The formula for the volume of a cone is V =
So the answer is 102.63
Answer:
Step-by-step explanation:
y=mx+b where m=slope and b=y intercept
m=(y2-y1)/(x2-x1)
m=(-2-4)/(2+1)
m=-2 so far we have the slope
y=-2x+b, using point (2,-2) we can solve for b, the y intercept
-2=-2(2)+b
-2=-4+b
2=b so we have our line
y=-2x+2, slope is -2 and y intercept is 2
Answer:
2.6
Step-by-step explanation:
3/5 ---> ?/100
100/5 ---> 20
3 20 60
-- x = -------
5 20 100
60/100 = 6/10
6/10 as a decimal is 0.6
2 + 0.6
= 2.6
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Hope this helps!!</h2>
Answer:
(a) E(X) = -2p² + 2p + 2; d²/dp² E(X) at p = 1/2 is less than 0
(b) 6p⁴ - 12p³ + 3p² + 3p + 3; d²/dp² E(X) at p = 1/2 is less than 0
Step-by-step explanation:
(a) when i = 2, the expected number of played games will be:
E(X) = 2[p² + (1-p)²] + 3[2p² (1-p) + 2p(1-p)²] = 2[p²+1-2p+p²] + 3[2p²-2p³+2p(1-2p+p²)] = 2[2p²-2p+1] + 3[2p² - 2p³+2p-4p²+2p³] = 4p²-4p+2-6p²+6p = -2p²+2p+2.
If p = 1/2, then:
d²/dp² E(X) = d/dp (-4p + 2) = -4 which is less than 0. Therefore, the E(X) is maximized.
(b) when i = 3;
E(X) = 3[p³ + (1-p)³] + 4[3p³(1-p) + 3p(1-p)³] + 5[6p³(1-p)² + 6p²(1-p)³]
Simplification and rearrangement lead to:
E(X) = 6p⁴-12p³+3p²+3p+3
if p = 1/2, then:
d²/dp² E(X) at p = 1/2 = d/dp (24p³-36p²+6p+3) = 72p²-72p+6 = 72(1/2)² - 72(1/2) +6 = 18 - 36 +8 = -10
Therefore, E(X) is maximized.
