An activity has an optimistic time estimate of 25 days, a most likely estimate of 29 days, and a pessimistic estimate of 34 days. What is the expected duration of the activity

The expected duration of the activity is 29 days and 4 hours.

Step-by-step explanation:

Step 1:

The optimistic time, = 25 days,

The most likely estimate, = 29 days.

The pessimistic time, = 34 days.

According to PERT, the expected duration of the activity,

Step 2:

By substituting the given values, we get

0.1666 days =

29.1666 days approximately equal 29 days and 4 hours.

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.