Z is centroid of triangle RST. What is RW, if RV=4x+3, WS=5x-1, and VT=2x+9?
1 answer:
Part (a):
We are given that Z is the <span>centroid of triangle RST. This means that Z is the point of intersection of the three medians of the triangle.
In other words:
W is the midpoint of RS
V is the midpoint of RT
We are given that:
RV = 4x + 3 and VT = 2x + 9
Since V is the midpoint, then:
RV = VT
4x + 3 = 2x + 9
4x - 2x = 9 - 3
2x = 6
x = 3
Part (b):
We are given that:
WS = 5x-1
x = 3
Therefore:
WS = 5(3) - 1
WS = 15 - 1 = 14
Part (c):
Since W is the midpoint of RS, therefore RW = WS
We calculated WS = 14
Therefore:
RW = 14
</span>
We are given that Z is the <span>centroid of triangle RST. This means that Z is the point of intersection of the three medians of the triangle.
In other words:
W is the midpoint of RS
V is the midpoint of RT
We are given that:
RV = 4x + 3 and VT = 2x + 9
Since V is the midpoint, then:
RV = VT
4x + 3 = 2x + 9
4x - 2x = 9 - 3
2x = 6
x = 3
Part (b):
We are given that:
WS = 5x-1
x = 3
Therefore:
WS = 5(3) - 1
WS = 15 - 1 = 14
Part (c):
Since W is the midpoint of RS, therefore RW = WS
We calculated WS = 14
Therefore:
RW = 14
</span>
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Answer:
the probability that the woman is taller than the man is 0.1423
Step-by-step explanation:
Given that :
the men's heights are normally distributed with mean 68
standard deviation = 3.1
And
the women's heights are normally distributed with mean 65
standard deviation = 2.8
We are to find the probability that the woman is taller than the man.
For woman now:
mean = 65
standard deviation = 2.8
= 1-P (z , 1.07)
Using z table,
= 1 - 0.8577
= 0.1423
Thus, the probability that the woman is taller than the man is 0.1423