volume of the box is 675 cubic inches
A machine produces open boxes using square sheets of plastic.
It is a square sheet so length and width are same
Lets assume length as x so width is also x
The machine cuts equal-sized squares measuring 3 inches on a side from each corner of the sheet.
After turning up the sides the height of the box becomes 3 inches
We know the volume of a box formula
Volume = Length * width * height
We know length is x , width is x and height = 3
So V = x * x * 3
Given volume = 675 cubic inches
Divide by 3 on both sides
Now we take square root on both sides
x = 15
the length of one side of the open box is 15 inches.
The complete question is
"The cafeteria staff made sandwiches. Each sandwich had either rye or white bread, either ham or turkey, and either cheese or no cheese. The staff made an equal number of each type of sandwich.
The sandwiches were placed on a tray. Without looking, Mary will choose a sandwich.
What are the chances that Mary will get a sandwich with cheese?"
The chances of Mary getting a sandwich with cheese is 1/2.
<h3>How to calculate the number of different ways?</h3>
The number of different sandwiches is calculated by multiplying all of the possibilities for each material being used.
rye or white bread: 2 options
ham or turkey: 2 options
cheese or no cheese: 2 options
So the number of different sandwiches = 2*2*2 = 8.
4 have cheese and 4 have no cheese, as the staff made an equal number of each type of sandwich.
So, The chances of Mary getting a sandwich with cheese is 4/8 = 1/2.
Learn more about possibilities ;
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(x^3 - y^3)(x^3 + y^3)
You can get this by factoring based on the a^2 - b^2 model
The value of 8 is Hundred Thousand
X=270 units
270 units can be manufactured per month
