Answer:
i)
Find the attached
ii)
The mathematical model that best fits the data is;
The quadratic model
Step-by-step explanation:
i)
A scatter-plot can easily be constructed using applications such as Ms. Excel.
In Ms. Excel, enter the data into any two adjacent columns. Next, highlight the data, then click the insert ribbon and select the scatter-plot option.
Excel returns a scatter-plot chart as shown in the attachment below.
ii)
After obtaining the scatter-plot, we shall need to add a trend line in order to determine the mathematical model that best fits the data given.
Click anywhere inside the chart, then select the design tab under chart tools. Click on the Add Chart element in the upper left corner of the excel workbook and select more trend-line options. This feature will enable us to fit any trend-line to our data.
Select any trend line option ensuring you check the boxes; Display Equation on chart and Display R-squared value on chart.
Find the attached for the various trend-lines fitted.
The mathematical model that best fits the data is;
The quadratic model
Since it has the largest R-squared value of 1.00
-3/4 = -0.75
5/8 = 0.625
-1/2 and 0.9 are between them
9. y=-1/4x^2+4x-19
group
y=(-1/4x^2+4x)-19
undistribute -1/4
y=-1/4(x^2-16x)-19
take 1/2 of -16 and squer it to get 64 then add neg and pos inside
y=-1/4(x^2-16x+64-64)-19
factorperfect square
y=-1/4((x-8)^2-64)-19
expand
y=-1/4(x-8)^2+16-19
y=-1/4(x-8)^2-3
vertex is (8,-3)
10.
group
y=(1/4x^2-3x)+18
undistribute
y=1/4(x^2-12x)+18
take 1/2 of -12 and square it and add neg and pos isndie
y=1/4(x^2-12x+36-36)+18
factor
y=1/4((x-6)^2-36)+18
expand
y=1/4(x-6)^2-9+18
y=1/4(x-6)^2+9
get to form (x-h)^2=4p(y-k)
minus 9 both sides and times 4
(x-6)^2=4(y-9)
(x-6)^2=4(1)(y-9)
so 1>0 so opens up and focus is 1 above vertex
vertex is (6,9)
so focus i (6,10)
11.
y=(-1/6x^2+7x)-80
y=(-1/6)(x^2-42x)-80
take 1/2 of linear coefient and squer it and add negative and positive inside
-42/2=-21, (-21)^2=441
y=(-1/6)(x^2-42+441-441)-80
factor perfect square the square
y=(-1/6)((x-21)^2-411)-80
expand
y=(-1/6)(x-21)^2+73.5-80
y=(-1/6)(x-21)^2-6.5
add 6.5 to both sid
y+6.5=(-1/6)(x-21)^2
times both sides by -6
-6(y+6.5)=(x-21)^2
(x-21)^2=-6(y+6.5)
(y-21)^2=4(-3/2)(y-(-6.5))
vertex is
-3/2<0 so directix is above
it is -3/2 or 1.5 units above the vertex
up is y so
-6.5+1.5=-5
the directix is y=-5
11.
in form (y-1)^2=4p(x+3)
opens left or right
(y-1)^2=4(4)(x+3)
vertex is (-3,1)
4>0 so opens right
dirextix is to left
it is 4 units to left
(-3,1)
left right is x
4 left of -3 is -4-3=7
x=-7 is da directix
Answer: Your answer would be x = y^3/5
Hope this helped
:D
53.24-34.99=18.25
$1 will buy 20 minutes of long distance calling
x$18.25 = 365 minutes @ $34.99
$132-$34.99=$97.01
20x97=1,940 minutes
minimum=365 minutes
maximum=1,940 minutes
Hope this helps.
