A cylinder has an 18-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed w
1 answer:
The water in the cylinder will be 1179π in³. Thus, 2nd answer choice is correct.
<h3>What is the volume of a right circular cylinder?</h3>Suppose that the radius of the considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
A cylinder has an 18-inch diameter and is 15 inches tall. It is filled to the top with water.
A 6-inch-diameter ball is placed within the cylinder, and then the cylinder is filled with water.
We have to find the volume of the empty cylinder and then the volume of the ball.
Subtract the latter from the former.
The volume of the cylinder = πr^2h.
= π(9 in)²(15 in)
= 1215π in³
Volume of the ball = (4/3)π(3 in)³
= 36π in³
Subtracting
= 1215π in³ - 36π in³
= 1179π in³
Thus, 2nd answer choice is correct.
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Answer:
a)0.7
b) 10.03
c) 0.0801
Step-by-step explanation:
Rate of return Probability
9.5 0.1
9.8 0.2
10 0.3
10.2 0.3
10.6 0.1
a.
P(Rate of return is at least 10%)=P(R=10)+P(R=10.2)+P(R=10.6)
P(Rate of return is at least 10%)=0.3+0.3+0.1
P(Rate of return is at least 10%)=0.7
b)
Expected rate of return=E(x)=sum(x*p(x))
Rate of return(x) Probability(p(x)) x*p(x)
9.5 0.1 0.95
9.8 0.2 1.96
10 0.3 3
10.2 0.3 3.06
10.6 0.1 1.06
Expected rate of return=E(x)=sum(x*p(x))
Expected rate of return=0.95+1.96+3+3.06+1.06=10.03
c)
variance of the rate of return=V(x)=
Rate of return(x) Probability(p(x)) x*p(x) x²*p(x)
9.5 0.1 0.95 9.025
9.8 0.2 1.96 19.208
10 0.3 3 30
10.2 0.3 3.06 31.212
10.6 0.1 1.06 11.236
sum[x²*p(x)]=9.025+19.208+30+31.212+11.236=100.681
variance of the rate of return=V(x)=sum(x²*p(x))-[sum(x*p(x))]²
variance of the rate of return=V(x)=100.681-(10.03)²
variance of the rate of return=V(x)=100.681-100.6009
variance of the rate of return=V(x)=0.0801