A circle has a radius of 48 millimeters. What is the length of the arc intercepted by a central angle that measures 3π/4 radians?

Express the answer in terms of π.

Question (1):
Part (a):
We are given that:
Total number of files = 250 files
% of photos = 12%
This means that:
number of photos = percentage of photos * total number of files
number of photos = 12% * 250
number of photos = 0.12 * 250

Part (b):
We need to get the number of photos. This means that we will simply compute the result of the equation we obtained from part (a) as follows:
number of photos = 0.12 * 250
number of photos = 30 photos

Question (2):
Part (a):
We know that:
Total amount spent should be less than $80
Amount spent on food = $68.25
Price per each carton of juice = $3
Assuming that number of juice cartons is x, therefore:
amount spent on juice = $3x
Putting the above into inequality, we can find that:
total amount spent > amount spent on food + amount spent on juice
80 > 68.25 + 3x
80 - 68.25 > 68.25 + 3x - 68.25
11.75 > 3x

Part (b):
Now, we want to get the number of cartons, this means that we will solve the inequality in part (a) for x as follows:
11.75 > 3x
11.75 / 3 > 3x / 3
3.9 > x
Now, we can not buy 0.9 carton of juice. This means that we need to approximate the result.
We have:
x < 3.9
The nearest whole number that satisfies this inequality is 3.
This means that Quan can buy a maximum of 3 cartons of juice to satisfy his budget inequality

Question (3):
Part (a):
We can represent the hexagonal using trapeziums and rectngles which are considered simpler polygons.
The division as well as the dimensions are shown in the attached image.

Part (b):
To get the area of the hexagonal, we will get the area of the overall rectangle and remove from it the area of the two dotted triangles.
This can be done as follows:
area of rectangle = length * width = 11 * 24 = 264 in²
area of top right triangle = 0.5 * base * height = 0.5 * 4 * 5 = 10 in²
area of bottom left triangle = 0.5 * base * height = 0.5 * 10 * 4 = 20 in²
Now, we have:
area of hexagonal = 264 - 10 - 20
area of hexagonal = 234 in²

Another solution to get the area:
We can get the area by getting the area of each of the simpler polygons and add them.
This can be done as follows:
area of left trapezium =  in²

area of middle rectangle = 10 * 11 = 110 in²

area of right trapezium =  in²

Therefore:
area of hexagonal = 90 + 110 + 34 = 234 in²

Hope this helps :)