Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width: w = 12 - 2x
length: l = 18 - 2x
height: h = x
Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x
Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6
Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160
Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224
And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
We can’t answer the question because we need a graph or points.
Answer:
The correct answer to the question is
e. If is likely that between 35% and 41% percent of the driving population would be willing to pay higher gas prices to protect the environment.
Step-by-step explanation:
The margin of error expresses the number of percentage points of error is contained within survey result. A large error margin therefore reduces the level of dependence on a given statistic. The margin of error describes the expected variation between the statistic sample and the real population value.
In the question, the option
e. If is likely that between 35% and 41% percent of the driving population would be willing to pay higher gas prices to protect the environment , clearly depicts the definition of margin of error as it shows the expected variance from te real population
Answer:
2.3=v+0.47v=
We move all terms to the left:
2.3-(v+0.47v)=0
We add all the numbers together, and all the variables
-(+1.47v)+2.3=0
We get rid of parentheses
-1.47v+2.3=0
We move all terms containing v to the left, all other terms to the right
-1.47v=-2.3
v=-2.3/-1.47
v=1+0.83/1.47
