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White raven [17]

3 years ago

12

We have a jar of coins, all pennies and dimes. All together, we have 309 coins, and the total value of all coins in the jar is $

19.2. How many pennies are there in the jar?

1 answer:

Vinvika [58]3 years ago

8 0

There are 130 pennies in the jar

Step-by-step explanation:

We have a jar of coins

All coins are pennies and dimes
There are 309 coins in the jar
The total value of all coins in the jar is $ 19.2

We need to find the number of pennies in the jar

Assume that there are p pennies and d dimes in the jar

∵ There are p pennies and d dimes in the jar

∵ There are 309 coins in the jar

∵ All the coins in the jar are pennies and dimes

∴ p + d = 309 ⇒ (1)

∵ The total value of all coins in the jar is $ 19.2

∵ $1 = 100 cents

∴ $19.2 = 19.2 × 100 = 1920 cents

∵ 1 penny = 1 cent

∵ 1 dime = 10 cents

∴ p + 10 d = 1920 ⇒ (2)

Now we have system of equations, we can solve them to find p

∵ p + d = 309 ⇒ (1)

∵ p + 10 d = 1920 ⇒ (2)

- Multiply equation (1) by -10 to eliminate d

∵ (-10)(p) + (-10)(d) = (-10)(309)

∴ -10 p - 10 d = -3090 ⇒ (3)

Add equations (2) , (3)

∴ -9 p = -1170

- Divide both sides by -9

∴ p = 130

There are 130 pennies in the jar

Learn more:

You can learn more about the system of equations in brainly.com/question/3739260

#LearnwithBrainly

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Step-by-step explanation:

We have the following info given by the problem

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The degrees of freedom for this case are:

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The confidence is 95%so then the significance is $\alpha=0.05$ and the $\alpha/2 =0.025$ , we need to find a critical value in the t distribution with 22 degrees of freedom who accumulates 0.025 of the area on each tail and we got:

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