Answer:
The ride will take 2 h
Step-by-step explanation:
From the question,
Deon plans to ride a 20-mi bicycle trail, that is the total distance he plans to cover is 20-mi
Distance, d = 20 mi
Also, his average speed is 10 mi/h
rate of speed, r = 10 mi/h
To determine how many hours the ride will take,
From the formula,
d = rt
where
d is the distance covered
r is the average rate of speed
and t is the time.
We can solve for t, such
d = rt becomes
t = d/r
Now, from the question
d = 20 mi
r = 10 mi/h
∴ t = (20 mi) / (10 mi/h)
t = 2 h
Hence, the ride will take 2 h (hours)
Answer:
t3 = 8, t5 = 14
Step-by-step explanation:
t3 = 2 + (3-1) × 3
t3 = 2 + (2) × 3
t3 = 2 + 6
t3 = 8
t5 = 2 + (5-1) × 3
t5 = 2 + (4) × 3
t5 = 2 + 12
t5 = 14
The is a 50% chance of being a boy or a girl.....previous siblings do not matter. Every child is an independent event. So even if u had 2 siblings that were boys, the result of the next one being a boy is still gonna be 50%...just as the odds of it being a girl, is 50% as well.
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:
8+1/4
Step-by-step explanation:
8+1/4 because 10-2 is 8.
