In the diagram shown, m <AOC =124 and OA=10 cm. Which of the following is closest to the length of arc ABC?

(1) 20.6
(2) 21.6
(3) 40.4
(4) 41.2

(2) 21.6

Step-by-step explanation:

The segment OA is the radius of the circle

The arc of the complete circle is equivalent to its perimeter

perimeter = 2*π*radius = 2*π*10 = 62.83 cm

This arc is proportional to 360°. So, for 124°:

360°/124° = 62.83 cm/ x cm

x = 124*62.83/360

x = 21.6 cm

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;