Ariel also has a collection of coins. her collection is worth $4.80. she has nickels, dimes, and
quarters. the number of nickels that she has is 6 less than the total number of dimes and quarters,
while the number of dimes is equal to the sum of the number of nickels and quarters. find how many
of each coin ariel has.

There are 25 nickels, 28 dimes and 3 quarters

Step-by-step explanation:

- Ariel has a collection of coins

- Her collection is worth $4.80

- She has nickels, dimes, and  quarters

- The number of nickels that she has is 6 less than the total number of

dimes and quarters

- The number of dimes is equal to the sum of the number of nickels

and quarters

- Assume that the number of nickels is x , the number of dimes is y and

the number of quarters is z

∵ 1 nickel = 5 cents

∵ 1 dime = 10 cents

∵ 1 quarter = 25 cents

∵ 1 dollar = 100 cent

∵ Her collection worth $4.80

∵ 4.80 dollars = 4.80 × 100 = 480 cents

∴ 5x + 10y + 25z = 480 ⇒ (1)

∵ The number of nickels  is 6 less than the total number of dimes

and quarters

∴ x = y + z - 6 ⇒ (2)

∵ The number of dimes is equal to the sum of the number of nickels

and quarters

∴ y = x + z

- subtract z from both sides

∴ x = y - z ⇒ (3)

- Equate equation (2) and (3)

∴ y - z = y + z - 6

- Subtract y from both sides

∴ - z = z - 6

- Add 6 to both sides

∴ 6 - z = z

- Add z to both sides

∴ 6 = 2z

- Divide both sides by 2

∴ z = 3

- Substitute the value of z in equation (3)

∴ x = y - 3

- Substitute x and z in equation (1)

∴ 5(y - 3) + 10y + 25(3) = 480

∴ 5y - 15 + 10y + 75 = 480

∴ 15y + 60 = 480

- subtract 60 from both sides

∴ 15y = 420

- Divide both sides by 15

∴ y = 28

- Substitute value of y in equation (3)

∴ x = 28 - 3

∴ x = 25

* There are 25 nickels, 28 dimes and 3 quarters

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3