The expression 8x2 − 64x + 720 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998. choose the equivalent expression that is most useful for finding the year where the population was at a minimum.

Step-by-step explanation:

we have

The expression  

This is a vertical parabola open upward

The vertex is a minimum

Convert the expression in vertex form

Factor the leading coefficient

Complete the square

Rewrite as perfect squares

The vertex is the point (4,592)

That means -----> 4 years since 1998 the population has a minimum

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;