If the project is finished within 26 weeks of its start, the project manager will receive a bonus of $1,000; and if the project
is finished within 27 weeks of its start, the bonus will be $500. Find the probability of each bonus. (Round Mean, Standard Deviation, z-value to 2 decimal places and Probability to 4 decimal places.) Path Mean Std. Dev. a-d-e-h 24.33 1.35 a-f-g 15.50 1.26 b-i-j-k 14.83 1.02 c-m-n-o 26.17 1.66 Probability ($1,000) .4099 Probability ($500)
1 answer:
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Answer:
Tan(b°) = 3/4 = three fourths (C)
Step-by-step explanation:
Triangle JKL is a right angled triangle in which angle K is a right angle and angle L= b°
We would apply SOHCAHTOA from trigonometry to determine the value for each sides.
For ∆JKL
Sin(b°) = opposite/hypotenuse
Sin(b°) = 3/5
Cos(b°) = adjacent/hypotenuse
Cos(b°) = 4/5
Tan(b°) = 3/4
From the above we know the value of each sides of ∆JKL
Find attached the diagram of the above triangle (1)
∆JKL is dilated by a scale factor = 2
Meaning we would multiply each sides of ∆JKL by 2. The values of the new triangle become:
Opposite = 2(3) = 6
Adjacent = 2(4) = 8
Hypotenuse = 2(5) = 10
To find tan(b°) of the new triangle, we would apply tangent ratio
Tan(b°) = opposite/adjacent
Tan(b°) = 6/8
Tan(b°) = 3/4
Find attached the diagram for the new triangle (2)
Diagram 3 shows the drawing of both triangles together.
From the above, we can see the angle doesn't change when a shape is dilated by a scale factor.
Therefore, tan(b°) = three fourths (C)
Answer:
The lines blue and green are perpendicular
Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)
The formula to calculate the slope between two points is equal to
step 1
Find the slope of the blue line
we have the points
(-1,-3) and (0,3)
substitute
step 2
Find the slope of the red line
we have the points
(3,-3) and (4,2)
substitute
step 3
Find the slope of the green line
we have the points
(-4,-1) and (2,-2)
substitute
step 4
Compare the slopes
Blue line ---->
Red line ----.
Green line --->
so
The slope of the blue line and the green line are opposite reciprocal ( their product is equal to -1)
therefore
The lines blue and green are perpendicular