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meriva
2 years ago
5

Express 120 as a product of its prime factors.

Mathematics
2 answers:
kolezko [41]2 years ago
8 0
120 = 2 x 2 x 2 x 3 x 5 or 120 = 2^3 x 3 x 5
raketka [301]2 years ago
7 0
By the Fundamental Theorem of Arithmetic, all number can be expressed as a product of prime numbers.

So naturally, lets divide 120 by an easy prime number.
We know that 120 is even, so lets try 2 120/2 = 60 lets keep dividing it by two until it becomes odd or prime 60/2 = 30 30/2 = 15 now lets see, what are some factors of 15?

Well the obvious ones are 3 and 5, both of which are prime. So now we can just count up how many times we divided it by 2
 
120/2 = 60 60/2 = 30 30/2 = 15 and 15 is just 3 x 5, so: <span>
120=(<span>23</span>)×(3)×(5)</span>
or <span><span>
120 = 2 × 2 × 2 × 3 × 5</span></span>
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insens350 [35]
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4) So, we have that the probability that you get a red or purple or yellow sector is 2/7. We have that the probability for the blue sector is only 1/7 since there are 7 vectors and only one is blue. Similarly, the 2nd row of the table needs to be filled with the product of probability and expectations. Hence, for the red sector we have 2/7*(-1)=-2/7, for the yellow sector we have 2/7*1=2/7, for the purple sector it is 2/7*0=0, for the blue sector 1/7*3=3/7. The average payoff is given by adding all these, hence it is 3/7.
5) We can approach the problem just like above and set up an equation the value of one sector as an unknown. But here, we can be smarter and notice that the average outcome is equal to the average outcome of the blue sector.  Hence, we can get a fair game if we make the value of the blue sector 0. If this is the case, the sum of the other sectors is 0 too (-2/7+0+2/7) and the expected value is also zero.
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7) Let us use the expections formula we mentioned in 1. Substituting the possibilities and the values for all 4 events (each event is the different profit of the business at the end of the year).
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8 0
3 years ago
Read 2 more answers
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