x^2 + y^2 - 10y + (-85) is equation of the circle with center (0, -5) containing the point (-√109,-6).
How do you find the equation of a circle?To find the equation of a circle with a given center and containing a given point, we can use the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) is the center of the circle and (x2, y2) is the point on the circle. In this case, the center of the circle is (0, -5) and the point on the circle is (-√109, -6). Plugging these values into the distance formula, we get:
d = √((-√109 - 0)^2 + (-6 - (-5))^2)
d = √((-√109)^2 + (-1)^2)
d = √(109 + 1)
d = √110
Since the point (-√109, -6) is on the circle, the distance from the center of the circle to this point is the radius of the circle. Therefore, the radius of the circle is √110.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (0, -5) and the radius is √110, so the equation of the circle is:
(x - 0)^2 + (y - (-5))^2 = (√110)^2
x^2 + y^2 - 10y + 25 = 110
x^2 + y^2 - 10y + (-85) = 0
This is the equation of the circle with center (0, -5) and containing the point (-√109, -6).
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The box plots summarize the attendance for the spring musical and the fall musical. Each musical was performed for six evenings.
The cost of boring a tube well 600 meter deep is as follows 25 paisa for the first metre and an additional 4paisa for every subsequent meter find the cost of boring a 500th meter long
A recent article in Business Week listed the "Best Small Companies." We are interested in the current results of the companies' sales and earnings. A random sample of 8 companies was selected and the sales and earnings, in millions of dollars, are reported below. Sales ($million) 89.2 18.6 18.2 71.7 58.6 46.8 17.5 11.9 Earnings ($million) 4.9 4.4 1.3 8 6.6 4.1 2.6 1.7 Let sales be the independent variable and earnings be the dependent variable. (i) Determine the estimated regression equation and comment on the coefficient of X. (ii) For a small company with $50.0 million in sales, estimate the earnings. (iii) Calculate the standard error of estimate and comment on it. (iv) Find the coefficient of determination and interpret the result.
Answer:
(i) The estimated regression equation is;
[tex]\hat y[/tex] ≈ 1.6896 + 0.0604·X
The coefficient of 'X' indicates that [tex]\hat y[/tex] increase by a multiple of 0.0604 for each million dollar increase in sales, X
(ii) The estimated earnings for the company is approximately $4.7096 million
(iii) The standard error of estimate is approximately 29.34
The high standard error of estimate indicates that individual mean do not accurately represent the population mean
(iv) The coefficient of determination is approximately 0.57925
The coefficient of determination indicates that the probability of the coordinate of a new point of data to be located on the line is 0.57925
Step-by-step explanation:
The given data is presented as follows;
[tex]\begin{array}{ccc}Sales \ (\$million)&&Earning \ (\$million) \\89.2&&4.9\\18.6&&4.4\\18.2&&1.3\\71.7&&8\\58.6&&6.6\\46.8&&4.1\\17.5&&2.6\\11.9&&1.7\end{array}[/tex]
(i) From the data, we have;
The regression equation can be presented as follows;
[tex]\hat y[/tex] = b₀ + b₁·x
Where;
b₁ = The slope given as follows;
[tex]b_1 = \dfrac{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}{\Sigma(x_i - \overline x)^2}[/tex]
b₀ = [tex]\overline y[/tex] - b₁·[tex]\overline x[/tex]
From the data, we have;
[tex]{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}[/tex] = 364.05
[tex]\Sigma(x_i - \overline x)^2}[/tex] = 6,027.259
[tex]\overline y[/tex] = 4.2
[tex]\overline x[/tex] = 41.5625
∴ b₁ = 364.05/6,027.259 ≈ 0.06040059005
b₀ = 4.2 - 0.06040059005 × 41.5625 ≈ 1.68960047605 ≈ 1.69
Therefore, we have the regression equation as follows;
[tex]\hat y[/tex] ≈ 1.6896 + 0.0604·X
The coefficient of 'X' indicates that the earnings increase by a multiple of 0.0604 for each million dollar increase in sales
(ii) For the small company, we have;
X = $50.0 million, therefore, we get;
[tex]\hat y[/tex] = 1.6896 + 0.0604 × 50 = 4.7096
The estimated earnings for the company, [tex]\hat y[/tex] = 4.7096 million
(iii) The standard error of estimate, σ, is given by the following formula;
[tex]\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{n - 1}}[/tex]
Where;
n = The sample size
Therefore, we have;
[tex]\sigma =\sqrt{\dfrac{6,027.259 }{8 - 1}} \approx 29.34[/tex]
The standard error of estimate, σ ≈ 29.34
The high standard error of estimate indicates that it is very unlikely that a given mean value within the data is a representation of the true population mean
(iv) The coefficient of determination (R Square) is given as follows;
[tex]R^2 = \dfrac{SSR}{SST}[/tex]
Where;
SSR = The Sum of Squared Regression ≈ 21.9884
SST = The total variation in the sample ≈ 37.96
Therefore, R² ≈ 21.9884/37.96 ≈ 0.57925
The coefficient of determination, R² ≈ 0.57925.
