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3 years ago

How many ways can 5 people be arranged in a line?

Mathematics

1 answer:

Rasek [7]3 years ago

7 0

Answer: 120 ways

Step-by-step explanation: In this problem, we're asked how many ways can 5 people be arranged in a line.

Let's start by drawing 5 blanks to represent the 5 different positions in the line.

Now, we know that 5 different people can fill the spot in the first position. However, once the first position is filled, only 4 people can fill the second spot and once the second spot is filled, only 3 people can fill the third spot and so on. So we have 5 4 3 2 1.

Now, based on the counting principle, there are 5 x 4 x 3 x 2 x 1 ways for all 5 spots to be filled.

5 x 4 is 20, 20 x 3 is 60, 60 x 2 is 120, and 120 x 1 is 120.

So there are 120 ways for all 5 spots to be filled which means that there are 120 ways that 5 people can be arranged in a line.

I have also shown my work on the whiteboard in the image attached.

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A 30-year loan of $1,000 is repaid with payments at the end of each year. Each of the first ten payments equals the amount of in

Lilit [14]

Answer:

X = $374.16

Step-by-step explanation:

First we have to calculate for the amount of interest using compound interest formula

A = P(1+(r/n))^(nt)

P (principal) = 1000

r (rate) = 10% = 0.1

t (time in year) = 30

n (number of recursion per year) = 1

A = 1000(1+(0.1/1))^(1*30) = 17,449.40

Amount of compound interest for 30 years is

I = A - P = 17,449.40 -1000 = 16,449.40

Amount of interest due per year

= I/30

= 16,449.40/30 = 548.313

The guy paid the same amount of interest due for the first 10 years

548.313*10 = 5483.13

And the next 10 payments equal to 150% of the interest due (150% = 1.5 times)

548.313*10*1.5 = 8224.7

Total of paid interest is

8224.7 + 5483.13 = 13707.83

So, the balance unpaid loan is

17449.40 - 13707.83 = 3741.57

This balance payment is dividend for the last 10 years, so

3741.57/10 = 374.16

So X = $374.16

8 0

2 years ago

We found the correlation coefficient for the comparison between height and weight in babies to be -0.12. That meanscorrelation i

qwelly [4]

Answer:

The taller the baby, the lighter the baby

Explanation:

A correlation coefficient is a number between -1 and 1. The correlation is strong when it is a number closer to -1 or closer to 1 and the relation is independent when it is a number closer to 0.

In this case, we get that the correlation coefficient is -0.12, so there is a weak negative correlation. The negative means that when one variable increases, the other decrease, so the taller the baby, the lighter the baby.

Then, the answer is:

The taller the baby, the lighter the baby

6 0

1 year ago

After 45 seconds, Camden’s bathtub fills with 3 inches of water. How many seconds will it take to fill Camden’s tub with 20 inch

Pepsi [2]

So you have to find how many seconds it takes to fill up with 1 inch.
TO find that, you have to divide 45/3 which equals to 15.
So it takes 15 seconds for 1 inch. The question is asking you to find out how many seconds will it take to fill the tub with 20 inches.
SO your gonna multiply 15*20.
15*20 = 300
So it would take 300 seconds to fill up Camden's tub.

5 0

3 years ago

You are given a choice of taking the simple interest on $100,000 invested for 2 years at a rate of 3% or the interest on $100,00

valentinak56 [21]

Answer:

Step-by-step explanation:

the simple interest formula= principal* interest rate*time

simple interest : 100000*%2*2 years

simple interest= 4000 dollars

compound quarterly : A=principal(1+r/4)^t

since it is quarterly and have 4 quarters in a year, and 8 in two years.

compound quarterly: 100000(1+0.03/4)^8=106159.88

it is better to invest with compound interest because it add 6159 dollars in two years to the investment of 100000 dollars.

the difference between the interest: 6159.88-4000=2159.88

5 0

3 years ago

6 = -4x + y -5x - y = 21 Please Help Fast!!!!!! Substitution

Vera_Pavlovna [14]

Answer:

y = 4x + 6

-5x - 4x - 6 = 21

-9x - 6 = 21

-9x = 27

x = -3

y - 4(-3) = 6

y + 12 = 6

y = -6

(-3, -6)

5 0

3 years ago