Answer:
y = (1/8)x
Step-by-step explanation:
The relevant basic formula is y = kx, where k is the constant of proportionality.
We must find k. To do this, let y = 15/6 and x = 20 in the above formula:
15/6 = k(20)
We solve for k by dividing both sides by 20: 15/(6*20) = k = 1/8
Then the specific formula for this situation is y = (1/8)x
Greatest common factor in this case is 2s^2. The resulting polynomial would be 2s^2(s^2-2)
Answer:
<em>It will occur zero times between midnight and one o'clock.</em>
Step-by-step explanation:
<u>Least Common Multiple (LCM)</u>
Three events keep James from sleeping: his clock ticking every 20 seconds, a tap dripping every 15 seconds, and his dog snoring every 27 seconds.
All three events happened together at midnight. They will happen together again the first time the numbers 20, 15, and 27 have a common multiple. This is the LCM.
List the prime factors of each number:
20: 2,2,5
15: 3,5
27: 3,3,3
Now multiply all the factors the maximum number of times they appear:
LCM=2*2*3*3*3*5=540
(a) All the events will happen together again after 540 minutes.
(b) Since 540 minutes = 9 hours, this event won't happen again until 9 am. Thus, it will occur zero times between midnight and one o'clock.
Okay, the image is a little tough to see, but I believe it looks something like this:
(5² -10 / 17 - 3 * 4) -1
The first step [remember PEMDAS] is parentheses
Next comes Exponents:
(25 - 10 / 17 - 3 * 4) -1
Then Multiplication:
(25 - 10 / 17 - 12) - 1
Then Division [which we can't do yet since it isn't fully simplified], so we skip to Addition... nothing again, then subtraction.
(15 / 5) - 1
Then we can divide:
(3) - 1
Then subtract!
2
The answer to your problem is 2.
Hope that helps!
These are the only combinations of exactly 3 tiles that add to 33.
5,7,21
5,9,19
5,11,17
5,13,15
7,9,17
7,11,15
9,11,13
All tiles with numbers above 21 do not help you. 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45. There are 12 of them.
Every three-number combination must have one of the numbers 5, 7, or 9, so if the six numbers from 13 to 21 are picked, in addition to the 12 higher numbers mentioned above, you already picked 18 tiles, and you still have no solution. To obtain the solutions 5,7,21; 5,9,19; 7,9,17; he needs two more numbers in addition to the 18 he already has, so he needs 20 tiles in total to be guaranteed three of them add to exactly 33.
Answer: 20 tiles
