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denpristay [2]
3 years ago
10

Which of the following is the contrapositive of the following statement: If it is past 5:00 p.m., Megan’s office building is not

empty
A: If Megan’s office building is empty, then it is past 5:00 pm.

B: If Megan’s office building is empty, then it is not past 5:00 p.m.

C: If Megan’s office building is empty, then it is past 5:00 p.m.

D: If it is not past 5:00 p.m. Megan’s office building is empty.
Mathematics
1 answer:
scoundrel [369]3 years ago
7 0

Answer:

B

Step-by-step explanation:

A contrapositive statement is one that switches the hypothesis and conclusion of a conditional statement and negates both. In our hypothesis,

"If it is past 5:00 p.m., Megan’s office building is not empty", we shall break it into two statements and show the contarpositive of each like shown below.

Hypothesis                                             Contrapositive

Megan’s office building is not empty- Megan’s office building is empty

It is past 5:00 p.m  - it is not past 5:00 p.m

And thus the contrapositive statement becomes

If Megan’s office building is empty, then it is not past 5:00 p.m.

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for the school play adult tickets cost 4$ and children tickets cost 2$ natalie is working at the ticket counter and just sold 20
lilavasa [31]
Let us formulate the independent equation that represents the problem. We let x be the cost for adult tickets and y be the cost for children tickets. All of the sales should equal to $20. Since each adult costs $4 and each child costs $2, the equation should be

4x + 2y = 20

There are two unknown but only one independent equation. We cannot solve an exact solution for this. One way to solve this is to state all the possibilities. Let's start by assigning values of x. The least value of x possible is 0. This is when no adults but only children bought the tickets.

When x=0,
4(0) + 2y = 20
y = 10

When x=1,
4(1) + 2y = 20
y = 8

When x=2,
4(2) + 2y = 20
y = 6

When x=3,
4(3) + 2y= 20
y = 4

When x = 4,
4(4) + 2y = 20
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When x = 5,
4(5) + 2y = 20
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When x = 6,
4(6) + 2y = 20
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A negative value for y is impossible. Therefore, the list of possible combination ends at x =5. To summarize, the combinations of adults and children tickets sold is tabulated below:

   Number of adult tickets             Number of children tickets
                  0                                                   10
                  1                                                    8
                  2                                                    6
                  3                                                    4
                  4                                                    2
                  5                                                    0




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