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Ira Lisetskai [31]
3 years ago
7

A choir teacher is dividing 3 sopranos and 12 altos into singing groups. he wants each group to have the same combination of sop

ranos and altos, with no singers left over. what is the greatest number of groups he can make?
Mathematics
1 answer:
Andreyy893 years ago
7 0
You can have a maximum of 3 groups. This is due to the fact that you only have 3 sopranos to equally divide between groups. Over 3 you would have a group lacking a soprano so 3 is the greatest you can make it.
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Read 2 more answers
A pharmacist has 30% and 60% iodine solutions on hand. How many liters of each iodine solution will be required to produce 6 lit
kkurt [141]

Answer:

4 liters of 60% solution; 2 liters of 30% solution

Step-by-step explanation:

I like to use a simple, but effective, tool for most mixture problems. It is a kind of "X" diagram as in the attachment.

The ratios of solution concentrations are 3:6:5, so I've used those numbers in the diagram. The constituent solutions are on the left; the desired mixture is in the middle, and the numbers on the other legs of the X are the differences along the diagonals: 6 - 5 = 1; 5 - 3 = 2. This tells you the ratio of 60% solution to 30% solution is 2 : 1.

These ratio units (2, 1) add to 3. We want 6 liters of mixture, so we need to multiply these ratio units by 2 liters to get the amounts of constituents needed. The result is 4 liters of 60% solution and 2 liters of 30% solution.

_____

If you're writing equations, it often works well to let the variable represent the quantity of the greatest contributor—the 60% solution. Let the volume of that (in liters) be represented by v. Then the total volume of iodine in the mixture is ...

... 0.60·v + 0.30·(6 -v) = 0.50·6

... 0.30v = 0.20·6 . . . . subtract 0.30·6, collect terms

... v = 6·(0.20/0.30) = 4 . . . . divide by the coefficient of v

4 liters of 60% solution are needed. The other 2 liters are 30% solution.

6 0
3 years ago
For a regular 30 sided polygon , what is the degree of rotation
Mashcka [7]
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6 0
2 years ago
Look at the figure below: an image of a right triangle is shown with an angle labeled y degrees If sin y° = s divided by 8 and t
Elena L [17]

Answer:

Cos y = t / 8

Step-by-step explanation:

Using the hints given in the question, the omitted tribagke will look like the triangle attached on the picture ;

From trigonometry :

Sin y = opposite / hypotenus

Sin y = s / 8

Opposite side = s ; hypotenus = 8

Tan y = opposite / Adjacent

Tan y = s / t

Adjacent side = t

Then ;

Cos y = Adjacent / hypotenus

Hence,

Cos y = t / 8

5 0
2 years ago
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