If three points (5,1) , (1,-1) and (m,4) are collinear.Find m
1 answer:
Answer:
m = 11
Step-by-step explanation:
Since the points are collinear then the slope between points are equal.
Calculate the slope m using the slope formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (1, - 1)
m = =
=
Repeat with
(x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (m, 4)
m = =
=
Cross- multiply
m - 1 = 10 ( add 1 to both sides )
m = 11
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Answer:
Option <em>B</em> is not the most common correct choice.
Step-by-step explanation:
The multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E.
The probability that any of these five option is the correct answer is:
A random sample of 400 multiple-choice questions on Advanced Placement exam are selected.
The results showed that 90 of the 400 questions having B as the answer.
To test the hypothesis that option B is more likely the correct answer for most question, the hypothesis can be defined as:
<em>H₀</em>: All the options are equally probable, i.e. <em>p</em> = 0.20.
<em>Hₐ</em>: Option B is more likely the correct option, i.e. <em>p</em> > 0.20.
Compute the sample proportion as follows:
The test statistic is:
The test statistic is 1.25.
Decision rule:
If the <em>p</em>-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
Compute the <em>p</em>-value as follows:
*Use a <em>z</em>-table.
The <em>p</em>-value is 0.1057.
The <em>p</em>-value of the test is quite large. Thus, the null hypothesis was failed to rejected.
Hence, it can be concluded that option <em>B</em> is not the most common correct choice.