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What is the vertex of the absolute value function defined by f(x) = 1x + 21 +4?
O (2.4)
O (-2,-4)
O (-24)
O 12,-4)

  (-2, 4)

Step-by-step explanation:

The vertex of the absolute value function ...

  f(x) = |x|

is located at (x, y) = (0, 0).

Translating the function h units horizontally and k units vertically makes the function ...

  f(x -h) +k

and moves the vertex to (x, y) = (h, k).

Comparing the translated function to the one you're given, you see that ...

  h = -2, k = +4

That means the vertex is located at ...

  (h, k) = (-2, 4) . . . . matches the 3rd choice

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;

0.85% : )

step-by-step explanation: