How would you find the quadratic that goes through the point (4,0), the axis of symmetry is x=7, and it also goes through the po
int (1,5)?
1 answer:
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Answer:
y = (5/27)(x -7)^2 -5/3
Step-by-step explanation:
Use the given points to find the unknowns in the equation.
If the axis of symmetry is x=7, then the equation can be written in the form ...
y = a(x -7)^2 +b
Filling in the two point values, we have two equations:
0 = a(4 -7)^2 +b ⇒ 9a +b = 0
5 = a(1 -7)^2 +b ⇒ 36a +b = 5
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Subtracting the first equation from the second, we have ...
(36a +b) -(9a +b) = (5) -(0)
27a = 5
a = 5/27
Substituting that value into the first equation gives ...
9(5/27) +b = 0
5/3 +b = 0
b = -5/3
So, the quadratic can be written in vertex form as ...
y = (5/27)(x -7)^2 -5/3
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a) The point estimate of the proportion of people aged 65–69 who are working is p=0.3 or 30%.
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c) We conclude that there is not enough evidence that the proportion of people aged 65–69 who are working has increased from 2005.
Step-by-step explanation:
a) Develop a point estimate of the proportion of people aged 65–69 who are working
If we take into account the sample taken, the point estimate is
b) Set up a hypothesis test so that the rejection of h0 will allow you to conclude that theproportion of people aged 65–69 working has increased from 2005
To conclude some claim, we have to reject the null hypothesis. In this case, to claim that the proportion has changed and the mean is no longer 27%, we have to reject the null hypotesis that π=0.27.
We can express this null and alternative hypothesis as:
c) Conduct your hypothesis test using α=0.05. What is your conclusion?
First we calculate the standard deviation, as we will need it to calculate the test statistic:
In this case, we have a test statistic of
If we take into account that it is a two-tailed test, P-value for z=1.61 is P=0.1074.
As the P-value is bigger than the significance level, the effect is not statistically significant, so the hypothesis can not be rejected.
We conclude that there is not enough evidence that the proportion of people aged 65–69 who are working has increased from 2005.
