Question

Tistics

Answer 1

Answer: The temperature on the fifth day is -14°C

Step-by-step explanation:

When we have a set of N elements, that can be written as:

{a₁, a₂, ..., aₙ}

The mean of these N elements is be written as:

Mₙ = (a₁ + a₂ + ... + aₙ)/N

Now, when we take in account the temperature for the first four days of January, we will have a set of 4 elements, {a₁, a₂, a₃, a₄}

Where each one of these elements represents the temperature of one particular day.

The mean temperature for the first four days will be:

M₄ = (a₁ + a₂ + a₃ + a₄)/4

And we know that this is equal to 4°C

Now we also could do the next replacement:

(a₁ + a₂ + a₃ + a₄) = T

Then we can write:

M₄ = -4°C =  (a₁ + a₂ + a₃ + a₄)/4 = T/4

Then we can solve:

-4°C = T/4

-4°C*4 = T

-16°C = T

This is the sum of the temperatures for the first four days of January.

Now we know that the mean for the first five days is -6°C

Then we have:

M₅ = (a₁ + a₂ + a₃ + a₄ + a₅)/5 = -6°C

Where a₅ is the temperature on the fifth day of January, which is the value we want to find.

And we know that:

a₁ + a₂ + a₃ + a₄ = -16°C

We can replace that in the equation to get:

(-16°C + a₅)/5 = -6°C

(-16°C + a₅) = 5*(-6°C) = -30°C

a₅ = -30°C + 16°C = -14°C

a₅ = -14°C

The temperature on the fifth day is -14°C