The mean is μ = 15.2 and the standard deviation is σ = 0.9. find the probability that x is greater than 17.
2 answers:
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Step-by-step explanation:
Let a, b, c be the measures of the interior angles and x, y, z be the measures of the exterior angles of the triangle. Where x and adjacent to a, y is adjacent to b and z is adjacent to c.
By interior angle sum postulate of a triangle:
a + b + c = 180°... (1)
Therefore, by remote interior angle theorem:
x = b + c.... (2)
y = a + c..... (3)
z = a + b.... (4)
Adding equations (2), (3) & (4)
x + y + z = b + c + a + c + a + b
x + y + z = 2a + 2b + 2c
x + y + z = 2(a + b + c)... (5)
From equations (1) & (5)
Thus, the sum of exterior angles so formed is equal to four right angles.
Proved.
The spider's movement is an illustration of a parabola.
- The equation of a parabola is:
- The focus of a parabola is: (40,-30)
- The axis of symmetry is:
- The directrix is:
<u>(a) The equation</u>
The spider passes through the origin.
So, we have:
The spider jumps to a maximum height of 10mm, midway 80mm.
So, the vertex is:
The equation of a parabola is:
So, we have:
Subtract 10 from both sides
Solve for a
Substitute and
in
<u>(b) The focus, directrix and the axis of symmetry</u>
The focus of a parabola is:
Where:
So, we have:
So, we have:
The axis of symmetry is:
So, we have:
The directrix is:
Read more about parabolas at: