The third quadrant are both negative numbers so the answer is B.
A combination is an unordered arrangement of r distinct objects in a set of n objects. To find the number of permutations, we use the following equation:
n!/((n-r)!r!)
In this case, there could be 0, 1, 2, 3, 4, or all 5 cards discarded. There is only one possible combination each for 0 or 5 cards being discarded (either none of them or all of them). We will be the above equation to find the number of combination s for 1, 2, 3, and 4 discarded cards.
5!/((5-1)!1!) = 5!/(4!*1!) = (5*4*3*2*1)/(4*3*2*1*1) = 5
5!/((5-2)!2!) = 5!/(3!2!) = (5*4*3*2*1)/(3*2*1*2*1) = 10
5!/((5-3)!3!) = 5!/(2!3!) = (5*4*3*2*1)/(2*1*3*2*1) = 10
5!/((5-4)!4!) = 5!/(1!4!) = (5*4*3*2*1)/(1*4*3*2*1) = 5
Notice that discarding 1 or discarding 4 have the same number of combinations, as do discarding 2 or 3. This is being they are inverses of each other. That is, if we discard 2 cards there will be 3 left, or if we discard 3 there will be 2 left.
Now we add together the combinations
1 + 5 + 10 + 10 + 5 + 1 = 32 choices combinations to discard.
The answer is 32.
-------------------------------
Note: There is also an equation for permutations which is:
n!/(n-r)!
Notice it is very similar to combinations. The only difference is that a permutation is an ORDERED arrangement while a combination is UNORDERED.
We used combinations rather than permutations because the order of the cards does not matter in this case. For example, we could discard the ace of spades followed by the jack of diamonds, or we could discard the jack or diamonds followed by the ace of spades. These two instances are the same combination of cards but a different permutation. We do not care about the order.
I hope this helps! If you have any questions, let me know :)
<u>Answer:</u>
Option(b) = 10
The Number 6 in the thousands place is 10 times bigger than the Number 6 in the hundreds place
<u>Explanation:</u>
We are given the value recorded = 16,652
Now the Number 6 in hundreds place means it is equal to 600 and the Number 6 in thousands place means that it is = 6000
from the given value 6 in hundreds place = 652 and
that in thousands place = 6520 ,
so the six in thousands place is obtained by multiplying 10 with the 6 in hundreds place hence the latter is 10 times bigger than the former.
The given expression is
We see from the possible answers they are all in reduced form - variables are grouped together. That means we should also reduce the given expression to see which answer is equivalent to it.
Let's expand the term inside the parentheses first, by multiplying each term inside by the coefficient of the parentheses, -3.
Now let's group terms which have the same variables.
We can see that there are two groups:
Let's evaluate them separately. We just need to reduce each group now, since we've already grouped similar terms.
If we put the groups back together into the expression,
We can see that
. So (D) is the answer. Hope this helped.
Answer:
405 cm^3
Step-by-step explanation:
We can find the volume by first counting the number of cubes
5+4+3+2+1 = 15
Each cube is 3 cm on a side so the volume of 1 cube is
V = 3*3*3 = 27 cm^3
We have 15 of them
15*27 cm^3
405 cm^3
