Answer with Step-by-step explanation:
Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors
Mean=(Sum of all observations)/(Total number of observations)
=(36+14+21+39+11+2)/6
= 123/6
= 20.5
Standard deviation is the square root of mean of squares of deviation around mean
Deviation around mean:
36-20.5, 14-20.5, 21-20.5, 39-20.5, 11-20.5, and 2-20.5
15.5,-6.5,0.5,18.5,-9.5 and -18.5
Square of deviations:
240.25,42.25,0.25,342.25,90.25 and 342.25
Mean of square of deviations
=(240.25+42.25+0.25+342.25+90.25+342.25)/6
=176.25
square root of mean of deviations=
Hence, Standard deviation=13.28
and Mean=20.5
Answer:
(x -6)^2 +(y -3)^2 = 2
Step-by-step explanation:
The midpoint (C) is the center of the circle:
C = ((5, 4) +(7, 2))/2 = ((5+7)/2, (4+2)/2) = (6, 3)
A circle with center (h, k) that goes through point (a, b) can be written as ...
(x -h)^2 +(y -k) ^2 = (a -h)^2 +(b -k)^2
Using the values for this problem, we get ...
(x -6)^2 +(y -3)^2 = (5 -6)^2 +(4 -3)^2
(x -6)^2 +(y -3)^2 = 2
Answer:
The correct option is C
Step-by-step explanation:
I attached an image that forms the complete question.
The converse Pythagorean theorem states that, "If the square of the longest side of a triangle is equal to the square of the other two sides, then the triangle is a right triangle."
That is if c is the longest side of a triangle and then a and b are the other sides, then if,
c² = a² + b², the triangle is a right triangle.
Looking at all the options, option C fits the theorem well. Because
3² + 4² = 5² implies the triangle is a right triangle and the converse theorem is established.
The option D also looks close, but it's not correct because you can just draw any two sides and put the right angle in between them. The longest is always the part of the triangle that is opposite to the right angle, 90°. If for instance, you draw 3 and 5 then put the right angle in between them, 4 will take the position of the longest side which is wrong.
Therefore, the correct option is c.
