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svetoff [14.1K]
4 years ago
15

BEST ANSWER GETS BRAINLIEST!! 83 exponent 2 + 252

Mathematics
1 answer:
yKpoI14uk [10]4 years ago
3 0
So I guess you mean 83 raised to the 2nd? If so, you multiply 83 by 83, then add 252. You get 7,141.
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How many 10-digit ternary strings are there that contain exactly two 0s, three 1s, and five 2s?
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There are \dbinom{10}2 ways of picking 2 of the 10 available positions for a 0. 8 positions remain.

There are \dbinom83 ways of picking 3 of the 8 available positions for a 1. 5 positions remain, but we're filling all of them with 2s, and there's \dbinom55=1 way of doing that.

So we have

\dbinom{10}2\dbinom83\dbinom55=\dfrac{10!}{2!(10-2)!}\dfrac{8!}{3!(8-3)!}\dfrac{5!}{5!(5-5)!}=2520

The last expression has a more compact form in terms of the so-called multinomial coefficient,

\dbinom{10}{2,3,5}=\dfrac{10!}{2!3!5!}=2520

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Zach has a basic cell phone plan that does not include texting. He is going to add a multimedia texting package to his
Vedmedyk [2.9K]

Zach have to send 300 number of multimedia texts for the same cost in two packages.

<u>Step-by-step explanation:</u>

Package A charges $0.25 per multimedia  text with no monthly fees.

Package B charges $0.20 per multimedia text and has a  $15 monthly fee.

<u>To frame the equations :</u>

  • Let x be the any amount of multimedia  texts are sent.
  • Let y be the total cost for using the multimedia package.

<u>Package A Equation :</u>

Total cost = No.of text sent × cost per text.

⇒ y = x × 0.25

⇒ y = 0.25x

∴ The equation of package A is y = 0.25x

<u>Package B Equation :</u>

Total cost = (No.of text sent × cost per text) + Monthly fee

⇒ y = (x × 0.20) + 15

⇒ y = 0.2x + 15

∴ The equation of a package B is y = 0.2x + 15

Now, the question is about how many multimedia texts will Zach have to send each month for the two multimedia texting packages to be  the same cost.

⇒ equation of package A = equation of package B

⇒ 0.25x = 0.2x + 15

⇒ 0.25x - 0.2x = 15

⇒ 0.05x = 15

⇒ x = 15 / 0.05

⇒ x = 300

∴ Zach have to send 300 number of multimedia texts for the same cost in two packages.

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