Which of the following measures of central tendency are resistant to outliers? (May be more than one correct answer) Group of an
1 answer:
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Answer:
see below
Step-by-step explanation:
This is solved by simplifying each expression and identifying the column heading it matches.
1. (6 x^2/(x^2 - 7 x + 10)) / (2 x)/(x - 5))
= (6 x^2/(x^2 - 7 x + 10)) · (x -5)/(2 x) . . . . invert and multiply
= (6x^2)/(2x) · (x -5)/((x -2)(x -5)) . . . . . . . factor so common factors can cancel
= 3x/(x -2) . . . . matches column 1
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2. (x - 4) (x + 2)/(x^2 + 5 x + 6) + (-3 x^2 + 24 x - 20)/((x + 3) (4 x - 5))
= (x -4)(x +2)/((x +3)(x +2)) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . factor
= (x -4)/(x +3) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . . cancel common factor
= ((x -4)(4x -5) +(-3x^2 +24x -20))/((x +3)(4x -5)) . . . . use common denominator
= (4x^2 -21x +20 -3x^2 +24x -20)/((x +3)(4x -5)) . . . expand product
= (x^2 +3x)/((x +3)(4x -5)) . . . . . . collect terms
= (x)(x +3)/((x +3)(4x -5)) . . . . . . factor numerator
= x/(4x -5) . . . . . . . . . . . . . . . . . . cancel common factor ... matches column 2
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3. 3 x^2/(x + 3) · (2 x + 6)/(2 x^2 - 4 x)
= 3·2·x·(x +3)/((x +3)(2·x)(x -2)) = 3/(x -2) . . . . matches column 1
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4. 3 x/(4 x - 5) - 4 x^2/(8 x^2 - 10 x)
= 3x/(4x -5) - 4x^2/(2x(4x -5)) = (3x -2x)/(4x -5) = x/(4x -5) ... matches col 2
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5. 5 x^2/(x - 2) · (2 x + 6)/(8 x^2 - 4 x) . . . . no match (has a denominator factor of 2x-1 that doesn't cancel any numerator factors)
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6. -x/(4 x - 5) - 4 x^2/(16 x^2 - 22 x)
In order to match one of the columns, the term on the right must reduce to 2x/(4x-5), which it does not, or must have a denominator factor of x-2, which it also does not. no match.
Answer:
So he can travel a total of 90 miles
Step-by-step explanation:
Given:
Total he has to pay = $130
Per week cost = $94
Per mile cost = $0.40
To Find:
No of miles = ?
Solution:
The total he has to pay can be found out by the equation
Total = weekly cost + Miles cost
Now here
Miles cost = total no of miles traveled * per mile cost
This is due to the reason that he is travelling miles and we have to multiply it with it per mile cost to get the total miles cost
so
Let Total miles traveled be x then
Miles cost = $ 0.40 * x
Now we have
Total = weekly cost + Miles cost
Putting in the values we get
130 = 94 + 0.40 *x
subtracting 94 from both sides
130-94 = 94 + 0.40*x - 94
36 = 0.40*x
Dividing both sides by 0.4 we get
90 miles = x
or x= 90 miles
So he can travel a total of 90 miles