Answer:
The number of gallons of 20% alcohol solution is 12 and the number of gallons of 60% alcohol solution is 4
Step-by-step explanation:
Let
x ----> the number of gallons of 20% alcohol solution
y ----> the number of gallons of 60% alcohol solution
we know that
20%=20/100=0.20
60%=60/100=0.60
30%=30/100=0.30
x+y=16
x=16-y ------> equation A
0.20x+0.60y=16(0.30) ------> equation B
Solve by substitution
Substitute equation A in equation B and solve for y
0.20(16-y)+0.60y=16(0.30)
3.2-0.20y+0.60y=4.8
0.40y=4.8-3.2
0.40y=1.6
y=4 gal
Find the value of x
x=16-y
x=16-4=12 gal
therefore
The number of gallons of 20% alcohol solution is 12 and the number of gallons of 60% alcohol solution is 4
Answer:
B
Step-by-step explanation:
To find the answer, plug in 2 anywhere you see x and solve
1/3 x 4^(2)
When you simplify, this becomes
1/3 x 16.
Now multiply the two numbers and get 16/3, which is B
This is just a cylinder, with a cone and half of a sphere carved out of it.
Just find the volume of the cylinder, then subtract the volume of the cone and the volume of the half-sphere from it, and you'll have the volume of the part that's left.
Now I'll tell you why this problem was assigned: The purpose is
to give you an opportunity to recall the formulas for the volumes
of these three shapes. To hep you recall them, here they are:
Volume of a cylinder = (pi) (radius of the round end)² (length)
Volume of a cone= (1/3) (pi) (radius of the round end)²
Volume of a whole sphere= (4/3) (pi) (radius of the whole sphere)³
Notice that in the weird contraption in the picture, the cylinder,
the cone, and the half-sphere all have the same radius.