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vredina [299]
3 years ago
8

Consider a cube whose sides are 1.43 m long. how many kg of sand would it take for the total surface area of all the grains of s

and to equal the surface area of the cube? answer in units of kg.
Mathematics
1 answer:
defon3 years ago
4 0
We can't solve this without knowing the density of the sand. We are given with the side of the cube. From this, we can calculate for the volume. However, to end up with units of mass, you have to use the density. From literature, the density of sand is 1,520 kg/m³. The solution is as follows:

Density = Mass/Volume
1,520 = Mass/s³ = Mass/(1.43)³
Mass = 4,444.79 kg
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A poker hand is a set of 5 cards randomly chosen from a deck of 52 cards. Find the probability of a (a) royal flush (ten, jack,
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a) 0.000001539

b) 0.00001385

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Step-by-step explanation:

Since there are 52 deck of cards, and the hand of the poker is 5 set, then the total number of hands achievable would be

T = 52! / 5!(52 - 5)!

T = 52! / 5! 47 !

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a) There are 4 ways of getting a royal flush. So the probability of getting a royal flush is

4 / 2598560 =

0.000001539

b) There are 9 hands from the 5 card hands, and also, there are 4 possible suits. So then, the probability is

9 * 4 / 2598560 =

36 / 2598560 =

0.00001385

c) There are 13 possible ways to get a four of a kind, since there are 5 cards with the poker, the remaining would be taken from the 48 remaining cards, thus

13 * 48 / 2598560 =

624 / 2598560 =

0.0002401

d) 3 of a kind in conjunction with a pair is needed to form a full house. This 3 of a kind can be gotten from any 4 suits. Then again, the pair has two cards with the same face value. So,

4! / 2! (4 - 2)! =

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Now, recall that the question specifically asked us not to include any straight. There are 10 straights that can be gotten, and thus, we subtract it.

1287 - 10 = 1277

Since there are 4 suits, the probability of getting a flush is

1277 * 4 / 2598560 =

5108 / 2598560 = 0.001966

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3 years ago
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