A researcher is interested in the decrease in mean bone fractures in postmenopausal women treated with vitamin and calcium supplementation. Assuming that the population under investigation has a standard deviation of 3 bone fractures, and that the goal margin of error of the estimate is plus or minus 0.4 fractures. How many women should be sampled to attain an estimate with 95% confidence

217 women should be sampled to attain an estimate with 95% confidence.

Step-by-step explanation:

Let s be the prior population standard deviation.

Formula to find the sample size: , E=Margin of error

Given: s= 3

E= 0.4

Critical zvalue for 95% = 1.96

So,

Hence, 217 women should be sampled to attain an estimate with 95% confidence.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet