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Alex Ar [27]
3 years ago
11

In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and

fifth seats?
Mathematics
1 answer:
Damm [24]3 years ago
3 0

Answer:

36 ways.

Step-by-step explanation:

There are  3 seats available to the 3 girls.

So we need to find the number of ways  we can arrange 3 girls.

This is 3!  which works out to 3*2*1 = 6 ways.

Now the 3 boys can also be arranged in 6 ways in their 3 seats.

So the total number of arrangements are 6*6 = 36.

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A restaurant owner was experimenting with the taste of her homestyle lemon drink. She started with 60 litres of water. She remov
Burka [1]

Answer:

ratio of pure lemon juice to water in the homestyle lemon  drink is 5 : 19.

Step-by-step explanation:

In order to solve the final ratio of lemon juice to water, let us start by determining the initial ratio of pure lemon juice to water in the first mix. This is done as follows:

Total volume of mixture = 60 liters

initial volume of water = 60 liters

initial volume of lemon juice = 0 liters

1) She removed 15 liters of the water and replaced it with 15 liters of pure lemon juice.

Volume of water = 60 - 15 = 45 liters

Volume of lemon juice = 15 liters

 \therefore \frac{15}{60}\ = \frac{1}{4}\  of\ the\ first\ mix\ is\ lemon\ juice\\\frac{45}{60}\ = \frac{3}{4}\  of\ the\ first\ mix\ is\ pure\ water

2) She removed 10 liters of the new mixture

Let us convert this amount removed into ratio:

lemon\ juice\ = \frac{1}{4}\ \times 10 = \frac{10}{4} = \frac{5}{2}\ liters.\\  \therefore the\ owner\ removes\ \frac{5}{2}\ liters\ of\ pure\ lemon\ juice\\pure\ water\ = \frac{3}{4}\ \times 10 = \frac{30}{4} = \frac{15}{2}\ liters\\  \therefore\ the\ owner\ removes\ \frac{15}{2}\ liters\ of\ water\ from\ the\ first\ mix.

New volumes of water and lemon juice after removing the 10 liters of mixture is calculated as follows:

lemon\ juice\ = 15 - \frac{5}{2} = \frac{30-5}{2} = \frac{25}{2}\ liters\ of\ lemon\ juice\\pure\ water\ = 45 - \frac{15}{2} = \frac{90-15}{2} = \frac{75}{2}\ liters\ of\ pure\ water

3) and replaced it with 10 liters of water.

New\ volume\ of\ water\ = 10 + \frac{75}{2} = \frac{20+ 75}{2} = \frac{95}{2}\ liters

The final ratio of lemon juice to water:

\frac{25}{2} : \frac{95}{2}\\= 25 : 95\\= 5 : 19

Therefore, the final ratio of pure lemon juice to water in the homestyle lemon  drink is 5 : 19.

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JulijaS [17]

Answer:

9 : 3

Step-by-step explanation:

To get from 21 to 3 we divided 21 by 7, therefore we have to do the same to the other side and so we get...

63 / 7 = 9

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