A new drug claims to reduce the number of migraines an individual suffers. In a study on the effectiveness of the new drug, 50 subjects were given the new drug and another 50 subjects were given a placebo. At the end of the 6-month study, the group given the new drug reported an average of 1.3 migraines a week. The group given the placebo reported an average of 2.5 migraines a week.

The data from the study are rerandomized 10 times. The difference of the means from rerandomization are

1.2, 3.4, 1.8, 1.3, 1.1, 0.9, 2.5, 0.7, 1.1, and 0.9.

What is the most appropriate conclusion about the new drug to draw from this information?

The new drug appears to reduce the number of migraines since the rerandomized mean differences are close to the mean difference found between the two groups studied.

The new drug does not appear to reduce the number of migraines since the rerandomized mean differences are considerably greater than the mean difference found between the two groups studied.

The new drug appears to reduce the number of migraines since the rerandomized mean differences are considerably less than the mean difference found between the two groups studied.

The new drug does not appear to reduce the number of migraines since the rerandomized mean differences are close to the mean difference found between the two groups studied.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

hope this is what you were asking for!

step-by-step explanation: