Which point is a solution to the inequality shown in this graph?
2 answers:
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Answer:
Step-by-step explanation:
Let's answer these questions in an all-encompassing kind of explanation. If you plot the vertex and the directrix, you see that the vertex is below the directrix. Because of the fact that a parabola opens AWAY from the directrix, and wraps itself around the focus, we know it's an upside down parabola of the form
The p value from the equation is a distance, specifically the distance between either the vertex and the directrix, or the vertex and the focus. The vertex is exactly in the middle of the directrix and the focus. So that tells us that the focus is 3 units below the vertex (because the directrix is 3 units above the vertex). We also know from this that p = 3.
Filling in the equation with a vertex of (0, 0) which is our h and k respectively:
which simplifies to
and multiplying both sides by -1:
. This is not standard form, but it matches what your equation is in the choices. So to sum up:
The focus is located at (0, -3) and the first choice is true.
The parabola opens upside down and the second choice is not true.
The p value is found by counting the units between the vertex and the directrix, so the third choice is not true.
We solved the equation by filling in the values for h, k, and p and got that the equation in the fourth choice is true.
So the fifth choice is not true.
Answer:
Null hypothesis be H₀ : μ = 100
Alternative hypothesis Hₐ : μ < 100
There is sufficient statistical evidence to suggest that the average location of Wade Tract is 100
Step-by-step explanation:
Here we have;
Let our null hypothesis be H₀ : μ = 100 Average location of trees in the Wade Tract is 100
Our alternative hypothesis becomes Hₐ : μ < 100 at 95% confidence level
Proposed average location in Wade Tract, μ = 100
Sample mean, = 99.74
Standard deviation, s = 58
Sample size, n = 584
The t test formula is therefore;
Therefore, with df = 584 -1 = 583, and α = (1 - 0.95)/2 = 0.025
We have = -1.65
Plugging in the values into the t test formula, we have t = -0.108338, from which the p-value is given as p = 0.4569 which is much more than the value of α, therefore, we accept the null hypothesis as follows;
There is sufficient statistical evidence to suggest that the average location of Wade Tract = 100.