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puteri [66]
3 years ago
9

Eben rolls two standard number cubes 36 times. Predict how many times he will roll a sum of 4.

Mathematics
1 answer:
trasher [3.6K]3 years ago
8 0
Lets make a list
assuming they have 2 cubes with 1-6 on them
combos are
1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5 
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6


out of all 36 times, only 3 times did the sum equal 4
3 times he will roll a 4 

ALL CREDIT GOES TO ANOTHER ANSWER THIS IS NOT MINE!

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Answer:

Solutions are 2,  -1 +  0.5 sqrt10 i  and -1 - 0.5 sqrt10 i

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Step-by-step explanation:

The real solution is x = 2:-

x^3 - 8 = 0

x^3 = 8

x = cube root of 8 = 2

Note that a cubic equation must have  a total of 3 roots ( real and complex in this case).  We can find the 2 complex roots by using the following identity:-

a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Here  a = x and b = 2 so we have

(x - 2)(x^2 + 2x + 4) = 0

To find the complex roots we solve x^2 + 2x + 4 = 0:-

Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2

= -1 +/- (sqrt( -10)) / 2

= -1 +  0.5 sqrt10 i  and -1 - 0.5 sqrt10 i

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