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3 years ago

How many distinct permutations are there of the letters of the word BOOKKEEPER?

Mathematics

2 answers:

ASHA 777 [7]3 years ago

8 0

Answer:

The answer is There are 10 letters in the word bookkeeper. There is 1 B; 2 O's; 2 K's; 3 E's; 1 P; and 1 R.

Step-by-step explanation:

emmainna [20.7K]3 years ago

7 0

The letters of the word BOOKKEEPER can be arranged in 151,200 ways.

The group can be arranged in 8640 ways with all students of the same major together.

Explanation
There are 10 letters in the word bookkeeper. There is 1 B; 2 O's; 2 K's; 3 E's; 1 P; and 1 R.

An arrangement of n total objects where n₁ is one kind, n₂ is another, etc. is given by:
$\frac{n!}{n_1!\times n_2!\times ... \times n_k!}
\\
\\=\frac{10!}{1!2!2!3!1!1!} = \frac{10!}{2!2!3!} = 151,200$

Keeping all of the students of each major together makes each one essentially a "unit." With this in mind, there are 3 units, that can be arranged in 3!=6 ways.

Within the English unit, the students can be arranged in 3!=6 ways.
Within the anthropology unit, the students can be arranged in 2!=2 ways.
Within the history unit, the students can be arranged in 5!=120 ways.

This gives us 6(6*2*120) = 8640

You might be interested in

A rectangle measures 12 cm by 4 cm what is the area

Maslowich

In order to find the area you have to multiply length x width
In this case our length and width are 12cm and 4cm
So lets multiply those. :P
12 x 4 = 48 cm

Your area = 48cm²

Good Luck! :)

6 0

3 years ago

How Much Have I Saved? Portfolio

avanturin [10]

The time value of money calculation can be performed using formula equations or online calculators.

The correct responses are;

1) Option 3

2) Option 2

3) The difference in principal is approximately $8,000

The difference in interest earned is approximately $2,977.87

4) It is better to invest more money at the beginning of the 30 years

Reasons:

Option 1: Present value = 0

Amount invested per month, A = $25/month

The Annual Percentage Rate, APR, r = 3.25%

Number of years = 30

The future value of an annuity is given by the formula;

$\displaystyle FV_{A} = \mathbf{A \cdot \left (\frac{ \left(1 + \frac{r}{m} \right)^{m\cdot t} - 1}{\frac{r}{m} } \right)}$

In option 1, m = 12 periods per year

Therefore;

$\displaystyle FV_{A} = 25 \times \left (\frac{ \left(1 + \frac{0.0325}{12} \right)^{12 \times 30} - 1}{\frac{0.0325}{12} } \right) \approx \mathbf{15,209.3}$

Contribution = $25 × 12 × 30 = $9,000

Total interest earned = $15,209.3 - $9,000 = $6,209.3

Final balance = $15,209.3

Option 2: Present value = 0

Amount, A = $75/quarter

m = 4 periods per year

The Annual Percentage Rate, APR = 4.00%

Therefore;

The effective interest rate is therefore;

$\displaystyle r_{eff} = \left(1 + \frac{0.04}{4} \right)^4 - 1 \approx \mathbf{0.04060401}$

$\displaystyle FV_{A} = 75 \times \left (\frac{ \left(1 + \frac{0.04060401}{4} \right)^{4 \times 30} - 1}{\frac{0.04060401}{4} } \right) \approx 17,437.7$

Using an online calculator, FV = $17,467.04

Contribution = $75 × 4 × 30 = $9,000

Total interest earned = $17,467.04 - $9,000 = $8,467.04

Final balance = $17,467.04

Option 3: Present value = $1,000

APR = 6.25%

m = 12 period per year

Number of years, t = 30 years

Therefore;

$\displaystyle FV = \left (1 + \frac{0.0625}{12} \right)^{12 \times 30} \approx \mathbf{6,489.17}$

Contribution = $1,000

Total interest earned = $6,489.17 - $1,000 = $5,489.17

Final balance = $6,489.17

The table of values is therefore;

$\begin{tabular}{|c|c|c|c|}Option \# &Contribution &Total Interest Earned&Final Balance\\1&\$9,000&\$6,209.3 & \$15,209.3\\2&\$9,000&\$8,467.04 &\$17,467.04\\3&\$1,000&\$5,489.17&\$6,489.17\end{array}\right]$

1) The option that has the least amount invested are option 3

Option 3 investment plan is a present value of $1,000, invested for 30 years at 6.25% APR compounded monthly.

2) Option 2 yielded the highest amount at the end of 30 years, given that the APR is higher than the APR for option 1, although the amount invested over the period are the same.

The basis of option 2 investment plan is $75 invested quarterly at 4.00% APR compounded monthly for 30 years.

3) The difference in the principal invested for the highest and lowest final balance is $9,000 - $1,000 = $8,000

The difference in the interest earned is; $8,467.04 - $5,489.17 = $2,977.87

4) In option 1 the present value is zero, therefore zero amount was invested at the beginning.

The interest to investment ration is 6,209.3:9,000 ≈ 0.7:1

In option 3, all the money was invested at the beginning.

The interest to investment ratio of option 3 is; 5,489.17:1,000 ≈ 5.5:1

Given that the interest to investment ratio, which is the return on investment is larger when more money is saved at the beginning as in option 3, it is better to invest more money at the beginning.

Learn more about future value of an annuity here:

brainly.com/question/8243704

3 0

2 years ago

Please answer with explanation of how you got the answer !!

Irina18 [472]

Answer:

−24

Step-by-step explanation:

Since there is only one negative, this means when all the values are multiplied together the product will be negative. Just multiply all three together to get −24.

(3)(−4)(2)

(−12)(2)

−24

It doesn't matter which order you multiply in in this case.

7 0

3 years ago

How to find the power of area of a square 3.5² i know the answer is 12.25 but i want the formula of 3.5²

LiRa [457]

Answer:

$3.5^{2}$ = 3.5 * 3.5 = 12