Find the slope of the line passing through the points (-6,9) and (-6, -7).
1 answer:
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Answer:
A) y = 3(x -3)^2 -46
B) (3, -46)
C) look at the y-coordinate of the vertex
Step-by-step explanation:
A) Factor the leading coefficient from the variable terms.
y = 3(x^2 -6x) -19
Inside parentheses, add the square of half the x-coefficient. Outside, subtract the same value.
y = 3(x^2 -6x +9) -19 -3(9)
y = 3(x -3)^2 -46
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B) Compared to the vertex form, ...
y = a(x -h)^2 +k
we find a=3, (h, k) = (3, -46).
The vertex is (3, -46).
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C) The vertex is an extreme value (as is any vertex). The sign of the leading coefficient tells you whether the parabola opens upward (+) or downward (-). This parabola opens upward, so the vertex is a minimum.
If the leading coefficient is positive, the y-coordinate of the vertex is a minimum. If the leading coefficient is negative, the y-coordinate of the vertex is a maximum.
Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
c) So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of American families owning stocks or stock funds is significantly less than 0.53 .
Step-by-step explanation:
Data given and notation
n=300 represent the random sample taken
estimated proportion of American families owning stocks or stock funds
is the value that we want to test
represent the significance level
Confidence=99% or 0.99
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
Part a
We need to conduct a hypothesis in order to test the claim that proportion is less than 0.53 or 53%.:
Null hypothesis:
Alternative hypothesis:
Part b
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
Part c
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of American families owning stocks or stock funds is significantly less than 0.53 .