Over ten years, the population of fish in a lake increases by 3%. After the increase, there are 10,094 fish. Which expressions a
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Answer:
a
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to show that there is a difference between the performances of these two models
b
The 95% confidence interval is
Step-by-step explanation:
From the question we are told that
The sample size is n = 36
The first sample mean is
The first standard deviation is
The second sample mean is
The second standard deviation is
The level of significance is
The null hypothesis is
The alternative hypothesis is
Generally the test statistics is mathematically represented as
=>
=>
From the z table the area under the normal curve to the left corresponding to 2.3 is
Generally the p-value is mathematically represented as
=>
=>
From the value obtained we see that hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to show that there is a difference between the performances of these two models
Considering question b
From the question we are told the confidence level is 95% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of is
Generally the margin of error is mathematically represented as
=>
=>
Generally 95% confidence interval is mathematically represented as
=>
=>
The specific equation of the parabola can be found by plugging the given
values of the variables of the general equation.
<h3>Correct Response;</h3>The vertex of the parabola is at the origin with coordinates (0, 0)
The location of the focus = 3 cm from the vertex
<h3>Required:</h3>The equation that models the parabola.
<h3>Solution:</h3>The vertex form of the equation of a parabola is y = a·(x - h)² + k
The above equation can be expressed as (x - h)² = 4·p·(y - k)
Where in a vertical parabola;
(h + p, k) = The coordinates of the focus
(h, k) = The coordinates of the vertex = (0, 0)
p = 3 = The distance of the focus from the vertex
Therefore, the coordinates of the focus = (0 + 3, 0) = (3, 0)
The equation of the parabola is therefore;
(x - 0)² = 4×3 × (y - 0) = 12·y
x² = 12·y
Learn more about the equation of a parabola here: