A soft drink machine is regulated so that the amount of drink it dispenses follows a normal distribution with a known standard deviation, and it is believed that standard deviation of the drinks dispensed is 20 milliliters. However a random sample of 30 drinks from the machine produced an average value of 373 milliliters and standard deviation of 23.4 milliliters; therefore, based on the results from sample data, there is concern that population standard deviation might be higher than what is believed. Required:
Check the validity of the concern by determining a 95% confidence interval for the standard deviation of all drinks dispensed by this machine.

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Ответ:

kaseyvn03

24.02.2021

Mathematics

Option A is correct

(–6, –36)

Step-by-step explanation:

A quadratic equation is in the form of y=ax^2+bx+c ,....[1] then the axis of symmetry is given by:

$x = -\frac{b}{2a}$

Vertex of the function is given by:

$\text{vertex} = (-\frac{b}{2a}, f(-\frac{b}{2a}))$

As per the statement:

Given the function:

y=f(x)=x^2+12x ....[2]

Compare this with equation [1] we have;

a = 1 and b = 12

then;

$x = -\frac{12}{2(1)}$

⇒ $x = -\frac{12}{2}=-6$

⇒x = -6

Substitute the value of x in [2] we have;

f(-6) = (-6)^2+12(-6) = 36-72 = -36

⇒f(-6) = -36

⇒Vertex = (-6, -36)

Therefore, the vertex of the function f(x) is, (–6, –36)

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