Triangle angle sum theorem and exterior angle theorem

5.

7.

Step-by-step explanation:

5.

By triangle angle sum theorem

Addition property of integers

By using subtraction property of equality

By using exterior angle theorem

By using triangle angle sum theorem

Addition property of integers

Using subtraction property of equality

7.We are given that

BC bisects angle ACD

Therefore,

By using triangle angle sum theorem

Substitute the value

By addition property of integers

By using subtraction property of equality

By using triangle angle sum property

Substitute the values

Using addition property of integers

Using subtraction property of equality

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;