If the endpoints of a diameter are (6,3) and (2,1) the midpoint is the center of the circle so:
(x,y)=((6+2)/2, (3+1)/2)=(4,2)
Now we need to find the radius....the diameter is:
d^2=(6-2)^2+(3-1)^2
d^2=16+4
d^2=20 since d=2r, r=d/2, and r^2=d^2/4 so
r^2=5
The standard form of the circle is (x-h)^2+(y-k)^2=r^2 and we know:
(h,k)=(4,2) from earlier so:
(x-4)^2+(y-2)^2=5
Answer:
x = 10
Step-by-step explanation:
A triangle's angles add up to 180 degrees, so 180-90 (the right angle) is 90 degrees. That means that
4x+6+3x+14 = 90. Then we simplify so
7x + 20 = 90. Then we can subtract 20 from each side so
7x = 70. Then, we find that
x = 10.
Answer:
11
Step-by-step explanation:
1.80m + 0.6s = 12.00
[substitute the value of m into the equation]
1.80×(3) + 0.6s = 12
5.4 + 0.6s = 12
[make s the subject of the formula]
0.6s = 12 - 5.4
0.6s = 6.6
[divide both sides of the equation by 0.6]
0.6s / 0.6 = 6.6 / 0.6
s = 11
To prove that 11 is correct
[substitute the value of m and s into the equation]
1.80m + 0.6m = 12.00
1.80×(3) + 0.6×(11) = 12.00
5.4 + 6.6 = 12.00
12.00 = 12.00
Answer:
The 95% confidence interval of the mean time it took a person to find their dream home is between 5.64 months and 6.16 months.
Step-by-step explanation:
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of 
.
So it is z with a pvalue of 
, so 
Now, find the margin of error M as such
In which 
is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.26 = 5.64 months
The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.26 = 6.16 months.
The 95% confidence interval of the mean time it took a person to find their dream home is between 5.64 months and 6.16 months.
