The price of a car was decreased by 16% to £2400. What was the price before the decrease?

Answer:

Step-by-step explanation:

There are 15 antennas in total.

Out of these, 3 are defective.

This means that 12 antennas are functioning: 15-3=12.

To ensure that no two defective antennas are adjacent, we need to have only one defective at a time placed between the functional ones.

So,

We align the 13 functional antennas, then look for the spaces where the defective antennas can fit

__G __ G __ G __ G __ G __G __ G __ G __ G __ G __ G __ G __G __

Each gap represented by an underscore indicates a possible location for a defective antenna, allowing for just one per space.

Consequently, there are 14 potential spots for the defective antennas. With 3 defectives, we are dealing with a combinatorial arrangement.

ⁿCr= n!/(n-r)!r!

The total number of arrangements possible is

14C3=14!/(14-3)!3!

14C3=14×13×12×11!/11!×3×2

14C3=14×13×12/6

That gives us 364 distinct ways to arrange them.

Wallet = belt + 31
jacket = 3 · belt

176 = belt + wallet + jacket

176 = belt + (belt + 31) + (3 · belt)
176 = (2 · belt) + 31 + (3 · belt)
176 = (5 · belt) + 31
5 ·belt = 145
belt = 29

The final choice is your answer.

Answer:

(a) 1 in 365 or 0.2740%

(b) 0.8227%

Step-by-step explanation:

(a) For the first person's birthday, the probability that the second person has the same birthday is 1 out of 365, so the chance that the first two share a birthday is:

(b) There are four scenarios possible where at least two individuals share a birthday: first and second, first and third, second and third, all three sharing the same birthday. Hence, the probability that at least two share their birthdays is:

An obtuse angle is one that measures more than 90 degrees but less than 180 degrees.