Answer: 288ways
Step-by-step explanation:
There are 5men and 5women to be arranged, since the men must seat together, they will be arranged in 5! ways. For the women, since they must also seat together but with siamese twins between them, they can be arranged in 4! ways instead of 5! ways and this is due to presence of the twins among them.
Note that Siamese twins cannot be separated as such both are taken as one making it 4!.
Since the women and men are always sitting together, they can be arranged in 2! ways i.e 2 sexes
The final seating arrangement can be done in 2!×(5!+4!) ways
= 2× (120+24)
= 2×144
= 288ways.
Note that the arrangement of the men and women are added because they can only be arranged differently to ensure different sex are not sitting together.
Since the common difference is 6, we can assume that the sequence is arithmetic, with rule
T(n)=6n+5 where T(1)=11
T(9)=6(9)+5=59
Time = Distance / speed
Time = 20 miles / 12mph
Time = 1 and 2/3 hours ( 1 hour and 40 minutes)
Answer:
Step-by-step explanation:
let the amount spent on popcorn be x and amount spent on drinks be y
If the total bill paid is $17.94, then x+y = $17.94
If she spend twice as much on popcorn as on drinks, then y = 2x
Substitute y = 2x into the original equation
x+y = $17.94
x + 2x = $17.94
3x = $17.94
x = $17.94/3
x = $5.98
Since y = 2x
y = 2($5.98)
y = $11.96
Therefore she spent $5.98 on popcorn and $11.96 on drinks
Answer:
Step-by-step explanation:
<u>Given recursive formula:</u>
- a₁ = -1
- aₙ = - 3aₙ₋₁ + 6 for n ≥ 2
<u>The first 4 terms are:</u>
- a₁ = - 1, given
- a₂ = - 3*(-1) + 6 = 3 + 6 = 9
- a₃ = - 3*(9) + 6 = - 27 + 6 = - 21
- a₄ = - 3*(-21) + 6 = 63 + 6 = 69
