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kaheart [24]
2 years ago
15

11. A child has a repertoire of four piano pieces

Mathematics
1 answer:
drek231 [11]2 years ago
7 0

Answer:

286

Step-by-step explanation:

First, we can tell that this is either a combination or permutation because we have to determine the number of possible combinations based on a limited number of options and a set number of pieces to practice each day.

Next, because order doesn't matter (it doesn't matter if she practices P1 or P3 first, for example), this is a combination.

After that, we can repeat a piano piece, so there is repetition

If there are n things to choose from, and we have to choose r things, our formula for a combination with repetition is

(r+n-1)!/(r!(n-1)!)

Here, we choose from 4 pieces and we need to choose 10 each day, so we have

(r+n-1)!/(r!(n-1)!) = (4+10-1)!/(10!(4-1)!) = 13!/(10!3!) = 13*12*11/(3*2*1) = 286 possible combinations

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The admision fee at a basket ball game is 350$ for children and 750$ for adults. On a certain night,1500 people enter the basket
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<u>Note: The only way to solve this problem is by adjusting the fees to $3.50 and $7.50.</u>

Answer:

<em>1300 children attended the basketball game</em>

Step-by-step explanation:

System of Equations

Let's call:

x = number of children attending the basketball game

y = number of adults attending the basketball game

On a certain night, 1500 people enter the game, thus:

x + y = 1500           [1]

Since each admission fee for children cost $3.50 and $7.50 for adults and it was collected $6050, thus:

3.50x + 7.50y = 6050            [2]

From [1]:

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Substituting in [2]:

3.50x + 7.50(1500 - x) = 6050

Operating:

3.50x +  11250 - 7.50 = 6050

-4x = 6050 - 11250

Solving:

x = 1300

1300 children attended the basketball game

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3 years ago
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Step-by-step explanation:

5 0
3 years ago
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Answer:

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