3. Si al doble de un número se le resta su mitad resulta 30. ¿Cuál es el número? Plantear ecuación y resolverla
1 answer:
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Answer:
The coordinates of the centroid are (0, 5)
Step-by-step explanation:
The coordinates of the centroid of a triangle whose vertices (x1, y1), (x2, y2), and (x3, y3) are ( ,
)
In Δ ABC
∵ A = (-20, 0), B = (0, 15), C = (20, 0)
∴ x1 = -20, x2 = 0, x3 = 20
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ( ,
) = (
,
) = (0, 5)
∴ The coordinates of the centroid of Δ ABC are (0, 5)
In Δ DBE
∵ D = (-15, 0), B = (0, 15), E = (15, 0)
∴ x1 = -15, x2 = 0, x3 = 15
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ( ,
) = (
,
) = (0, 5)
∴ The coordinates of the centroid of Δ DBE are (0, 5)
In Δ FBG
∵ F = (-5, 0), B = (0, 15), G = (5, 0)
∴ x1 = -5, x2 = 0, x3 = 5
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ( ,
) = (
,
) = (0, 5)
∴ The coordinates of the centroid of Δ FBG are (0, 5)
∵ The three triangles are symmetric about the y-axis
→ That means they have the same centroid and it lies on the y-axis
∴ The coordinates of the centroid are (0, 5)
Answer:
a. 4.05 b. 3.84 c. 1.2475 and 1.1344 d. 1.1169 and 1.0651 e. We can say that the overall job satistaction of senior executives and middle managers is about 4; however, there is more variability in the job satisfaction for senior executives than in the job satisfaction for middle managers.
Step-by-step explanation:
a. (1)(0.05)+(2)(0.09)+(3)(0.03)+(4)(0.42)+(5)(0.41) = 4.05
b. (1)(0.04)+(2)(0.1)+(3)(0.12)+(4)(0.46)+(5)(0.28) = 3.84
c. We compute the variances as follow: = 1.2475 and
= 1.1344
d. The standard deviation is the squared root of the variance, therefore, we have and
e. The expected value of the job satisfaction score for senior executives is very similar to the job satisfaction score for middle managers. We can say that the overall job satistaction of senior executives and middle managers is about 4; however, there is more variability in the job satisfaction for senior executives than in the job satisfaction for middle managers.