Isolated triangle 68 perimeter equal sides more than 10 ft use x for the shorter side formula
1 answer:
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Answer:
a) The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
b) The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 48 - 1 = 47
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 47 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.0117
The margin of error is:
M = T*s = 2.0117*2.3 = 4.6
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 7.1 - 4.6 = 2.5 hours of sunlight per day
The upper end of the interval is the sample mean added to M. So it is 7.1 + 4.6 = 11.7 hours of sunlight per day
a) Compute the 95% confidence interval for the mean.
The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
b) Explain your confidence interval from part (a) in context.
The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
Answer:
centre = (2, - 1), radius = 6
Step-by-step explanation:
Rearrange the equation by placing the x and y terms together and adding 31 to both sides
Given
x² + y² - 4x + 2y - 31 = 0, then
x² - 4x + y² + 2y = 31
Use the method of completing the square
add ( half the coefficient of the x/y term )² to both sides
x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1
(x - 2)² + (y + 1)² = 36
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
compare to (x - 2)² + (y + 1)² = 36, then
centre = (2, - 1) and r = = 6