Assume that you have a sample of n 1 equals 8n1=8, with the sample mean upper x overbar 1 equals 42x1=42, and a sample standard deviation of upper s 1 equals 4s1=4, and you have an independent sample of n 2 equals 15n2=15 from another population with a sample mean of upper x overbar 2 equals 34x2=34 and a sample standard deviation of upper s 2 equals 5s2=5.
what assumptions about the two populations are necessary in order to perform thepooled-variance t test for the hypothesis upper h 0 : μ 1 equals μ 2h0: μ1=μ2 against the alternative upper h 1 : μ 1 > μ 2h1: μ1> μ2 and make a statistical decision?

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

where r the answers

step-by-step explanation:

what is the original number? you forgot to add it.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .