Answer:
4.472135955
Step-by-step explanation:
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.
Answer to your question
The base is X
What are the other stuff then?
2 is the power
3 is the constant
<h3>
Answer: 96 units</h3>
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Explanation:
Since ABDE is a rectangle, the opposite sides AE and BD are the same length. This makes BD = 24. Similarly, ED = 20 since AB = 20.
Focus on triangle BCD. Let x be the length of segment CD. We can use the pythagorean theorem to find x
a^2 + b^2 = c^2
(BD)^2 + (CD)^2 = (BC)^2
24^2 + x^2 = 25^2
576 + x^2 = 625
x^2 = 625 - 576
x^2 = 49
x = sqrt(49)
x = 7
Segment CD is 7 units long.
Since ED = 20, this means,
EC = ED + DC
EC = 20 + 7
EC = 27
The perimeter of this trapezoid is
P = sum of all exterior sides
P = AB+BC+CE+EA
P = 20+25+27+24
P = 96 units
Note that we didn't add in side BD as part of the perimeter because it is not an exterior side. Think of sides AB, BC, CE, and AE as outer walls of the house while BD is an interior wall. The perimeter is only worried about the outer walls.
The error is if you add all of those times up it is equal to 7.55 minutes and that's more than 6
