In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true, . a. a Type II error has been committed b. either a Type I or Type II error has been committed c. the correct decision has been made d. a Type I error has been committed

(c)

Step-by-step explanation:

Given : In a hypothesis testing the null hypothesis has been rejected when the alternative hypothesis has been true.

Find : to find that the given decision is create type I error , type II error or right decision has been taken

Step by step :

In hypothesis testing there are 2 types of error.

(1)Type I error :- if the null hypothesis is rejected when it is true, is known has Type I error .

(2)Type II error:- if the null hypothesis is accepted when alternative hypothesis is true, is known as type II error.

Since here null hypothesis has been rejected when alternative hypothesis has been true,i.e., the correct decision has been made

Hence option (c) is correct.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

step-by-step explanation:

once you graph it hit 2nd (the blue button) and graph

that takes you to a table of coordinates

on the left is x coordinates and on the right is y coordinates and an empty box

(you may have to scroll up/down in order to get ( x, 0)