Answer:
C.
Steps:
Using points (1,0) and (0,3), you can find the slope.
3 - 0 = 3
1 - 0 = 1
3/1 = 3
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 :)
I don’t see any images but any angle measured less than 90 degrees is an acute angle
Answer:
280000lb
Step-by-step explanation:
In this question, we shall be calculating the amount of carbon iv oxide prevented from entering the atmosphere.
Generally we know that 1kwh produces 1.37 lbs of Carbon iv oxide in the atmosphere
Now, using a 100 watt light bulb daily for 8 hours, for a year, the amount of Carbon iv oxide produced will be;
100 * 1.37 * 8 * 365 = 40040 lb
Using a 30 watt CFL for 8hrs/ day for a year, we have;
30 * 1.37 * 8 * 365 = 120012 lb
Now calculating the amount of CO2 prevented, we have 40040 - 120012 = 280028 lb = 280000 after rounding up
Answer:
$10
Step-by-step explanation:
The exact number is $11.65 which is closet to $10
