Which of the following equations best represents the relationship in the table?
1 answer:
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Consider the contrapositive of the statement you want to prove.
The contrapositive of the logical statement
<em>p</em> ⇒ <em>q</em>
is
¬<em>q</em> ⇒ ¬<em>p</em>
In this case, the contrapositive claims that
"If there are no scalars <em>α</em> and <em>β</em> such that <em>c</em> = <em>α</em><em>a</em> + <em>β</em><em>b</em>, then <em>a₁b₂</em> - <em>a₂b₁</em> = 0."
The first equation is captured by a system of linear equations,
or in matrix form,
If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be
and this is what we wanted to prove. QED
Answer:
The minimum percentage of recently sold homes with prices between $197,200 and $232,800 is 75%.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by .
In this question:
Mean of $215,000, standard deviation of $8900.
What is the minimum percentage of recently sold homes with prices between $197,200 and $232,800?
215000 - 2*8900 = 197200
215000 + 2*8900 = 232800
Within 2 standard deviations of the mean, so:
The minimum percentage of recently sold homes with prices between $197,200 and $232,800 is 75%.