Answer: Angle N
Explanation:
For triangle ABC, we refer to the middle angle, Angle B.
For triangle MNP, we refer to its middle angle, Angle N.
Good luck!
Answer: r = 4 sec θ
Explanation: Using: x = r cos θ then r cos θ = 4 ⇒ r = 4 cos θ = 4 sec θ
Answer:
Bisecting an angle ⇒ answer a
Step-by-step explanation:
* <em>Lets revise the steps of bisecting an angle</em>
- <em><u>How to construct a bisector of angle XYZ</u></em>
1. Open the compass to any width, and place its pin at the angle’s
vertex Y and draw an arc cuts the two rays of the angle YX and YZ
at two points M and N respectively
2. Open the compass to another width and place its pin at M and draw
an arc between the two rays YX and YZ
3. Without changing the width of the compass place its pin at N and
draw another arc intersects the arc from M at point Q
4. Join YQ which is the bisector of angle XYZ
* <em>Now lets compare these steps by the steps of the question</em>
∵ The vertex of the angle ABC is A represented by Y
∵ The rays of the angle AC and AB represented by YX and YZ
∵ Points D , E represented by points M , N
∴ The construction is " Bisecting an angle "
Question 1a - You have got this correct, the median mark is 35
Question 1b- To work out the range, you must do the largest value subtract the smallest value. For your data, this would be 57 - 13 = 44
Question 2 - You have drawn the lines in the correct places, but you have not used a ruler. In order to get full marks on a question like this you must use a ruler.
Question 3 - Your lower quartile and median is correct, to find the upper quartile, we do 3(n/4). 'n' is the number of data points - in this case 120.
120/4 = 30
30 x 3 = 90
Go across the graph at 90 to see when the line is hit.
From what I can tell, the Upper Quartile is 3.
Next just find the maximum value.
Again, by the looks of it, the Maximum value is 8.5.
Now you have all the data needed for the box plot.
Min = 0
LQ = 0.8
Med = 2.1
UQ = 3
Max = 8.5
Using this information, draw a box plot like you did on the previous question.
<em>Again, I must stress that any line that you draw (unless purposely curved) must be drawn with a ruler; even on the graph at the top, during you working out. If you do not use a ruler, marks can be lost/taken away.</em>
Question 4a - For the median on a cumulative frequency chart, you must find the halfway point in the data. For this, we do n/2. In this case, n = 40
40/2 = 20
Draw a line (using ruler) across at 20 until you reach the line.
Draw another one down to help you read the number.
The median looks like 34 seconds.
Question 4b - For this question, we already know the Min, Med and Max. Now we must work out the LQ and UQ.
Remember, LQ = n/4
In this case, n = 40
40/4 = 10
Look across at ten and you will find that the LQ = 16 seconds
To work out the UQ, we multiply the LQ place by 3 3(n/4).
3 x 10 = 30
30 on the graph takes us up to 45 seconds.
We now know that the:
Min = 9
LQ = 16
Med = 34
UQ = 45
Max = 57
With this information, draw a box plot like you have in the previous questions.
Question 5 - Good things to always compare on box plots are the Min/Max/Range and the Inter Quartile Range.
The boys had a lowest minimum and a higher maximum, this means that their range is larger, resulting in a large spread of data in comparison to the girls.
The Inter Quartile Range is the difference between the Upper Quartile and the Lower Quartile (how wide the box is).
The boy IQR = 45 - 16 = 29
The girls IQR = 34 - 23 = 11
Again, the girls have much more concise results; even though they did not get the quickest result, they were more like one another.
Question 5a - The median in a box plot is always the line down the centre of the box. In this case:
Median = 24 marks
Question 5b - The IQR is always the UQ - LQ
With this data, the IQR is the following:
36 - 17 = 19 marks
Hope this helps
