6x+15=27
6x/6=12/6
X=2
27-15=12
Answer:
Option A
Step-by-step explanation:
The standard form of an equation of a circle is represented by the formula
. Remember that
is the center and
is the radius squared.
So, the equation of the circle must be
. Complete the square to change the form of the equations listed in the options and find the one that is equal.
Let's try this with option A. Move the constants to the right side, then use the completing the square method to place the equation in standard form:
![x^2 + y^2 +2x -8y -3 = 0\\x^2 + y^2 +2x-8y = 3\\x^2 + 2x +y^2-8y = 3\\(x^2 +2x+1)+(y^2-8y +16)=3+1+16\\(x+1)^2 + (y-4)^2=20](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2%20%2B2x%20-8y%20-3%20%3D%200%5C%5Cx%5E2%20%2B%20y%5E2%20%2B2x-8y%20%3D%203%5C%5Cx%5E2%20%2B%202x%20%2By%5E2-8y%20%3D%203%5C%5C%28x%5E2%20%2B2x%2B1%29%2B%28y%5E2-8y%20%2B16%29%3D3%2B1%2B16%5C%5C%28x%2B1%29%5E2%20%2B%20%28y-4%29%5E2%3D20)
The end result matches with the equation determined before, so option A is the answer.
Answer:
Critical value: T = 2.8314
The 99% confidence interval for the population mean iron concentration is between 0.364 cc/m³ and 0.454 cc/m³
Step-by-step explanation:
We are in posession of the sample's standard deviation. So we use the student 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 = 22 - 1 = 21
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 21 degrees of freedom(y-axis) and a confidence level of
. So we have T = 2.8314, which is the critical value that should be used in constructing the interval.
The margin of error is:
M = T*s = 2.8314*0.016 = 0.045
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 0.409 - 0.045 = 0.364 cc/m³
The upper end of the interval is the sample mean added to M. So it is 0.409 + 0.045 = 0.454 cc/m³
The 99% confidence interval for the population mean iron concentration is between 0.364 cc/m³ and 0.454 cc/m³
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Answer: (d) Blocks: the three age groups. Treatments: using the standard tablet or the reduced blue light tablet before bed. Response variable: time it takes to fall asleep
Step-by-step explanation: