a-conductor-needs-5-cellists-and-5-violinists-to-play-at-a-diplomatic-event-to-do-this-he-ranks-the-

Name: a conductor needs 5 cellists and 5 violinists to play at a diplomatic event to do this he ranks the
Uploaded: 2020-02-24
Duration: 1 min 18 s
Channel: Numerade
Description: A conductor needs 5 cellists and 5 violinists to play at a diplomatic event. To do this, he ranks the orchestra’s 10 cellists and 16 violinists in order of musical proficiency. What is the ratio of the total cellist rankings possible to the total violinist rankings possible?

Question

A conductor needs 5 cellists and 5 violinists to play at a diplomatic event. To do this, he ranks the orchestra’s 10 cellists and 16 violinists in order of musical proficiency. What is the ratio of the total cellist rankings possible to the total violinist rankings possible?

Heather Zimmers · Accepted Answer

Okay, so 10 cellists are being ranked and 16 violinists are being ranked and the number of ways to rank the 10 cellists is 10 factorial and the number of ways to rank. The 16 violinist is 16 factorial and were asked to find the ratio of these. So we have 10 factorial over 16 factorial now to simplify it. Keep in mind that 10 factorial is 10 times nine times eight et cetera. All the way down two times two times one and 16 factorial 16 times, 15 times 14 10 13 times 12 tons 11 times 10 9 et cetera. All the way down to one so we could cancel from the top of the bottom. The 10 the 9 38 and so on. All the way down to one. And all we have left in this ratio is one over 16 times, 15 times, 14 times, 13 times, 12 times 11. And when you work that out, you get the ratio one to five million 765,000 7 60

Alice . · Answer

this problem is concerning whether to use a combination or a permutation to solve a real life application. So the question acts. A conductor needs five cellists and five violinist to play a diplomatic event, and the orchestra has 10 cellists and 16 violinists, and he wants to rank them in order of musical proficiency and asks, What&#x27;s the ratio of total cellist drinking&#x27;s possible and total violinist rankings possible? So first, let&#x27;s break this problem down. Since the questions asking for total cellist rankings possible and total violinist rankings possible in a ratio, let&#x27;s first find those two values. So the total cellist rankings possible once when a problem asks for rankings. That means that order matters and the and the funk and the counting method that we use when order matters is a permutation. Soto find the total cellist ranking possible. We would need to d&#x27;oh ah, permutation. However he is not. It&#x27;s easy to go 10. She&#x27;s five with a permutation, but that&#x27;s just incorrect because it&#x27;s not ranking those five cellists as ranking the whole orchestra. So instead, it would just be 10 factorial because we always start with 10 factorial incest. The whole group of cellists before dividing by anything terminal cases. So now we have 10 factorial. Let&#x27;s find the total violinist rankings possible, and that ends up being 16 factorial because they&#x27;re 16 violinists and you would not divide because you&#x27;re not removing any cases. So to find the final ratio, you need to divide by the smaller number, which ends up being 10 factorial. So it&#x27;s 1 to 16 factorial over 10 factorial and bye Factorial Rules ends up being 1 to 60 cents 15 times 14 times, 13 times 12 times 11 which all comes out to 12 ah, 576 576 zero. And that&#x27;s the final answer. So the main takeaway is don&#x27;t get distracted by the first part of the problem because the five, uh, the groups of five don&#x27;t

Lisa Tarman · Answer

in Problem 58. We have to violinist sitting one behind the other and then directly in front of them is a listener. And the question I ask, What&#x27;s the smallest separation between the two violinist to have destroy active interference for the listener when they play a note that has a frequency of 4 40? Well, we know the conditions for destructive interference. There&#x27;s destructive interference when the path length difference is half a wavelength or, um, the rehabs of wavelength or 5/2 civil wavelength or 7/2 salute wavelength. You got it. Um, so there their separation for the smallest separation would be when they have a pathway difference of careful wavelength. So we just have to find what, half a wave like this. So I know that the wavelength for sound I&#x27;m gonna follow the wave equation. The velocity of sound is 3 43 I&#x27;m looking for the wavelength. When the frequency is for 40 I just divide and I get that has a wavelength of 0.780 so half a wavelength will be half of 0.780 And that is point 390 so that&#x27;s how four report. There&#x27;s violinist must be sitting the next question. Ask with that separation increase or decrease tohave destructive interference when the frequency is increased. Well, if I think of my equation, if my frequency is increasing, my wavelength must be decreasing because the speed of sound doesn&#x27;t change. So if my wavelength is decreasing, then my separation must decrease because my separation is half of the wavelength. And then part See, I&#x27;m asked to find what their separation would be when they play a note of 5 40 hurts some funding the wavelength when the frequency is 5 40 speed of sound. 3 43 I&#x27;m looking for the wavelength. When the frequency is 5 40 I divide both sides by 5 40 and I get a wave like this. 0.635 So half a wavelength it&#x27;s half of 0.635 point 318 meters. It decreases just like we said it would

Jonathan Ibarra · Answer

we have a string of a violin that gives off a certain frequency with the given length of 0.35 meters and help solve this problem. We&#x27;re gonna make use of the formula that frequency F is equal to one divided by 20 times. Describe it of tea divided by, um, you And in this formula L is equal to the length of the string TZ go to the tension on the stream i m u is equal to the massacre unit length of the stream hard gave This problem is asking us to find the length of the string that gives us a frequency of 440 hertz. So using the formula that we just heard down, I&#x27;m gonna write FM. She is equal to one divided by two times l times the square it of tea divided by mu. I am also going to write that f of a Is he cool 82 times elevate times the square root of tea divided by new. And so from these two formulas, we can say that effigy divide by F today is equal to elevate divided by ill. And then when you take this equation and we saw them for the length a little bit. And so this will be equal to F G divide by every day times. Oh, so now we&#x27;re gonna get elevate is equal to effigy. So you plug in effigy divided by F today slogan f of a times l So we plug in Oh, and then this will give us a length of 0.3 12 meters. It&#x27;s not to find the location where the player needs to put their finger and we&#x27;ll call that distance D We needed subtracted hell minus L V. So this location e is he cool to 0.35 meters minus 0.31 meters is your 0.3 12 meters and then this will give us 3.8 centimeters. Now for part B, we need to find the maximum allowable percentage change in the string tension. So again, I&#x27;m not right down. That s a They is equal to two times l. A. They times the square root of tea divided by me and going to rewrite this as elevate is equal to one divided by two times every day times the spirit of tea divided by me And now we&#x27;re gonna differentiate both sides. So after differentiating both sides, we&#x27;re gonna get de of Elevate is equal She went over four times f of a times distribute but one over tee times mu times DT. And now what we&#x27;re gonna do is running. We&#x27;re going to divide this equation here. We&#x27;re gonna divide it divided with this equation here. And then after doing that, we&#x27;re going to get do you elevate. Delighted by l b is equal She wanted before times f of a times the square root of one over tee times in you e t then divided by the right side of L V and then simplifying this This will give us e t divided by two times t. So I write this also down here to make it look simpler. So we&#x27;re gonna take this equation and solve it for DT over teeth. So DT over tea is equal to two times de of El of a divided by Elvis. So now all that&#x27;s left is to substitute So DT over t is equal two times de of elevate. And we can write that as your 0.6 centimeters divided by elevate, which is 0.3 12 meters. And then to convert this, she covered the numerator and two meters. You can write down the following expression and then doing the calculations here. This will give us 0.0 385 and then we multiply this 500 to get a percentage which is equal 23.8 5%.

Khoobchandra Agrawal · Answer

Hello, friends. Here it is, given our vibrant string having the length 135 m on his student for concert G Different Quincy 3. 92 words There must the violinist place our finger toe play concert at a frequency off A is for 40 years if this position to remain correct tohave the bit of the finger bit of the finger is around six. Intimate er I writing in bit off finger while six centimeters calculate maximum allowable for simplest changing extreme tension. Let us start solving it, right. Violent off geek will be to win toe white 35 meter that is be upon every so lambda they will be so I saw and a that will be be upon f A. Okay, thanks Lent for the on the length for eight lent for G minus frequency off g simplify such value land for these given 0.35 m frequency off He is 3 92 and for that in notice for 40 So it would be while zero 382 m Yeah, that later that strength for a concert is and d minus while 0382 m that is, while 35 minus while Jiro, 382 m. It would be while we went 2 m, so he should place the finger. Sure. 31.2 centimeters from the bridge. Length for a concert is be upon to Evie that is going upon to f a be upon you so d n a. If we differentiate it even get duty upon four F eight rude off InterMune. That means so change intention off the string which is allowed is to into while six upon 35 minus 3.82 in 200 scent emitted. So attention which can be changed in the X A string off the violin is 3.84% maximum. That&#x27;s all for it. Thanks for

Ankit Gupta · Answer

we have to arrange five words books in a program. So let us consider that these are the sequence of books 1st 2nd 3rd 4th and fifth. So first we will be displayed with this work. Secondly, this third this and considered these air support and 50 books in a program. So for our first work, we have five choices for our second work. As one as one choice has already been made as the first work has been done here. So we have four choices for 3rd 1 We have three choices. And for 4th 1 we have two choices. And lastly, we are left with only one book. Therefore, by using a fundamental principle of counting, we can find principal off counting. You can find the total number off these. Can a program be a ring? We will multiply all these choices we have That is 5432 and one. So we get after multiplication. The total number off these are program can be arranged. And after multiplying these terms, we get 1 20 So we have 1.8 different ways to arrange a program or five books

Problem

A motorcycle shop has 10 choppers, 6 bobbers, and…

Problem 315 Medium Difficulty

A conductor needs 5 cellists and 5 violinists to play at a diplomatic event. To do this, he ranks the orchestra’s 10 cellists and 16 violinists in order of musical proficiency. What is the ratio of the total cellist rankings possible to the total violinist rankings possible?

Answer

$1 : 5765760$

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