Roy wants to make a path from one corner of his yard to the other as shown below. The path will be 4 feet wide. He wants to find
the area of lawn that remains.
Roy claims that the area of the lawn is 300 square feet since it covers exactly one-half of the yard. Which statement about his claim is correct?
He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 440 sq ft.
He is incorrect. The path will have an area of 1/2(4)(40)=80 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 220 sq ft.
He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 140 sq ft.
He is incorrect. The path will have an area of (9)(40)=360 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 240 sq ft.
Roy claims that the area of the lawn is 300 square feet since it covers exactly one-half of the yard. Which statement about his claim is correct?
He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 440 sq ft.
He is incorrect. The path will have an area of 1/2(4)(40)=80 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 220 sq ft.
He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 140 sq ft.
He is incorrect. The path will have an area of (9)(40)=360 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 240 sq ft.
1 answer:
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Answer:
a)
b)
c)
d)
e)
f)
Step-by-step explanation:
- M(x) = 1 if the person x came to the meeting, and 0 otherwise.
- O(x) = 1 if the person is an officer of the club and 0 otherwise.
- D(x) = 1 if the person has paid hid/her club dues and 0 otherwise.
Lets also call C the set given by the members of the club. C is the domain of the functions M, O and D.
a) If someone is not an officer, the there should be at least one value x such that O(x) = 0. This can be expressed by logic expressions this way
b) If all the officers came on time to the meeting, then for a value x such that O(x) = 1, we also have that M(x) = 1. Thus, the set of officers of the Club is contained on the set of persons which came to the meeting on time, this can be written mathematically this way:
c) If everyone was in time for the meeting, then C is equal to the set of persons who came to the meeting on time, or, equivalently, the values x such that M(x) = 1. We can write that this way:
d) If everyone paid their dues or came on time to the meeting, then if we take the set of persons who came to the meeting on time and the set of the persons who paid their dues, then the union of the two sets should be the entire domain C, because otherwise there should be a person that didnt pay nor was it on time. This can be expressed logically this way:
e) If at least one person paid their dues on time and came on time to the meeting, then there should be a value x on C such that M(x) and D(x) are both equal to 1. Therefore
f) If there is an officer who did not come on time for the meeting, then there should be a value x in C such that O(x) = 1 (x is an officer), and M(x) = 0. As a result, we have
I hope that works for you!