Answer:
Step-by-step explanation:
i'm not sure what the answer options are since they're not provided, but it's whichever option has a steady rate of change. (ex: money, time spent earning it; location, time spent driving; length in inches, length in meters)
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:
- <em>To solve these first swap x and y, solve for y and name it inverse function</em>
3. <u>y = -8x + 2</u>
- x = -8y + 2
- 8y = -x + 2
- y = -x/8 + 2/8
- y = -(18)x + 1/4
f⁻¹(x) = -(18)x + 1/4
-----------------------------------------
4.<u> y = (2/3)x - 5</u>
- x = (2/3)y - 5
- (2/3)y = x + 5
- y = (3/2)x + (3/2)5
- y = 1.5x + 7.5
f⁻¹(x) = 1.5x + 7.5
-----------------------------------------
5. <u>f(x) = 2x² - 6</u>
- x = 2y² - 6
- 2y² = x + 6
- y² = 1/2x + 3
- y =
f⁻¹(x) =
-----------------------------------------
6. <u>y = (x - 3)²</u>
- x = (y - 3)²
= y - 3- y = 3 +
f⁻¹(x) = 3 +
yo sup??
the sum of trails taken should be less than 25 miles
Black bear=B
Eagle Ridge=E
Doe Run=D
(btw names sound cool XD)
we will now try different combinations
B+E=7 1/2 ++ 10 1/4 which is clearly less than 25
B+D=7 1/2 + 8 3/4 which also less than 25
E+D=10 1/4 + 8 3/4 which is also less than 25
B+D+E=7 1/2 + 10 1/4 + 8 3/4 which is greater than 25
Therefore only the 1st,2nd and 3rd case are possible
Hope this helps.
Answer:
x = -2.5
x = 2
Step-by-step explanation:
Hello!
We can remove the denominators by multiplying everything by it.
Solve:
Let's make one side equal to 0.
Solve by factoring, and then the zero product property.
Multiply 2 and -10. You get -20. Think of two number that multiply to -20, and add to 1. If we think about the standard form of a quadratic, 
, think two numbers that equal "ac" and add up to "b".
Using the zero product property, set each factor to 0 and solve for x.
- 2x + 5 = 0
2x = -5
x = -5/2 = -2.5 - x - 2 = 0
x = 2
The two answers are x = -2.5, and x = 2.
