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bulgar [2K]
3 years ago
13

Justin has been giving a list of 5 bands and asked to place a vote. his vote must have the names of his favorite, second favorit

e, and third favorite bands from the list. how many different votes are possible?​
Mathematics
1 answer:
Alina [70]3 years ago
6 0

Answer:

20 different total voting combinations.

Step-by-step explanation:

so lets called them A, B, C, D, and E

If John has to vote on his favorite and second favorite that means we will be selecting 2 bands out of the 5 possible to choose from.

To find the TOTAL amount of different combinations we need to pair up bands and find all the combo's.

Here are the results/totals:

AB

AC

AD

AE

BA

BC

BD

BE

CA

CB

CD

CE

DA

DB

DC

DE

EA

EB

EC

ED

If you want to do it simpler without listing you can take the the 5 bands and multiple by 4 since you know each initial band (A, B, C, D, and E) will be paired with another band other than itself.

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Answer:

A and D

Step-by-step explanation:

We are given that

(3/4,2/3),(1/4,1),(1,1/2) and (1/2,1)

x_1=\frac{3}{4}

y_1=\frac{2}{3}

x_2=\frac{1}{4},y_2=1

x_3=1,y_3=\frac{1}{2}

x_4=\frac{1}{2},y_4=1

k=\frac{1}{2}

Direct proportion:

\frac{x}{y}=k

Inverse proportion:xy=k

\frac{x_1}{y_1}=\frac{3}{4}\times \frac{3}{2}=\frac{9}{8}\neq \frac{1}{2}

Therefore, it is not in direct proportion.

\frac{1}{4\times 2}=\frac{1}{8}\neq\frac{1}{2}

\frac{1}{\frac{1}{2}}=2\neq \frac{1}{2}

x_1y_1=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}

x_2y_2=\frac{1}{4}\times 2=\frac{1}{2}

x_3y_3=1\times \frac{1}{2}=\frac{1}{2}

x_4y_4=\frac{1}{2}\times 1=\frac{1}{2}

Therefore, xy=k=\frac{1}{2}

Hence, the given points form an inverse variation .

xy=\frac{1}{2}

y=\frac{1}{2x}

Option A and D is true.

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