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11Alexandr11 [23.1K]
3 years ago
8

There are 3 marbles (yellow, blue, green) you pick a marble and flip a coin. How many outcomes are possible?

Mathematics
1 answer:
Ede4ka [16]3 years ago
5 0
This is a problem dealing with probability. First of all, you pick a marble, at random, from three marbles. It stands to reason then that the likelihood of you picking any specific marble is a 1 in 3 chance, or 1/3.

Then you flip a coin. There are only two possible outcomes here, so the chance of the coin landing on any particular side is a 1 in 2 chance, or 1/2.

You then multiply these probabilities by each other to come out with a 1/6 probability of getting any specific outcome, meaning that there are <u>6 possible outcomes</u>

Now there might be some confusion to as why I multiplied the probabilities together and as to why this works. If I may, allow me to alleviate any confusion. 

If one thinks about it, it makes perfect sense why it should work. If you pick the green marble the option remains that you will either flip heads or tails. Hence, via picking the green marble you are left with two possible outcomes.

This remains true for the blue and the yellow marble, picking either will still leave you with two outcomes, giving 6 outcomes all together. 
Hope this helps :) 
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The cube root of 5 times the square root of 5 over the cube root of 5 to the 5th power
Fiesta28 [93]
(cube root of 5)  * sqrt(5)
--------------------------------- = ?
(cube root of 5^5)

This becomes easier if we switch to fractional exponents:


  5^(1/3) * 5^(1/2)         5^(1/3 + 1/2)       5^(5/6)
------------------------ = --------------------- = ------------- = 5^[5/6 - 5/3]
[ 5^5 ]^(1/3)                  5^(5/3)                 5^(5/3) 

Note that 5/6 - 5/3 = 5/6 - 10/6 = -5/6.

                                                            1
Thus,  5^[5/6 - 5/3] = 5^(-5/6)  =  --------------
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That's the correct answer.  But if you want to remove the fractional exponent from the denominator, do this:

    1            5^(1/6)         5^(1/6)
---------- * ------------- = --------------    (ANSWER)
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3 years ago
How to solve 2x-1/2=3-x
ValentinkaMS [17]
To solve for x:
Move all the terms containing "x" to the left side of the equation. Do this by adding x to both sides.

2x+x=3x. The new equation is:
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Now, move all terms not containing "x" to the right side of the equation. Do this by adding 1/2 to both sides.
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The final step is to isolate x. To do so, divide each side by 3.
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(7,2) is the answer.
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