The average (arithmetic mean) of the measures of angle x, its complementary angle, and its supplementary angle is 80 degrees. what is the measure of the complementary of angle x? (hint: the complementary angle of x can be represented as (90-x))

60°

the mean is the sum of the 3 angles divided by 3

complementary angle = 90 - x

supplementary angle = 180 - x

sum of angles = x + 90 - x + 180 - x = 270 - x

Hence

mean = = 80 ( multiply both sides by 3 )

270 - x = 240 ( subtract 270 from both sides )

- x = - 30 ( multiply both sides by - 1 )

x = 30

complement of x = 90 - 30 = 60°

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;

answer: a) 56% women

b)44% men

step-by-step explanation: