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Vitek1552 [10]
3 years ago
11

A contractor purchases 4 dozen pairs of padded work gloves for ​$56.16. She incorrectly calculates the unit price as ​$14.04 per

pair for the expense report. What is the correct unit​ price? What is the​ error? Why is the​ contractor's unit price​ incorrect?
Mathematics
1 answer:
8090 [49]3 years ago
6 0

Answer:

The correct unit price is $1.17 per pair of gloves. The error is she used number of dozens so, firstly convert it to number of pairs of gloves then divide.

Step-by-step explanation:

It is given 4 dozen pairs of gloves for $56.16.

So, unit price = Divide the price by number of pairs of gloves.

And 1 dozen =12

So 4 dozen =4*12=48 pairs of gloves

So, to find unit rate divide 56.16  by 48.

Unit price =\frac{56.16}{48}= $1.17

So, the error is she didn't convert the dozen to units.

That made mistake in finding unit price.

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Let p be "it is raining" and q be "the track meet will be canceled."<br> write p-&gt;q in words
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The statement for the logic \text{p}\rightarrow\text{q} is \fbox{\begin\\\ \text{If it is raining then the track meet will be cancelled}\\\end{minispace}}

Further explanation:

The logic given in the question is \text{p}\rightarrow\text{q}.

The logic \text{p}\rightarrow\text{q} is a symbol of implication.

Statement p is “It is raining” and the statement q is “The track meet will be canceled”.

The statement formed for the logic \text{p}\rightarrow\text{q} is called a compound statement.

The truth table for the logic \text{p}\rightarrow\text{q} is attached below.

From the table attached below  it is observed that there are four cases for the compound statement.

Case1:

If p statement is true and the q statement is true then the compound statement for \text{p}\rightarrow\text{q} is also true.

Case 2:

If p statement is true and the q statement is false then the compound statement for \text{p}\rightarrow\text{q} is false.

Case 3:

If p statement is false and the q statement is true then the compound statement for \text{p}\rightarrow\text{q} is true.

Case 4:

If p statement is false and the q statement is false then the compound statement for \text{p}\rightarrow\text{q} is true.

For a true statement it can also be said that it is a positive statement and for a false statement it can be said that it is a negative statement.

Statement p is given as “It is raining”, which is a positive statement or a true statement.

Statement q is given as “The track meet will be cancelled”, which is a positive statement or a true statement.

As per the table attached for the logic \text{p}\rightarrow\text{q} it is observed that the given statements p and q resembles with the case 1 as both of the statement are true.

So, the compound statement for \text{p}\rightarrow\text{q} is also a true statement.

The compound statement for the logic \text{p}\rightarrow\text{q} is as follows:

\fbox{\begin\\\ \text{If it is raining then the track meet will be cancelled}\\\end{minispace}}

Therefore, the compound statement for the logic \text{p}\rightarrow\text{q} is \fbox{\begin\\\ \text{If it is raining then the track meet will be cancelled}\\\end{minispace}}

Learn more:

  1. A problem on composite function brainly.com/question/2142762
  2. A problem on simplification brainly.com/question/894273
  3. A problem in inverse function brainly.com/question/1632445

Answer details

Grade: High school

Subject: Mathematics

Chapter: Logic

Keywords: Logics, implications, compound, compound statement, true statement, false statement, positive statement, negative statement, p->q.  

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