88 points answer pls

Step-by-step explanation:

I'm going to try to format this in the best way possible, but forgive me if it isn't perfect.

Statment: Reason

JK = NK: Given

JA = NA: Definition of a midpoint

Triangle NJK is isosceles: Definition of an isosceles triangle

m<J = m<N: Base angle converse theorem

AK = KA: Reflexive property

m<NKA = m<JKA: The Isosceles Decomposition Theorem (If midpoint, also angle bisector in an isosceles triangle)

m<JAK = m<NAK: The isosceles Decomposition theorem (If midpoint, also altitude in an isosceles triangle)

Triangle JAK = Triangle NAK: SAS, SSS, ASA, and AAS (All the angles and sides were congruent to one another, so you can use every shortcut in this case)

Stuff that isn't required on there:

What we can conclude from this is that in an isosceles triangle, if there is a midpoint from the angle that's not a base angle, then the two triangles it creates are congruent.

Please let me know if you have any questions.

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;

69.64%

step-by-step explanation: