Answer:
Step-by-step explanation:
<u>The full question:</u>
<em>"A committee has eleven members. there are 3 members that currently serve as the boards chairman, ranking members, and treasurer. each member is equally likely to serve in any of the positions. Three members are randomly selected and assigned to be the new chairman, ranking member, and treasurer. What is the probability of randomly selecting the three members who currently hold the positions of chairman, ranking member, and treasurer and reassigning them to their current positions?"</em>
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The permutation of choosing 3 members from a group of 11 would be:
P(n,r) = 
Where n would be the total [in this case n is 11] & r would be 3
Which is:
P(11,3) = 
So there are total of 990 possible way and there is ONLY ONE WAY for them to be reassigned. Hence the probability would be:
1/990
3^(-2) = 1/(3^2) = 1/(3*3) = 1/9
The rule used here is x^(-y) = 1/(x^y) to make the exponent positive.
3^2 turns into 3*3 because the exponent 2 tells us how many copies of the base '3' to multiply out.
Answer:
2.7 in²
Step-by-step explanation:
similar triangles have the same angles, and all side lengths (or other distances) of one triangle have the same scaling factor to the side lengths of the other triangle.
so, we know the relation between the 2 baselines is 2/3, as this is the factor to turn the baseline of the large triangle into the baseline of the smaller triangle.
in other words
EF = BC × 2/3
2 = 3 × 2/3
correct
how do we calculate the area of a triangle ?
Area = baseline × height / 2
from BAC we know
Area = 6
baseline = 3
height = ?
6 = 3 × height / 2
12 = 3 × height
height = 4
aha !
now, EDF has a height too that we need to calculate is Area. and this height has the same scaling factor compared to the larger triangle as the side lengths : 2/3
so, for EDF we know
Area = ?
baseline = 2
height = 4 × 2/3 = 8/3
therefore, the area is
Area = (2 × 8/3) / 2 = (16/3) / 2 = 8/3 = 2.66666... ≈ 2.7
the shirt answer would be :
we know from the 2 baselines that the scaling factor for each distance is 2/3.
for the area we need to multiply 2 distances, so that means we have to multiply both by 2/3. and so on the formula for the area we have to use 2/3 × 2/3.
2/3 × 2/3 = 4/9
=>
Area small = Area large × 4/9 = 6 × 4/9 = 24/9 = 8/3 ≈ 2.7
