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beks73 [17]
3 years ago
15

RSM wants to send four of its 18 Math Challenge teachers to a conference. How many combinations of four teachers include exactly

one of either Mrs. Vera or Mr. Jan?
Mathematics
1 answer:
tatiyna3 years ago
4 0

Answer:

1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.

Step-by-step explanation:

The order in which the teachers are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

1 from a set of 2(Either Mrs. Vera or Mr. Jan).

3 from a set of 18 - 2 = 16. So

C_{2,1}C_{16,3} = \frac{2!}{1!1!} \times \frac{16!}{3!13!} = 1120

1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.

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Form a sequence that has two arithmetic means between 13 and 88.
hichkok12 [17]

Answer:

Correct choice is A

Step-by-step explanation:

For the numbers 13 and 88, find the difference 88-13:

since 88-13=75 and \dfrac{75}{3}=25 (two arithmetic means tells you there will be three intervals), two arithmetic means will be

  • 13+25=38;
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7 0
2 years ago
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Serjik [45]

Answer:

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Step-by-step explanation:

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2 years ago
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Veronica has been saving dimes and quarters she has 110 coins in all and the total value is 18.50 how many dimes and quarters do
Lady_Fox [76]

This problem can be solved by the chicken rabbits method or you can just do simple algebra.

I.) Chicken and rabbits method

First assume all 110 coins are dimes and none are quarters.

We will have a total value of 11 dollars

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There are 750/15=50 group of 15 cents in the 7 dollars and 50 cents.

This also meant that we need to switch out 50 dimes for 50 quarters.

So we have 50 quarters.

That first method is very good and very quick once you get the hang of it, now I'm going to show you the algebraic way to solve this.

Let's say there are x dimes and y quarters.

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Now solve multiply first equation by 10

10x+10y=1100

subtract

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Now we set the numbers of quarters to y so the answer is 50 quarters.

I personally recommend using algebra whenever you can because the practice is very important and you will eventually get really fast at setting up and solving equations. The first method is faster in this case but the second is more generalize, hope it helps.

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2 years ago
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