Answer:
Step-by-step explanation:
It expresses how much money he had to pay in total for the sheet music and drumsticks altogether.
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-18-(-12)=-6
Since there is two negative sign, it turns into positive meaning the -12 becomes positive 12 and the -18 stays same. So -18+12=-6 because 18 is bigger than 12 and it's negative so the final answer should be negative.
Hint: when you see two negative sign just turn them into plus sign.
The experiment probabilities are listed below:
One: 2 out of 20 = 2 / 20 = 0.1 or 10%
Four: 5 out of 20 = 5 / 20 = 1 / 4 = 0.25 = 25%
The theoretical probability of any single number is 1 out of 6 or about 17%.
The experimental probability for ones was less than and for fours it was greater than the theoretical probability.
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:
sqrt(64)
Step-by-step explanation:
The square root of 64 = 8 and 8 is a rational number
