Hi! I provided an image that I hope helps!
Answer:
5
Step-by-step explanation:
b = 13 - 8 = 5
Answer:
129.9 kPa
Step-by-step explanation:
The relationship between temperature T, volume V and pressure P is given by the ideal gas equation which is given as
K = PV/T where K is a constant such that were there is a change of temperature T₁, volume V₁ and pressure P₁ to temperature T₂, volume V₂ and pressure P₂ then the relationship may be given
P₁V₁/T₁ = P₂V₂/T₂
where T is measured in ⁰K
T₁ = -50 + 273
= 223 ⁰K
T₂ = 102 + 273
= 379 ⁰K
5 × 107/223 = P₂ × 7/379
P₂ = 129.9 kPa
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 :)
Let x represent radius of circle.
We have been given that the height of a cylinder is twice the radius of its base. So height of cylinder would be 
.
Now we will use volume of cylinder formula to our given problem.
, where,
r = Radius of base of cylinder,
h = Height of cylinder.
Upon substituting our given values, we will get:
Therefore, our required volume expression would be 
.
