At brighton middle school, mr. yule asked 50 randomly selected students from each grade level about their favorite subject, and 12 chose science. he used this data to draw the inference that about 25% of middle school students will indicate science is their favorite subject. if there are 200 students altogether, did he make a reasonable inference?

Yes, he made a reasonable inference by saying about 25 percent of students choose the science.

Step-by-step explanation:

Given that

Number of students for survey = 50

Number of students who choose science = 12

Now

Percentage of student who choose science =

Percentage of student who choose science =

Percentage of student who choose science = 24 %

Now as Mr. Yule said "about 25" percent of students choose the science it can be treated as reasonable approximation.

Now if the number of students in survey become 200, then we can expect 12 out of every 50 students would choose the science. So, in total 48 students would choose the science.

Now lets calculate the percentage of students who choose science.

Percentage of student who choose science =

Percentage of student who choose science =

Percentage of student who choose science = 24 %

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.

step-by-step explanation:

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