25% off means that they are paying 75% of the original price. Multiply d by 75%:
0.75d
Now you need to multiply the price by 1 plus the sales tax to get the total cost:
0.75d x 1.08
Simplify by multiplying 0.75 by 1.08 to get:
0.81d
Answer:
70 m
Step-by-step explanation:
AB makes a 30-60-90 triangle with the wall.
AC makes a 45-45-90 triangle with the wall.
In a 30-60-90 triangle, the short leg (opposite of the 30° angle) is half the hypotenuse.
In a 45-45-90 triangle, the legs are the same length.
So the distance between the left wall and the laser is 60/2 = 30 m.
The distance between the right wall and the laser is 40 m.
The total distance is therefore 70 m.
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 :)
The equation for slope is:
(y2 - y1) / (x2 - x1)
-2 -(-7) = 5
-9 -(-1) = -8
Slope of the line:
5/-8 or -5/8
Answer:
The Answer is B.
Step-by-step explanation:
