The answer is 13. To figure this out I used 10 notebooks sold as a guide. I knew the answer could not be 10, because $27.95/10 was not a number stopping in the hundredths place (or a true money amount).
I tried numbers greater than 10 using a trial and error strategy until I got to 13 notebooks sold and found that it $27.95 was divisible by 13 to get an answer between $2 and $3 ($2.15 exactly).
Juice bottles are J, replace j with 6 in the equation and solve for w:
3w + 4(6) = 39
3w + 24 =39
Subtract 24 from both sides:
3w = 15
Divide both sides by 3:
w = 15/3
w = 5
You can buy 5 water bottles.
The Mean = (135 + 71 + 69 + 80 + 158 + 152 + 161 + 96 + 122 + 118 + 87 + 85 ) : 12 = 111.166
The smallest value : 69
The greatest value : 161
s² = ∑( x i - x )² / ( n - 1 )
s² = ( 568.274 + 1613.3 + 1777.97 + 971.32 + 2193.42 + 1667.4 + +2483.42 + 230 + 117.38 + 46.7 + 584 + 684.66 ) : 11
s² = 1176.1676
s = √s² = √1176.1676
s ( Standard deviation ) = 34.295
All the values fall within 2 standard deviations:
x (Mean) - 2 s and x + 2 s
From the given function modeling the height of the ball:
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x),
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft
b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.
c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.
Let us say that S is the total food sales therefore we can
create the following equation:
0.20 S = 625 + 0.10 S
Solving for S:
0.10 S = 625
S = 6250
<span>Therefore the food sales should amount to $6,250</span>
