Which employee's path is the critical path on this activity graph? explain how you know that this employee's path is the critical path.

Jim's path is the critical path on this activity graph.

Step-by-step explanation:

Critical Path:

Critical path is the the longest path in the project task paths. It shows the least amount of time in which project can be completed. It can be find by looking at the longest path in the network diagram of the project; not in term of nodes or activities instead in term of days.

In given case:

Path 1 Bill task's total duration= 6 days

Path 2 Jim's task's total duration= 17 days

Path 3 Betty task's total duration= 7 days

Path 4 Cynthia task's total duration= 14 days

Hence the longest path i.e. critical path is of Jim's activity path !

answer is the third choice:

3x^5+4x^4+x^3+2x^2-10x-7=0

step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.