Scientists researching the effect of dietary supplements such as multivitamins and supplements of folic acid, magnesium or zinc on the health of elderly women followed 38,772 women, whose average age was 62 at the start of the study, over a period of 19 years and recorded the death rates of those who did and did not use dietary supplements. the researchers found that women using supplements were more likely than women who did not to have died during that period. write the hypotheses for testing if the proportion of women elderly women who use dietary supplements is different than those who do not.

Null hypothesis :

Alternative hypothesis :

Step-by-step explanation:

Let be the proportion of women using supplements and be the proportion of women who did not to have died during that period .

Then the set of hypothesis for testing if the proportion of women elderly women who use dietary supplements is different than those who do not will be :-

Null hypothesis :     [∵ it takes equality sign]

Alternative hypothesis :    [∵ it takes ≠ sign to show difference]

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

step-by-step explanation:

in which figure is point g a centroid