... since the last war, some mitigation of slavery has been
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The standard form for a parabola is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix (d)
is x = h - p.
So directrix is: y = k - p and the focus is at:
(h, k+p)
Since our focus is: (1, 3) and directrix is: y = 1,
thus h = 1, k+p = 3, and k-p = 1
Therefore k = 3-p, 3-p-p = 1, k = 3-p = 3-1 = 2
3-2p = 1, -2p = -3+1, -2p = -2, p = 1
Now we plug p, k, & h into standard form:
(x - h)2 = 4p (y - k)
y = 1/4 (x-1)^2 + 2
is x = h - p.
So directrix is: y = k - p and the focus is at:
(h, k+p)
Since our focus is: (1, 3) and directrix is: y = 1,
thus h = 1, k+p = 3, and k-p = 1
Therefore k = 3-p, 3-p-p = 1, k = 3-p = 3-1 = 2
3-2p = 1, -2p = -3+1, -2p = -2, p = 1
Now we plug p, k, & h into standard form:
(x - h)2 = 4p (y - k)
y = 1/4 (x-1)^2 + 2
Answer:
Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>The significance level is 0.05.</em>
<em>The data is:</em>
<em>Brand X: 91, 100, 88, 89</em>
<em>Brand Y: 99, 96, 94, 99</em>
<em>Brand Z: 83, 88, 89, 76</em>
We have to check if there is a significant difference between the absorbency rating of each brand.
Null hypothesis: all means are equal
Alternative hypothesis: the means are not equal
We have to apply a one-way ANOVA
We start by calculating the standard deviation for each brand:
Then, we calculate the mean standard error (MSE):
Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:
The MSB is then:
Now we calculate the F statistic as:
The degrees of freedom of the numerator are:
The degrees of freedom of the denominator are:
The P-value of F=7.23, dfn=2 and dfd=9 is:
As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.
There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.