PLEASE HELP 20 POINTS
1 answer:
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Answer:
Width: 7
Length: 14
Step-by-step explanation:
The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let represent the width.
Since the length is 7 feet longer, we can represent the length by .
Now that we have our values for the length and the width we can multiply them together to find our area.
Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.
And multiply our area by 3.
set these equal to each other to find your new equation.
Now you need to solve for . To do this first muliply
and
.
Then multiply
Now you can begin solving for .
Subtract from both sides.
Subtract from both sides.
Divide by 2.
And finally take the sqaure root of both sides.
Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 <em>and</em> -7, in this case we <em>only </em>get +7.
Now that we have the value of , we can plug it into our original values.
For width we simply get 7.
For length we get 7+7=14
To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.
We're told that
where the last fact is due to the law of total probability:
so that and
are complementary.
By definition of conditional probability, we have
We make use of the addition rule and complementary probabilities to rewrite this as
By the law of total probability,
and substituting this into gives