Order the following probabilities from least to greatest: 1, 0.03, 5%, 0.07%
1 answer:
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Lets say that the two unknown integers are 
and 
.
We know the following things about and :
And, we want to find
.
To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:
So, given what we know about the unknown integers, the previous can be written as:
We can easily solve for:
The answer is 168.
Another approach to solve the problem is, from the two starting equations, compute the values of and , which are 12 and 14, and directly compute their product; however, the approach described is more elegant.
We know the following things about
And, we want to find
To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:
So, given what we know about the unknown integers, the previous can be written as:
We can easily solve for
The answer is 168.
Another approach to solve the problem is, from the two starting equations, compute the values of
<h3>Answer:</h3>
8x = 12
<h3>Explanation:</h3>Subtracting the first equation from the second, you get ...
... (5x +2y) -(3x +2y) = (7) -(5)
... 2x = 2 . . . . . the first answer choice is true
___
Multiplying this expression for x by 4, we get
... 8x = 8 . . . . . the second answer choice (8x=12) is false
___
Adding thee first equation to the second, you get ...
... (3x +2y) +(5x +2y) = (5) +(7)
... 8x +4y = 12
... 8 + 4y = 12 . . . . . . use the value of 8x just computed
... 4y = 4 . . . . . . . . . . subtract 8; the third answer choice is true
_____
<em>Alternate approaches</em>
In short, if you solve the system by any of the methods available, you find x=1 and y=1, so the second answer choice is clearly the correct one:
... 8x ≠ 12
By Cramer's method:
... x = (2·7-2·5)/(2·5-2·3) = 4/4 = 1
... y = (5·5-7·3)/4 = 4/4 = 1
By graphing, see attached.
By substitution (for 2y):
... 5x +(5-3x) =7 . . . . . using 2y=5-3x
... 2x = 2 . . . . . . subtract 5
... x = 1 . . . . . . . .divide by 2
... 5 -3·1 = 2y = 2 . . . . substitute x into the expression for 2y
... y = 1 . . . . . . . divide by 2
By matrix methods, see the second attachment. (x, y) = (1, 1), found in the rightmost column of the result.
Answer:
C. -(5/-4)
Step-by-step explanation: