Jason ran 5/7 of the distance around the school track. Sara ran 4/5 of Jason's distance. What fraction of the total distance aro
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Answer:
It can be concluded that the medicated lotion has an effect on treating skin irritations.
Step-by-step explanation:
In this case we need to determine whether the medicated lotion was effective in treating the skin irritation or not.
The hypothesis can be defined as follows:
<em>H₀</em>: There is no difference between the two proportions, i.e. <em>p</em>₁ - <em>p</em>₂ = 0.
<em>Hₐ</em>: There is a significant difference between the two proportions, i.e. <em>p</em>₁ - <em>p</em>₂ ≠ 0.
The information provided is:
n₁ = 40
n₂ = 40
X₁ = 36
X₂ = 16
Compute the sample proportions and total proportions as follows:
Compute the test statistic value as follows:
The test statistic value is 4.69.
The decision rule is:
The null hypothesis will be rejected if the <em>p</em>-value of the test is less than the significance level.
Compute the <em>p</em>-value as follows:
The <em>p</em>-value of the test is very small.
The null hypothesis will be rejected at any significance level.
Thus, there is a significant difference between the two proportions.
So, it can be concluded that the medicated lotion has an effect on treating skin irritations.
1) A quadratic will have no real roots when its discriminant is negative
Dividing by 4,
We have a positive coefficient on k^2 so this parabola is a CUP (concave up positive) so has a minimum at the vertex. If the vertex y value is less than zero, the inequality will be true in the range between the zeros.
That's true for
2) We look for the meet of the line and the parabola:
For two intersections we need a positive discriminant:
That's means two negative or two positive, so
or