Abag of coins contains 2 quarters, 5 dimes, 3 nickels, and 4 pennies. if 2 coins are randomly chosen from the bag, one after the other, and not replaced, and if the total value of the chosen coins is 26 cents, what is the probability that a third coin randomly chosen from the bag will be a penny?

The probability that a third coin randomly chosen is a penny is:

Step-by-step explanation:

a bag of coins contains 2 quarters, 5 dimes, 3 nickels, and 4 pennies.

This means that there are total 14 coins.

( Since 2 quarters+ 5 dimes + 3 nickels +4 pennies=14 coins)

Now, two coins were chosen one after the other without replacement.

So, the total number of coins left=14-2=12 coins.

As we know that:

1 nickel= 5 cents.

1 dime= 10 cents.

1 quarter= 25 cents

1 penny= 1 cent.

Hence, the two coins that were drawn to add up to 26 cents have to be a quarter and a penny. ( Since, 25 cents +1 cents=26 cents)

Hence, after the two draw we are left with 3 pennies.

Hence, the probability that a third coin randomly chosen will be a penny is calculated as:

( Since we have 3 choices i.e. 3 pennies out of total 12 coins left)

Hence, the probability is:

i have no

a

step-by-step explanation:

given the 2 equations

- x + y = - 2 → (1)

2x - 3y = 4 → (2)

multiplying (1) by 2 and adding to (2) will eliminate the x- term

- 2x + 2y = - 4 → (3)

add (2) and (3) term by term

(2x - 2x) + (- 3y + 2y) = (4 - 4), simplifying gives

- y = 0 ⇒ y = 0

substitute y = 0 in either of the 2 equations for corresponding value of x

substituting in (2) gives

2x = 4 ( divide both sides by 2 )

x = 2

solution is (2, 0 ) → a