Therefore, by the coefficient of determination, the likelihood of a new introduced data point to located on the line is 0.57925
8 squared + B squared = 10 squared
Right triangle Pythagorean theorem
Answer:
6
Step-by-step explanation:
It's 6. The Pythagorean Theorem details how to find the length of a right triangle's hypotenuse.
The equation is a² + b² = c²
C is the length of the hypotenuse. The side lengths you have are a leg as 8 and hypotenuse as 10. By substituting these values into the equation, we get 8² + b² = 10²
Therefore, 64 + b² =100
So b² = 36
By square rooting both sides we finally reach the answer b=6.
Hope I helped!! (p.s. maybe brainliest)
40 points for this answer thank you
help me find the perimeter please:)
Answer:
79.2 cm
Step-by-step explanation:
Add up all the lengths of all of the sides of the figure:
16.2 + 7.5 + 7.5 + 18 + 18 + 12 = 79.2
Answer:
79.2 m
Step-by-step explanation:
Well since all the units are the same and you have already labeled the missing/ congruent sides. Just add up all the sides and you’d end up with 79.2
HELPPPP ME NOW PLS LLS
Answer:
Angle one is 107 degrees and angle 2 is 83 degrees
Step-by-step explanation:
HELP!!! Use the properties of exponents to simplify the expression:
Find the area of the figure. Round your answer to the nearest tenth.
Answer:
18.0
Step-by-step explanation:
use distributive property to rewrite the expression 3x(x+4)
Answer:
3x^2 + 12x
Step-by-step explanation:
3x(x +4)
3x^2 + 12x
- Multiply 3x * x = 3x^2
- Multiply 3x * 4 = 12x
Which Gives You 3x^2 + 12x
Which statement is true about the equation (x – 4)(x + 2) = 16? O The equation x - 4 = 16 can be used to solve for a solution of the given equation. O The standard form of the equation is x2 - 2x - 8 = 0. O The factored form of the equation is (x + 4)(x - 6) = 0. O One solution of the equation is x = -6. vity
Answer:
The factored form of the equation is (x + 4)(x - 6) = 0
Step-by-step explanation:
(x - 4)(x + 2) = 16
[tex]x^{2} -2x - 8 = 16[/tex]
[tex]x^{2} -2x - 24[/tex] = 0
(x - 6)(x + 4) = 0
x = 6 or x = -4
Jacob sells homemade skateboard decks for a profit of $27 per deck. He is considering switching to a new type of material that will increase his profit, as expressed by the function y = 32x, where x is the number sold and y is the amount of profit.
How many more dollars will Jacob earn on each skateboard deck if he switches to the new material? Explain how you found your answer. (5 points)
The mulraneys hired a contractor to build an addition to their home. The contractor proposed a rectangular room with a perimeter of 50 feet. The mulraneys asked the contractor to change the perimeter to 60 feet by increasing both he length and the width by the same distance. By how many feet did the mulranys ask the contractor to increase the length of the room?
The volume of a cylinder is 8T cubic centimeters. The
radius and the height are equal. What is radius of the
cylinder? Explain how you know.
