The first year you obtain your Professional Engineer seal, you design and observe construction of 3 small dams, each of which is in a different area of the country. Each of these dams is designed to pass the 25-year storm without overtopping, since they are relatively small and no loss of life or damage to property is likely if they do fail. After that first year, you never design another dam for the rest of your career since you move into management. What is the probability that a) none of the dams will fail over the 35-year period and b) at least one of those 3 dams will be overtopped in your anticipated 35-year career?

  q

step-by-step explanation:

each line from a vertex to the midpoint of the opposite side is called a median. the point where the medians intersect, point q, is the centroid.

the centroid of δabc is point q.

7

step-by-step explanation:

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4