So the equation of a circle is (x - h)² + (y - k)² = r² where (h,k) are the coordinates of the center of the circle and r is the radius. The diameter of a circle is a line that goes from one point of the circle to the other through the center of the circle. Well the center would be midway through the diameter so use midpoint formula to find the center which is (h,k) Mid point formula is both given x's added together divided by 2 for h and both y coordinates added together divided by 2 to find k
(10+0)/2
10/2= 5
(12+2)/2
14/2 = 7
so the center of the circle is (5,7) now use distance formula using the center and one of the points to the radius
√((5-10)²+(7-12)²)
√(-5²+ -5²)
√(25 + 25)
√50 is the radius
Now plug all found information into circle equation
(x-5)² + (y-7)² =50 note the end is 50 because the circle equation is radius squared and since the radius is √50, radius² is 50.
Answer is c
Answer:
n=206
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by 
and 
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that 
, we can use as prior estimate of p 0.5, since we don't have any other info provided, and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=206
Answer:
8.94 (Rounded would be 9)
Step-by-step explanation:
By using the Pythagorean Theorem formula,
A^2+B^2 = C^2
You have the hypotenuse (c) = 12
and you have a leg (a) = 8
and you're trying to find another leg (b) = x
In order to find this, you'll have to change up the formula in order to find (B) instead of (C)
B^2 = C^2 - A^2
(B) = (12)^2 - (8)^2
(B) = 144 - 64
(B) = 80
Square root of 80
B = 8.9
Answer:
Answers for 1-126
Step-by-step explanation:
a. x + 8 = 21
-8 -8
x = 13
b. x - 32 = 55
+32. +32
x = 87
c. 3x = 54
÷3. ÷3
x = 18
d. x/5 = 10
×5. ×5
x = 50
Answer for 1-124
1/5 = 2/10 , so 2 of the 10 colors are blue and 3 of the 10 colors are green.
The probability is 5/10 = 1/2
this is all I could do. sorry
