Answer:
The area of this sector is 224*pi cm² or approximately 703.72 cm²
Step-by-step explanation:
In order to calculate the area of a sector for which we have an angle in radians, we need to apply a rule of three in such a way that pi*r² is related to 2*pi radians in the same proportion as the given angle is related to the area of the sector we want to find. This is shown below:
2*pi rad -> pi*r² unit²
angle rad -> sector area unit²
2*pi / angle = pi*r² / (sector area)
2*pi*(sector area) = pi*r²*angle
sector area = [pi*r²*angle]/2*pi
sector area = r²*angle/2 unit²
Applying the data from the problem, we have:
sector area = [(16)²*(7*pi/4)]/2 = [256*(7*pi/4)]/2 = 64*7*pi/2 = 32*7*pi = 224*pi
sector area = 224*pi cm²
sector area = 703.72 cm²
The best way to think about this question is that probability is always out of a total of 1. For example, someone may have a 1/4 chance of picking a certain marble but they will never have a 2 chance of picking a certain marble (that doesn't make any sense). Therefore, we can imagine that the sum of all three probabilities to pick prizes will be 1. We can then set the sum of the probabilities equal to 1:
x+3x+16x=1
You first combine like terms to get 20x=1. Then you divide both sides by 20 to get x=1/20, which is the value of x. This makes sense because you have a small chance of picking a toy in comparison to picking a pen or pencil.
I hope this helps.
Answer:
the not simplified answer is 6/28 The GCF is 2 the siplified answer is 3/14
Step-by-step explanation:
