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erma4kov [3.2K]
3 years ago
13

When a bakery opened this morning, the ratio of the number of pineapple muffins to the number of mango muffins was 3 : 2. After

244 pineapple muffins were sold, the ratio of the number of pineapple muffins to the number of mango muffins changed to 3 : 5. How many pineapple muffins were there when the bakery opened this morning?
Mathematics
1 answer:
NeX [460]3 years ago
8 0

<u>Answer:</u>

(x+244)/y=3/2

x/y=3/5

y=5x/3

(x+244)/(x5/3)=3/2

x+244=3/2 . 5x/3

x+244=15x/6

6(x+244)=15x

6x+1464=15x

1464=15x-6x

1464=9x

x=1464/9

x≈ 162

mm=162*5/3=270

162:270 = 3:5

pm before = 270*3/2=405

405:270 = 3:2

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A box of candy hearts contains 52 hearts, of which 19 are white, 10 are tan, 7 are pink, 3 are purple, 5 are yellow, 2 are orang
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<u>Answer-</u>

a. Probability that  three of the candies are white = 0.29

b. Probability that three are white, 2 are tan, 1 is pink, 1 is yellow, and 2 are green = 0.006

<u>Solution-</u>

There are 19 white candies, out off which we have to choose 3.

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As we have to draw total of 9 candies, after 3 white candies we left with 9-3 = 6, candies. And those 6 candies have to be selected from 52-19 = 33 candies, (as we are drawing candies other than white, so it is subtracted)

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\binom{33}{6} = \frac{33!}{6!27!} =1107568

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Drawing 9 candies out of 52 candies,

\binom{52}{9} = \frac{52!}{9!43!} = 3679075400

∴P(3 white candies) = \frac{1073233392}{3679075400} =0.29



Total number of ways of selecting 3 whites, 2 are tans, 1 is pink, 1 is yellow, and 2 are greens is,

\binom{19}{3} \binom{10}{2} \binom{7}{1} \binom{5}{1} \binom{6}{2}

=(\frac{19!}{3!16!}) (\frac{10!}{2!8!}) (\frac{7!}{1!6}) (\frac{5!}{1!4!}) (\frac{6!}{2!4!})

=(969)(45)(7)(5)(15)=22892625

Total number of selection = 3 whites + 2 are tans + 1 is pink + 1 is yellow + 2 greens = 9 candies out of 52 candies is,

\binom{52}{9}=\frac{52!}{9!43!} =3679075400

∴ P( 3 whites, 2 are tans, 1 is pink, 1 is yellow, 2 greens) =

\frac{22892625}{3679075400} = 0.006


6 0
4 years ago
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