Answer:
decreases
Step-by-step explanation:
Answer:
On the first day, they traveled 30 percents of the total distance. On the second day they traveled one fourth of the total distance. One fourth converted into percentage is 25 percent. Then you add 30 plus 25 because that is the to a
total distance that Murphy's family traveled for 2 days. It will be 55 percents, and you convert 55 percents into fraction will be 55/100, and you simplify it, will be 11/20.
Jamal's score is 80
<u>Explanation:</u>
Given:
Number of questions = 100
Let w be the number of wrong answers
Let r be the number of right answers
According to question,
r = 4w
r + w = 100
Solving both the equations we get:
4w + w = 100
5w = 100
w = 20
If w = 20 then r = 4 X 20 = 80
Therefore, Jamal's score is 80
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.
Answer:
Option A.
Step-by-step explanation:
According to triangle inequality theorem, a triangle exists if the sum of two sides is greater that third side.
Apply this theorem on each combination.
Case I: 
...(1)
Case II: 
...(2)
Case III: 
...(3)
On combining (1), (2) and (3), we get
Therefore, the correct option is A.