True or false.
A counter-clockwise turn of 270° will land you at the same location as a 90° clockwise turn.
Hmmmmmskksksksksksjsjsjdj
Answer:
Hmmm
Step-by-step explanation:
I don’t have any of the stuff pls help
Answer:
so 6/10 prefered ebooks pretty much and 1/10 didn't have a preference the other 3/10 liked traditional books you should be able to do the rest after that
HELP FOR 7 AND 8 Pleaseeeee
Can someone help asap
Please help me name the parts of the circle
Answer:
radius is gf diametor is ce chord is Ab and secant is ge tangent is dc
Which is the simplified form of p⁰?
O p
O 1/p
O 0
O 1
Answer:
It is p = 1
Step-by-step explanation:
p⁰=1 because it is basically saying and when simplifying fractional exponents we can flip the bottom exponent up to the top if we change the sign, leaving us with : (p⁵-p⁵)=p⁰
HI can you guys please help with these
AnswerЯ могу помочь вам, но я не знаю, как мне так жаль, но вы можете найти ответ, если вы умны и в каком вы классе буквально вы, люди, такие тупыеЯ могу помочь вам, но я не знаю, как мне так жаль, но вы можете найти ответ, если вы умны и в каком вы классе буквально вы, люди, такие тупыеЯ могу помочь вам, но я не знаю, как мне так жаль, но вы можете найти ответ, если вы умны и в каком вы классе буквально вы, люди, такие тупые
Step-by-step explanation:
2x^2-5x+1=4 factor step by step please
Answer in screen shot below
50 points plzz help Combine the radicals .
Answer:
D) [tex]-2\sqrt{3}[/tex]
Step-by-step explanation:
[tex]5\sqrt{27} =15\sqrt{3} \\\\15\sqrt{3}-17\sqrt{3} =-2\sqrt{3}[/tex]
Write an equation of the line that passes through the given points.
(-2,8) and (1, -1)
/Answer:
Short Answer Type:
P1 - (-2,8)
P2 - (1,1)
Slope: (1 - 8) / (1 + 2)
=> -7/3
Therefore: 1 = -7/3 + c
=> 10/3 = c
Therefore equation: y = -7x/3 + 10/3
Please help me to do this question with steps
Answer:
x = 71°
Step-by-step explanation:
Segments of tangents from the same external point are congruent, that is
AT = BT
Then Δ ABT is isosceles with base angles congruent , so
x = [tex]\frac{180-38}{2}[/tex] = [tex]\frac{142}{2}[/tex] = 71°
I NEED HELP RN PLSSS!!! (check whole picture) i’ll give brainiest if u don’t give a link just pls help immediately!!!)
Answer:
So I would say your answer is..............A
Step-by-step explanation:
For most places, global warming will result in more frequent hot days and fewer cool days, with the greatest warming occurring over land. Longer, more intense heat waves will become more common. Storms, floods, and droughts will generally be more severe as precipitation patterns change
Also, A is correct because lets say you put an ice cube in the sun...okay well if it keeps getting hotter and hotter multiply ice cubes into ice caps. Well same thing will happen. It will melt causeing water from the ice caps. Which will result into more water. Which will cause water to go above sea level!
Hope this helps!!!
When Bruce won a contest, he got a bronze medal with a radius
of 5 centimeters. What is the medal's diameter?
Answer:
10 centimeters
Step-by-step explanation:
diameter = 2r
r = radius
diameter = 2(5cm)
diameter = 10 cm
Please help NO LINKS
LINKS=REPORTED
Answer:
They didn't multiply the whole equation by 2 or -3 and only the first part
Answer:
when the first equation was multiplied by 2, the -22 did not get multiplied by 2
when the second equation was multiplied by -3, the -14 did not get multiplied by -3
the result is that x should be = 2
Step-by-step explanation:
Figure AAA maps to figure BBB with a scale factor of 0.750.750, point, 75.
Answer:
7.5
Step-by-step explanation:
x=10*0.75 = 7.5
note that b is smaller than a