Center (-1, 3) and tangent to the line y=2

Step-by-step explanation:

Standard form of the equation of a circle:  (x−h)2+(y−k)2=r2  

Where (h,k) is the center of the circle and r is the radius.

The center is given, just need to find the radius. A tangent line is given, and the radius drawn to the tangent point is perpendicular to the tangent line. Since the tangent line is horizontal the radius is vertical and the length can be counted. (If the tangent line was not horizontal or vertical, then a different method would be used (distance formula).) In this case the radius is 1. Thus the equation of the circle is:

(x+1)2+(y−3)2=1

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d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;