Which of the following statements would be represented with P → Q? Question 14 options: A) x = 5 if and only if y = 9. B) x = 5, and 2x ≠ 8. C) x = 5, but y = 9. D) If x = 5, then 2x = 10.

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Explanation:

Writing is another way of saying "if P, then Q".

P and Q are placeholders. Instead of holding numbers, they hold statements. The statements can be anything you want (generally they should be something that can be verified).

The two statements are

P: x = 5

Q: 2x = 10

So the format "if P, then Q" turns into "if x = 5, then 2x = 10" after replacing P and Q with the proper definitions.

Side note: it might help to think of the "search and replace" feature in many word documents.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363