Answer: n = -27
Step-by-step explanation:
2/9n = -6
divide both sides by 2/9
n = -27
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.
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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 :)
Answer:
f(x) = -7x² - x
g(x) = 9x² - 4x
To find ( f - g)(x) subtract g(x) from f(x)
That's
( f - g)(x) = - 7x² - x - ( 9x² - 4x)
= -7x² - x - 9x² + 4x
Group like terms
( f - g)(x) = - 7x² - 9x² - x + 4x
<h3>( f - g)(x) = - 16x² + 3x</h3>
To find (f - g)(1) substitute 1 into ( f - g)(x)
That's
(f - g)(1) = - 16(1) + 3(1)
= -16 + 3
<h3>= - 13</h3>
Hope this helps you
Let's have a variable for each rate
x = account 1 (2.5% rate of interest)
y = account 2 (8% rate of interest)
The formulas we need are:
0.025x + 0.08y = 830 (amount of interest paid)
x + y = 20 000 (combined amount invested)
To solve we will use substitution (isolate for one variable and plugging into the other formula):
x + y = 20 000
x = 20 000-y
0.025x + 0.08y = 830
0.025(20 000-y) + 0.08y = 830
500-0.025y+0.08y=830
500+0.055y=830
0.055y=330
y=6000
Now that we know y (the 2nd account) = $6000 we need to find x. We do this by using the previous formula.
x = 20 000-y
x=20 000 - 6000
x=14000
She invested $14 000 at a 2.5% interest rate and $6 000 at a 8% interest rate.
*Notes:
the percentages were converted into decimal form
you check your answer by plugging the numbers back into the 2 formulas we made
Answer:
Step-by-step explanation:
Reorder terms.
Factor out the greatest common factor from each group
Factor the polynomial by factoring out the greatest common factor, 
Factor.
hope this helps :)
