The Greatest Common Factor also known as GCF is the largest number that can divide equally into two or more numbers.
For the problem they ask 'Which number pair has a 'GCF' of 6.
First let's look at the answer choice 'A' that gives us 18 and 54.
Now for this we need to list the factors of both 18 and 54. A factor being a number that can be multiplied by another number to get the sum.
18: 1, 2, 3, 6, 9, 18
54: 1, 2, 3, 6, 9, 18, 27, 54
So right away we can see the the largest number that can be divided into both of them equally is not 6, it is 18. This means we can mark out A as a possible answer.
Next let's try B and list the factors of both 30 and 42.
30: 1, 2, 3, 5, 6, 15, 30
42: 1, 2, 3, 6, 7, 14, 21, 42
Looks like we found our answer! The largest factor they have in common is 6!
I'm still going to go ahead and list the GCF's for answers C and D.
So your total is 8876. On the first and the second level of the game you scored 3653 and 2375. But when you where done playing the third level your total from all of the levels ended up to be 8876. So if you wanted to find how much points you got on level 3, then you would add 3653 + 2375, then suntract the total of that from 8876.
, assuming that the assignment of dormitories is independent from the assignment of dining rooms.
Step-by-step explanation:
Assume that each of the dormitories has equal probability of being chosen.
Probability that Kharleen is assigned to one of the (out of ) dormitories that she likes:
.
In this fraction, the numerator is the number of dormitories that Khareen likes, while the denominator is the number of all possible dormitories.
Similarly, assume that each of the dining rooms have equal probability of being chosen.
Probability that Kharleen is assigned to one of the (out of ) dining rooms that she likes:
.
Similarly, the numerator of this fraction is the number of dining rooms that Khareen likes. The denominator of this fraction is the number of all possible dining rooms.
Assume that the assignment of dormitories and the assignment of dining rooms (two events) are independent.
Hence, the probability of both getting a preferred dormitories (first event) and getting a preferred dining room (second event) would be the product of the probability of the two events:
.
Hence, the probability that Kharleen is assigned to both a dormitory and a dining room that she likes would be under these assumptions.
So for finite series like these, you just plug in each number for k that it tells you. The first says the sum of 3k^2 from k=1 to k=4. Just plug integer k between 1 and 4 into the equation and add them together:
3(1^2)+3(2^2)+3(3^2)+3(4^2)=90
Same for the next one, except this is for all values of k between 3 and 6: (-5(3)+20)+(-5(4)+20)+(-5(5)+20)+(-5(6)+20)=<span>-10</span>