How many strings of length 5 can be written using the letters {a, b,c, d,e, f} if no two consecutive letters can be the same? for example, we'd count adede but not acdde.

3750 strings.

Step-by-step explanation:

First we have 6 different letters to choose from (a, b, c, d, e, f) and we will make a string of length 5.

First, we would have to choose one of the letters, to do this we would have 6 choices.

For our second choice, we can only choose from 5 letters since we cannot choose the one that we already chose (no two consecutive letters can be the same).

Then, for our third choice, we would have to choose from 5 different letters (any letter but the one before).

Similarly for our fourth and fifth choice, we can choose 5 different letters.

Then, the total amount of strings would be:

6 x 5 x 5 x 5 x 5 = 6 x 5⁴ = 3750 strings.

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.

0.4 liters = 400 milliliters (multiply the volume value by 1000 and it give you the answer). hope this ! ^-^