "The sales department can refer to fabric A as a medium - duty fabric" is wrong.

Answer:

The correct statements are:

• Fabric B is a more durable fabric because it has a higher double rub rating than fabric A.
• The sales department can refer to fabric B as a medium - duty fabric.

(In checkbox terms, the checkboxes for these two statements should be selected.)