Lena rolled two number cubes and recorded the results. What is the experimental probability that the sum of the next two numbers
1 answer:
Given:
Lena rolled two number cubes and recorded the results.
To find:
The experimental probability that the sum of the next two numbers rolled is greater than 5.
Solution:
If two number cubes rolled, then the total possible outcomes are:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (21,1), (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)
Total number of possible outcomes = 36
The possible cases in which the sum is less than or equal to 5 are (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1).
In 10 cases the sum is less than or equal to 5. So, the number of cases in which the sum is greater than 5 is:
So, the number of favorable outcomes = 26.
Now, the experimental probability that the sum of the next two numbers rolled is greater than 5 is:
Therefore, the required probability is .
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Answer:
If we want to expand the brackets, the fraction would be:
Explanation:
First, we can note that:
w² + w - 20 can be factorized as follows:
w² + w - 20 = (w+5)(w-4)
The given expression already has a (w+5) in the denominator, therefore, all we need to do is multiply the denominator by (w-4)
Since we want the new fraction to be equivalent to the original one, therefore, as we multiply the denominator by (w-4), we will also multiply the numerator by (w-4) to ensure that the value of the fraction is unchanged.
Based on the above, the new fraction would be:
If we want to expand the brackets, the fraction would be:
Hope this helps :)
If we want to expand the brackets, the fraction would be:
Explanation:
First, we can note that:
w² + w - 20 can be factorized as follows:
w² + w - 20 = (w+5)(w-4)
The given expression already has a (w+5) in the denominator, therefore, all we need to do is multiply the denominator by (w-4)
Since we want the new fraction to be equivalent to the original one, therefore, as we multiply the denominator by (w-4), we will also multiply the numerator by (w-4) to ensure that the value of the fraction is unchanged.
Based on the above, the new fraction would be:
If we want to expand the brackets, the fraction would be:
Hope this helps :)