Answer:
James' score: 28
Chris' score: 7
Step-by-step explanation:
Call x James' score and y Chris'
James scored 4 times as many points as Chris
x = 4y
The 2 players scored a total of 35 points
x + y = 35
Replace x in the second equation with 4y (they are equal)
4y + y = 35 ===> 5y = 35 ===> y = 35/5 ===> y = 7
replace now this value in the first equation
x = 4y = 4*7 = 28
So James' score: 28, Chris' score: 7
Answer:
if x is a full number, then yes it is a natural number!
Step-by-step explanation:
natural numbers are numbers that you would typically use for counting. (i.e. 1 2 3 4 5 6 7 8 9 10!)
Given the equation
which models the data tabulated below:
![\begin{tabular} {|c|c|} x&y\\[1ex] 0.5&10.4\\ 1&5.8\\ 2&3.3\\ 3&2.4\\ 4&2 \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7C%7D%0Ax%26y%5C%5C%5B1ex%5D%0A0.5%2610.4%5C%5C%0A1%265.8%5C%5C%0A2%263.3%5C%5C%0A3%262.4%5C%5C%0A4%262%0A%5Cend%7Btabular%7D)
The linear regression equation is given by
where:
and
We extend the given table as follows:
![\begin{tabular} {|c|c|c|c|} x&y&x^2&xy\\[1ex] 0.5&10.4&0.25&5.2\\ 1&5.8&1&5.8\\ 2&3.3&4&6.6\\ 3&2.4&9&7.2\\ 4&2&16&8\\[1ex] \Sigma x=10.5&\Sigma y=23.9&\Sigma x^2=30.25&\Sigma xy=32.8 \end{tabular} \\ \\ \\ \bar{x}= \frac{\Sigma x}{n} = \frac{10.5}{5} =2.1 \\ \\ \bar{y}=\frac{\Sigma y}{n} = \frac{23.9}{5} =4.78](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%20%7B%7Cc%7Cc%7Cc%7Cc%7C%7D%20x%26y%26x%5E2%26xy%5C%5C%5B1ex%5D%200.5%2610.4%260.25%265.2%5C%5C%201%265.8%261%265.8%5C%5C%202%263.3%264%266.6%5C%5C%203%262.4%269%267.2%5C%5C%204%262%2616%268%5C%5C%5B1ex%5D%20%5CSigma%20x%3D10.5%26%5CSigma%20y%3D23.9%26%5CSigma%20x%5E2%3D30.25%26%5CSigma%20xy%3D32.8%20%5Cend%7Btabular%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cbar%7Bx%7D%3D%20%5Cfrac%7B%5CSigma%20x%7D%7Bn%7D%20%3D%20%5Cfrac%7B10.5%7D%7B5%7D%20%3D2.1%20%5C%5C%20%5C%5C%20%5Cbar%7By%7D%3D%5Cfrac%7B%5CSigma%20y%7D%7Bn%7D%20%3D%20%5Cfrac%7B23.9%7D%7B5%7D%20%3D4.78)
Thus,
and
Therefore, the linearlized form of the equation is y = 9.234 - 2.12x
Part B:
At x = 1.6,
Answer:
Total cost of cementing the path = Rs. 17,000.
Step-by-step explanation:
Let the square garden be ABCD
Let the region inside the garden (ABCD) be WXYZ.
<u>Given the following data;</u>
Length of sides of ABCD = 90m
Width of path = 5m
Cost = Rs. 10 per m²
Area of ABCD = 90 * 90
Area of ABCD = 8100m²
<em>To find the area of WXYZ;</em>
WX = WZ = 90 - (5 + 5)
WX = WZ = 90 - 10
WX = WZ = 80m
Area of WXYZ = WX * WZ
Substituting into the equation, we have;
Area of WXYZ = 80 * 80
Area of WXYZ = 6400 m²
Area of path = Area of ABCD - Area of WXYZ
Area of path = 8100 - 6400
Area of path = 1700 m²
Total cost of cementing the path = Area of path * cost
Total cost of cementing the path = 1700 * 10
<em>Total cost of cementing the path = Rs. 17,000</em>
