The center of a circle whose equation is x^2 +y^2 – 12x – 2y +12 = 0 is (6,1)
<h3>Equation of a circle</h3>
The standard equation of a circle is expressed as:
x^2 + y^2 + 2gx + 2fy + c = 0
where:
(-g, -f) is the centre of the circle
Given the equations
x^2 +y^2 – 12x – 2y +12 = 0
Compare
2gx = -12x
g = -6
Simiarly
-2y = 2fy
f = -1
Centre = (6, 1)
Hence the center of a circle whose equation is x^2 +y^2 – 12x – 2y +12 = 0 is (6,1)
Learn more on equation of a circle here: brainly.com/question/1506955
Answer:
We conclude that the calibration point is set too high.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 1000 grams
Sample mean,
= 1001.1 grams
Sample size, n = 50
Alpha, α = 0.05
Population standard deviation, σ = 2.8 grams
First, we design the null and the alternate hypothesis

We use One-tailed(right) z test to perform this hypothesis.
Formula:

Putting all the values, we have

Now, 
Since,

We reject the null hypothesis and accept the alternate hypothesis. We accept the alternate hypothesis. We conclude that the calibration point is set too high.
Answer:
3x - y -6 = 0
Step-by-step explanation:
We need to find the Equation of the line parallel to the given equation of line . The given equation of the line is ,

<u>Slope </u><u>Intercept</u><u> Form</u><u> </u><u>:</u><u>-</u><u> </u>

where ,
- m is slope
- c is y intercept .
Therefore , the Slope of the line is 3 . Let the parallel line passes through ( 3,3) . We know that the parallel lines have same slope . Therefore the slope of the parallel line will also be 3 .
<u>Using</u><u> point</u><u> slope</u><u> form</u><u> </u><u>:</u><u>-</u><u> </u>

Answer:
E. 55 hours.
Step by step:
Multiple $15x40, equals $600
Subtract $600 from $937.50, equals $337.50
50% more over 40 hours is $22.50
Divide $337.50 by $22.50, equals 15
Add 15 to 40, equals 45
So she worked 55 hours to get paid $937.50
First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)
To find the zeros, you set the equation equal to 0 and solve for x
x^3+2x^2-8x=0
x(x^2+2x-8)=0
x(x+4)(x-2)=0
x=0 x=-4 x=2
So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)
And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.
Plugging in a -5 gets us -35
-1 gets us 9
1 gets us -5
3 gets us 21
So now you know end behavior, zeroes, and signs of intervals
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