A polling agency reported that the proportion of 12th grade students who are engaged is 0.34. Engagement is defined as​ students' involvement and enthusiasm with school. The superintendent of one high school district believes the engagement of her students is higher than the proportion reported. She randomly surveys 90 of the 3600 students in the district and finds that 38 reported being engaged in school. Complete parts​ (a) through​ (e) below. ​(a) What type of variable is​ "engaged"? The variable is qualitative. ​(b) What is the sample proportion of students in this high school district who are​ engaged? p=0.42220.4222 ​(Round to four decimal places as​ needed.) ​(c) Verify that the distribution of the sample proportion is approximately normal. The sample​ size, n=9090​, is less than ​5% of the population​ size, or 0.05N=180180. ​(Type integers or decimals. Do not​ round.) For this​ sample, np1−p=nothing less than or equals≤ 10.

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.

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,