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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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LUCKY_DIMON [66]

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as below

Step-by-step explanation:

\frac{2}{7} = \frac{6x}{4x + 17}

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2 years ago
No more asking me to click on links answer truthfully
Alborosie
Ok so the correct answers are both A. and B.

It would be A. between 1.5 and 2, because the number 1.77 is in between those two numbers. It is greater than 1.5 but also less than 2.

It would be B. to the right of 1.71, because the number 1.77 is greater than 1.71.

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3 years ago
PLZZZZ HELPPPP THIS IS A TIMED TESTTT!!
lorasvet [3.4K]

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2/3

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8 0
2 years ago
Three security cameras were mounted at the corners of a triangles parking lot. Camera 1 was 110 ft from camera 2, which was 137
Nata [24]

Answer:

<em>Camera 2nd has to cover the maximum angle, i.e. </em>78.70^\circ.

Step-by-step explanation:

Please have a look at the triangular park represented as a triangle \triangle ABC with sides

a = 110 ft

b = 158 ft

c = 137 ft

1st camera is located at point C, 2nd camera at point B and 3rd camera at point A respectively.

We can use law of cosines here, to find out the angles \angle A, \angle B, \angle C

As per Law of cosine:

cos C = \dfrac{a^{2}+b^2-c^2 }{2ab}\\cos B = \dfrac{a^{2}+c^2-b^2 }{2ac}\\cos A = \dfrac{b^{2}+c^2-a^2 }{2bc}

Putting the values of a,b and c to find out angles \angle A, \angle B, \angle C.

cos C = \dfrac{110^{2}+158^2-137^2 }{2\times 110 \times 158}\\\Rightarrow cos C = \dfrac{12100+24964-18769 }{24760}\\\Rightarrow cos C =0.526\\\Rightarrow C = 58.24^\circ

cos B = \dfrac{110^{2}+137^2-158^2 }{2\times 110 \times 137}\\\Rightarrow cos B = \dfrac{12100+18769 -24964}{30140}\\\Rightarrow cos B = \dfrac{5905}{30140}\\\Rightarrow cos B =0.196\\\Rightarrow B = 78.70^\circ

cos A = \dfrac{158^{2}+137^2-110^2 }{2\times 158 \times 137}\\\Rightarrow cos A = \dfrac{24964+18769-12100}{43292}\\\Rightarrow cos A = \dfrac{31633}{43292}\\\Rightarrow cos A = 0.731\\\Rightarrow A = 43.05^\circ

<em>Camera 2nd has to cover the maximum angle</em>, i.e. 78.70^\circ.

6 0
3 years ago
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