We have a right triangle that has am 8 meter and 21 meter leg .Find the hypotenuse
1 answer:
Answer:
hypotenuse is 22.47 m
Step-by-step explanation:
The length of both legs of a right angle triangle are 8m and 21 m
We need to find the hypotenuse
To find hypotenuse we use Pythagorean theorem
Hypotenuse is AC and other two legs are AB and BC
Hypotenuse ^2 = 8^2 + 21^2
hypotenuse =
=
=
= 22.47
So the length of the hypotenuse is 22.47 m
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Answer:
In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.
In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.
In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.
Step-by-step explanation:
We have to write the transition matrix M for the population.
We have three states (nonsmokers, smokers of one pack and smokers of more than one pack), so we will have a 3x3 transition matrix.
We can write the transition matrix, in which the rows are the actual state and the columns are the future state.
- There is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. <em>Then, the probability of staying in the same state is 90%.</em>
- For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. <em>Then, the probability of staying in the same state is 80%.</em>
- For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. <em>Then, the probability of staying in the same state is 82%.</em>
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The transition matrix becomes:
The actual state matrix is
We can calculate the next month state by multupling the actual state matrix and the transition matrix:
In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.
To calculate the the state for the second month, we us the state of the first of the month and multiply it one time by the transition matrix:
In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.
If we repeat this multiplication 12 times from the actual state (or 10 times from the two-months state), we will get the state a year from now:
In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.