Answered

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. The following scales are used for this type of testing.

\begin{tabular}{|l|c|}
\hline Fabric Grade & \begin{tabular}{c}
Number of Double Rubs \\
(in thousands)
\end{tabular} \\
\hline Heavy duty & [tex]$15+$[/tex] \\
\hline Medium duty & [tex]$9-15$[/tex] \\
\hline Light duty & [tex]$3-9$[/tex] \\
\hline Delicate duty & [tex]$\ \textless \ 3$[/tex] \\
\hline
\end{tabular}

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?

A. Fabric A is a more durable fabric because it has a lower double rub rating than fabric B.
B. The sales department can refer to fabric B as a medium-duty fabric.
C. Neither fabric meets the requirements of a medium-duty fabric.
D. The sales department can refer to fabric A as a medium-duty fabric.
E. Fabric B is a more durable fabric because it has a higher double rub rating than fabric A.



Answer :

GinnyAnswer
Let's analyze the information step-by-step according to the given data and see whether each statement is true or false. We'll break down each component of the question.

1. Check if Fabric A qualifies as medium-duty:

The double rub rating for Fabric A is 7,900. To qualify as medium-duty, a fabric must have a double rub rating between 9,000 and 15,000.

[tex]\[ 9,000 \leq 7,900 < 15,000 \][/tex]

This inequality is false because 7,900 is less than 9,000. Thus, Fabric A does not qualify as medium-duty.

2. Check if Fabric B qualifies as medium-duty:

The double rub rating for Fabric B is 9,200. To qualify as medium-duty, a fabric must have a double rub rating between 9,000 and 15,000.

[tex]\[ 9,000 \leq 9,200 < 15,000 \][/tex]

This inequality is true because 9,200 is within the range. Thus, Fabric B qualifies as medium-duty.

3. Compare the durability of Fabric A and Fabric B:

Durability in fabrics is typically measured by a higher double rub rating. Fabric B has a double rub rating of 9,200, and Fabric A has a double rub rating of 7,900.

Since:

[tex]\[ 9,200 > 7,900 \][/tex]

Fabric B is more durable than Fabric A.

Now, let's evaluate each statement given:

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

This statement is false. Higher double rub ratings indicate greater durability, so a lower rating means less durability. Fabric B, with a higher rating, is more durable than Fabric A.

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

This statement is true. Fabric B's double rub rating of 9,200 falls within the medium-duty range (9,000 to 15,000).

3. Neither fabric meets the requirements of a medium-duty fabric.

This statement is false. Fabric B meets the requirements of a medium-duty fabric, as previously determined.

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

This statement is false. Fabric A's double rub rating of 7,900 does not fall within the medium-duty range.

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

This statement is true. Fabric B's higher double rub rating of 9,200 compared to Fabric A's 7,900 indicates that Fabric B is indeed more durable.

Summary of evaluated statements:

- Statement 1: False
- Statement 2: True
- Statement 3: False
- Statement 4: False
- Statement 5: True