A. The slope is 55, representing the trip fee.
1 answer:
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Answer:
14.2cm
Step-by-step explanation:
The diagram representing the circle and its attributes has been attached to this response.
<em>As shown in the diagram;</em>
The circle is centered at o,
The length of radius OL = 6cm
The length of the arc LM = 6.3cm
The angle MON = 75°
The angle LOM = θ
<em>Remember that;</em>
The length, L, of an arc is given by;
L = (θ / 360) x (2πr) -------------(i)
Where;
θ is the angle subtended by the arc
r = radius of the circle.
Using the formula in equation (i), let's calculate the angle θ subtended by arc LM as follows;
L = (θ / 360) x (2πr)
Where;
L = length of arc LM = 6.3cm
r = radius of the circle = length of radius OL = 6cm
<em>Substitute these values into the equation to get;</em>
6.3 = (θ / 360) x (2 x π x 6)
6.3 = (θ / 360) x (12 x π)
6.3 = (θ / 30) x (π) [Take π = 22/7]
6.3 = (θ / 30) x (22 / 7)
θ =
θ = 60.14°
Therefore, the angle subtended by arc LM is 60.14°
Now, from the diagram,
The angle subtended by arc LMN is;
θ + 75° = 60.14° + 75° = 135.14°
Let's now calculate the length of arc LMN using the same equation (i)
L = (θ / 360) x (2πr)
Where;
L = length of arc LMN
θ = angle subtended by LMN = 135.14°
r = radius of the circle = length of radius OL = 6cm
<em>Substitute these values into the equation;</em>
L = (135.14° / 360°) x (2 x π x 6) [Take π = 22/7]
L = 14.15cm
Therefore, the length of arc LMN is 14.2cm to the nearest tenth.
Answer:
The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.
Step-by-step explanation:
Mean SAT scores = 1026
Standard Deviation = 209
Mean ACT score = 20.8
Standard Deviation = 4.8
We are given SAT and ACT scores of a student and we have to compare them. We cannot compare them directly so we have to Normalize them i.e. convert them into such a form that we can compare the numbers in a meaningful manner. The best way out is to convert both the values into their equivalent z-scores and then do the comparison. Comparison of equivalent z-scores will tell us which score is higher and which is lower.
The formula to calculate the z-score is:
Here, μ is the mean and σ is the standard deviation. x is the value we want to convert to z score.
z-score for junior scoring 860 in SAT exam will be:
z-score for junior scoring 16 in ACT exam will be:
The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.
Answer:
Mr. Chang will have 15714.90 dollars.
Step-by-step explanation:
p = 650
r =
Number of periods or n =
Future value formula is :
Putting the values in formula we get;
= $15714.90
Hence, Mr. Chang will have 15714.90 dollars.