Answer: (x - 2)² + (y - 14)² = 1
Step-by-step explanation:
<u>Concept:</u>
Here, we need to know the idea of the circle formula.
Circle formula: (x - h)² + (y - k)² = r²
Center = (h, k)
Radius = r
If you are still confused, please refer to the attachment below for a graphical explanation.
<u>Solve:</u>
Center = (2, 14)
Radius = 1
<em>Given formula</em>
(x - h)² + (y - k)² = r²
<em>Substitute the value into the formula</em>
(x - 2)² + (y - 14)² = (1)²
<em>Simplify</em>
(x - 2)² + (y - 14)² = 1
Hope this helps!! :)
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Answer: There is 162 ml of first brand and 108 ml of second brand.
Step-by-step explanation:
Since we have given that
Percentage of vinegar that the first brand contains = 7%
Percentage of vinegar that the second brand contains = 12%
Percentage of vinegar in mixture = 9%
Total amount of dressing = 270 ml
We will use "Mixture and Allegation":
First brand Second brand
7% 12%
9%
--------------------------------------------------------
12%-9% : 9%-7%
3% : 2%
So, ratio of first brand to second brand in a mixture is 3:2.
So, Amount of first brand she should use is given by

Amount of second brand she should use is given by

Hence, there is 162 ml of first brand and 108 ml of second brand.
Answer:
Answer: The mean increases by 3
Step-by-step explanation:
The original data set is
{50, 76, 78, 79, 79, 80, 81, 82, 82, 83}
The outlier is 50 because it is not near the group of values from 76 to 83 which is where the main cluster is.
The original mean is M = (50+76+78+79+79+80+81+82+82+83)/10 = 77
If we take out the outlier 50, the new mean is N = (76+78+79+79+80+81+82+82+83)/9 = 80
So in summary so far
old mean = M = 77
new mean = N = 80
The difference in values is N-M = 80-77 = 3
So that's why the mean increases by 3
Call the number : x
(1/3)x + 5 = x-6
=> (1/3)x + 5 - (x-6) = 0
=> (1/3)x + 5 - x + 6 = 0
Group (1/3)x with -x, 5 with 6
=> [(1/3)x - x] + (5+6) = 0
=> (-2/3)x + 11 = 0
=> (-2/3)x = -11
=> x = -11 : (-2/3) = 33/2.
Recheck : 1/3 x 33/2 + 5 = 33/6 + 5 = 63/6 = 21/2
33/2 - 21/2 = 12/2 = 6 (21/2 is 6 less than 33/2, satisfied.)