The equation of a circle exists:
, where (h, k) be the center.
The center of the circle exists at (16, 30).
<h3>What is the equation of a circle?</h3>
Let, the equation of a circle exists:
, where (h, k) be the center.
We rewrite the equation and set them equal :


We solve for each coefficient meaning if the term on the LHS contains an x then its coefficient exists exactly as the one on the RHS containing the x or y.
-2hx = -32x
h = -32/-2
⇒ h = 16.
-2ky = -60y
k = -60/-2
⇒ k = 30.
The center of the circle exists at (16, 30).
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Answer:
Yes, there is enough evidence to say the proportions are the same.
Step-by-step explanation:
Null hypothesis: The proportions are the same.
Alternate hypothesis: The proportions are not the same.
Data given:
p1 = 51% = 0.51
n1 = 200
p2 = 48% = 0.48
n2 = 150
pooled proportion (p) = (n1p1 + n2p2) ÷ (n1 + n2) = (200×0.51 + 150×0.48) ÷ (200 + 150) = 174 ÷ 350 = 0.497
Test statistic (z) = (p1 - p2) ÷ sqrt[p(1-p)(1/n1 + 1/n2) = (0.51 - 0.48) ÷ sqrt[0.497(1-0.497)(1/200 + 1/150)] = 0.03 ÷ 0.054 = 0.556
The test is a two-tailed test. At 0.10 significance level the critical values -1.645 and 1.645
Conclusion:
Fail to reject the null hypothesis because the test statistic 0.556 falls within the region bounded by the critical values.
The length and the width of the rectangle are 20 and 14 inches respectively
<h3>How to find the length and width?</h3>
The given parameters are:
Length = 6 + Width
Perimeter = 68 inches
The perimeter of a rectangle is calculated as:
Perimeter = 2 * (Length + Width)
So, we have:
2 * (Length + Width) = 68
Divide both sides by 2
Length + Width = 34
Substitute Length = 6 + Width in Length + Width = 34
6 + Width + Width = 34
Evaluate the like terms
2 * Width = 28
Divide both sides by 2
Width = 14
Substitute Width = 14 in Length = 6 + Width
Length = 6 + 14
Evaluate
Length = 20
Hence, the length and the width of the rectangle are 20 and 14 inches respectively
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I use it as a short way to say "okay" but I don't know how others may use it.
3,059 I don’t really care