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Svetlanka [38]
3 years ago
9

Your schools talent show will feature 12 solo acts and ensemble 2 acts. The show will last 90 min. The 6 solo performers judged

best will give a repeat performance at a second 60-min show, which will also feature the 2 ensemble acts. Each solo lasts x minutes, and each ensemble act lasts y minutes.
A. Write a system of equations to model the situation.
B. Solve the system from part(a). How long is each solo act? How long is each ensemble act?
Mathematics
1 answer:
kicyunya [14]3 years ago
3 0
A.  12*x + 2*y = 90
       6*x + 2*y = 60

To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.

B.  Here we can multiply second equation with negative 1 and add it to first equation.
6x = 30
x = 5

now we replace x in any of 2 equations to get y.
30+2y = 60
2y = 30
y=15

Solo acts are 5 minutes long and ensemble acts are 15 minutes long
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BRAINLIEST ANSWER AND 98 POINTS!!!!
Alex73 [517]

Answer:

P (g1, g2) = P(g1) * P(g2) = 1/2 * 1/2 = 1/4

P (r1, r2) = P(r1) * P(r2) = 1/5 * 1/5 = 1/25

P ( b1, g1 or g1 b2) = 3/20 + 3/20  = 6/20 = 3/10

P ( b1, g1 or g1 b2) = 1/10 + 1/10  = 2/10 = 1/5

Step-by-step explanation:

How many marbles are there?

5 green, 3 black, and 2 red marbles = 10 marbles

P ( green marbles) = green/ total = 5/10 = 1/2

Then she puts it back, so there are still 10 marbles

P (2nd marble is green) = green/ total = 5/10 = 1/2

These are independent events ( since the marble is replaced)

P (g1, g2) = P(g1) * P(g2) = 1/2 * 1/2 = 1/4


P ( red marble) = red/ total = 2/10 = 1/5

Then she puts it back, so there are still 10 marbles

P (2nd marble is red) = red/ total = 2/10 = 1/5

These are independent events ( since the marble is replaced)

P (r1, r2) = P(r1) * P(r2) = 1/5 * 1/5 = 1/25


P ( black marble) = black/ total = 3/10

Then she puts it back, so there are still 10 marbles

P (2nd marble is green) = green/ total = 5/10 = 1/2

These are independent events ( since the marble is replaced)

P (b1, g2) = P(b1) * P(g2) = 3/10 * 1/2 = 3/20

This is if order matters, but I will assume order does not matter since the key word then is not there it just says and

If order doesn't matter, just that she has a black and green marble

The we multiply it by 2  because

P (b2, g1) = P(b2) * P(g1) = 1/2 * 3/10 = 3/20

We add the probabilities when it is or

P ( b1, g1 or g1 b2) = 3/20 + 3/20  = 6/20 = 3/10


P ( green marble) = green/ total = 5/10=1/2

Then she puts it back, so there are still 10 marbles

P (2nd marble is red) = red/ total = 2/10 = 1/5

These are independent events ( since the marble is replaced)

P (g1, r2) = P(g1) * P(r2) = 1/2 * 1/5 = 1/10

This is if order matters but I will assume order does not matter since the key word then is not there it just says and

If order doesn't matter, just that she has a green and red marble

The we multiply it by 2  because

P (r1, g2) = P(r1) * P(g2) = 1/5 * 1/2 = 1/10

We add the probabilities when it is or

P ( b1, g1 or g1 b2) = 1/10 + 1/10  = 2/10 = 1/5

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Whats the question

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