Question 5
Law required: The law required to solve the unknown angles and lengths of the sides is the sine rule.
Explanation: The length of a side and its opposite angle are given.
To find the unknown angle C, use the sine rule for finding sides as illustrated below:
=
Substitute for the known sides and the known angle.
∠ C =
0.5893 = 36.1°
Calculate angle A
∠ A = 180° - (36.1° + 50°) = 93.9°
To calculate the unknown distances use the Sine rule for the unknown sides.
Substitute the known sides and angles
a =
= 16.93 (2 decimal places)
b.
Law required: The law required to solve the unknown angles and lengths of the sides is the cosine rule.
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Explanation: There is no side and its opposite angle that is known.
To find the unknown side b angle C, use the cosine rule for finding sides as illustrated below:
a² = b² + c² - 2bc Cos(A)
In this case, the rule can be represented as: b² = a² + c² - 2bc Cos(B)
Substitute the known sides and angle into the equation.
b² = 12² + 6² - (2 ×12 × 6 × Cos(25°)
b² = 49.49
b = √49.49 = 7.04
To find the angles use the cosine rule for finding the unknown angles
Cos(A) =
To find angle A substitute the known sides into the equation
Cos(A) =
Cos(A) = -0.6926
A =
(-0.6926) = 133.8° (1 decimal place)
To calculate angle C= 180° - (133.8° + 25°)= 21.2°
Question 6
The bar graph represents a bimodal distribution. Two distinct peaks are visible from the graph. The first peak occurs in the 16-25 years age group and the second at 56-65 years.
The 16-25 age group had the most accidents
The graph can be improved by choosing bin sizes that are similar in the different age groups. The selection of class intervals that are similar in size would allow enable making better comparisons since the bin sizes in these age agroups would have a standard interval.
New results.
| 16-25 | 26-38 | 39-45 | 46-55 | 56-65 | 66-75 | 76+ |
|
22 |
30 |
19 |
21 |
17 |
16 |
13 |
The age group that recorded the most accidents is the 26- 38.
The age group with the least number of accidents is the 76+ one.
Question 7
| Mean | Median | Mode | First Quartile | Third Quartile |
|
|
|
84.08824 |
85 |
84 |
79 |
94.5 |
64 |
| ˂ 50% | 50%-59% | 60%-69% | 70%-79% | 80%-89% | 90%-100% | |
| Tally | I | I | I |
|
|
|
| Frequency |
1 |
1 |
1 |
6 |
12 |
13 |
Question 8
Range
Range is the difference between the maximum entry and the minimum entry in a data set. The maximum entry is 304 while the minimum is 250.
Range = 304 – 250 = 54
Variance and Standard Deviation
| Variance | Standard Deviation | |||||
| Xn - mean | (Xn -mean) 2 | ∑ (X 1 - mean) 2 | ||||
| x 1 |
266 |
-14 |
196 |
2328 |
291 |
17.05872211 |
| x 2 |
250 |
-30 |
900 |
|||
| x 3 |
295 |
15 |
225 |
|||
| x 4 |
281 |
1 |
1 |
|||
| x 5 |
304 |
24 |
576 |
|||
| x 6 |
298 |
18 |
324 |
|||
| x 7 |
275 |
-5 |
25 |
|||
| x 8 |
271 |
-9 |
81 |
|||
| Average |
280 |
|||||
| Range |
54 |
