2x-1 < x+3
5x-1 > 6-2x
x-5 < 0
solve the inequality for x.
x < 4
x > 1
X < 5
find the intersection
X ∑ {1,4}
Alternative form: {x I 1 < x < 4}
∑ indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern. For example, the sum of the first 4 squared integers, 12+22+32+42, follows a simple pattern: each term is of the form i2, and we add up values from i=1 to i=4.
General Idea:
The volume of cylinder is given by
, where r is the radius and h is the height of the cylinder.
Applying the concept:
Step 1: We need to find the volume of full cylinder with the given dimensions using the formula.
Volume of full cylinder 
Volume of half cylinder 
Step 2: Let x be the number of minutes of filling the sand.
of sand filled every 15 seconds, there are four 15 seconds in a minute.
So volume of sand filled in 1 minute
.
of sand taken out of cylindrical vase every minute.
Net volume of sand filled in 1 minute = Volume of sand filled in the vase in one minute - Volume of sand taken out in 1 minute
Net volume of sand filled in 1 minute
Volume of sand filled in x minutes
.
We need to set up an equation to find the number of minutes need to fill half the volume in cylindrical vase.

Conclusion:
The number of minutes required for the base be half filled with sand is 57
V = 1/3 area of base * height
Area of base = h [(b₁ +b₂)]/2
[(3 + 6) * 4] : 2 =
18 ft²
Volume =
18 * 3 =
54 ft³
Answer:
She can only fill 10 pages completely.
Step-by-step explanation:
She can fill 10 pages, because 40/10=4. She does not have enough pages left to fill another page fully.