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Assoli18 [71]
3 years ago
11

A shopkeeper bought 5 dozen pen for rs 480 . If she sold all the pens at the rate of rs 9 per pen . Find profit / loss percent​

Mathematics
1 answer:
lakkis [162]3 years ago
5 0

Answer:

12.5%

Step-by-step explanation:

1 dozen=12

5 dozen= 60

Earnings= 9x60= rs 540

Profit= 540-480= rs 60

Percentage profit= 60/480×100%=12.5%

Brainlist please

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Answer:

10

Step-by-step explanation:

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Simplifying (5 * x³) / x²

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☁️ Answer ☁️

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WHAT IS THE REMAINDER WHEN <img src="https://tex.z-dn.net/?f=32%5E%7B37%5E%7B32%7D%20%7D" id="TexFormula1" title="32^{37^{32} }"
Feliz [49]

Recall Euler's theorem: if \gcd(a,n) = 1, then

a^{\phi(n)} \equiv 1 \pmod n

where \phi is Euler's totient function.

We have \gcd(9,32) = 1 - in fact, \gcd(9,32^k)=1 for any k\in\Bbb N since 9=3^2 and 32=2^5 share no common divisors - as well as \phi(9) = 6.

Now,

37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} =  32\cdot\left(32^{(\cdots)}\right)^6

where the c_i are positive integer coefficients from the binomial expansion. By Euler's theorem,

\left(32^{(\cdots)\right)^6 \equiv 1 \pmod9

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32^{37^{32}} \equiv 32\cdot1 \equiv \boxed{5} \pmod9

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2 years ago
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3 0
3 years ago
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Joan wants to set a 4-digit unlock code for her mobile phone. She plans to use only odd numbers and to make sure that no number
LuckyWell [14K]

Answer: 120

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There are 5 possibilities for the first digit, 4 for the second, 3 for the third, and 2 for the last, so there are 5 x 4 x 3 x 2 = 120

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