Answer:
2a^2b(5a-3b)
If not then the other way is
5a-3b
Step-by-step explanation:
The GCF of 10a^3b and -6a^2b^2 is 2a^2b
So divide by that you will get
2a^2b(5a-3b)
C(a,b), because the x-coordinate( first coordinate) is a (seeing as it is situated directly above point B, which also has an x-coordinate of a) and the y-coordinate ( second coordinate) is b (seeing as it is situated on the same horizontal level as point D, which also has a y-coordinate of b)
the length of AC can be calculated with the theorem of Pythagoras:
length AB = a - 0 = a
length BC = b - 0 = b
seeing as the length of AC is the longest, it can be calculated by the following formula:
It is called "Pythagoras' Theorem" and can be written in one short equation:
a^2 + b^2 = c^2 (^ means to the power of by the way)
in this case, A and B are lengths AB and BC, so lenght AC can be calculated as the following:
a^2 + b^2 = (length AC)^2
length AC = √(a^2 + b^2)
Extra information: Seeing as the shape of the drawn lines is a rectangle, lines AC and BD have to be the same length, so BD is also √(a^2 + b^2). But that is also stated in the assignment!
Explanation
Part A
We can use the formula below to find the mean.
![\text{Mean}=\sum ^{}_{}(\frac{fx}{f})](https://tex.z-dn.net/?f=%5Ctext%7BMean%7D%3D%5Csum%20%5E%7B%7D_%7B%7D%28%5Cfrac%7Bfx%7D%7Bf%7D%29)
We will then have;
![\begin{gathered} \text{Mean = }\frac{5\times3+4\times1+5\times1+6\times2+7\times2+8\times4+9\times3+10\times1}{19}=\frac{15+4+5+12+14+32+27+10}{19} \\ =\frac{119}{19}=6.2632 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BMean%20%3D%20%7D%5Cfrac%7B5%5Ctimes3%2B4%5Ctimes1%2B5%5Ctimes1%2B6%5Ctimes2%2B7%5Ctimes2%2B8%5Ctimes4%2B9%5Ctimes3%2B10%5Ctimes1%7D%7B19%7D%3D%5Cfrac%7B15%2B4%2B5%2B12%2B14%2B32%2B27%2B10%7D%7B19%7D%20%5C%5C%20%3D%5Cfrac%7B119%7D%7B19%7D%3D6.2632%20%5Cend%7Bgathered%7D)
Mean = 6.2632
Part B
Since the data set is odd.
![\begin{gathered} \text{Median}=\frac{(n+1)}{2}^{th}\text{observation} \\ =\text{Value of }\frac{\text{(19+1)}}{2}^{th}\text{observation} \\ =\text{value of 10th observation} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BMedian%7D%3D%5Cfrac%7B%28n%2B1%29%7D%7B2%7D%5E%7Bth%7D%5Ctext%7Bobservation%7D%20%5C%5C%20%3D%5Ctext%7BValue%20of%20%7D%5Cfrac%7B%5Ctext%7B%2819%2B1%29%7D%7D%7B2%7D%5E%7Bth%7D%5Ctext%7Bobservation%7D%20%5C%5C%20%3D%5Ctext%7Bvalue%20of%2010th%20observation%7D%20%5Cend%7Bgathered%7D)
Answer: From the column of cumulative frequency cf, the median is 7
1 meter = 3.2808399 feet
<span>810m * 3.2808399 ft/m </span>
<span>2657.48 feet </span>
<span>2657.48/5.4 </span>
<span>492.12592593 </span>
<span>Scale </span>
<span>1:492 </span>
A= first number
B= second number
C= third number
A + B + C
Then divide by 5