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3 years ago

Solve for x. 23(x−7)=−2

Mathematics

2 answers:

RoseWind [281]3 years ago

6 0

X= 6.913 the answer to your question is this^

Elenna [48]3 years ago

6 0

23(x-7)=-2

23x-161=-2
-23x -23x
---------------------
-161 = -25x

x = 6.44

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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,

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

so that

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

7 0

2 years ago

Alekssandra [29.7K]

Answer:

distributive proper

Step-by-step explanation:

mulitiply

7 0

2 years ago

What times what equals 216

BARSIC [14]

<span>The question ask us to find the products which equals 216. First we have to factorize 216: 216 = 2*2*2*3*3*3. So: 216 = 1 * 216; 216 = 2 * 108; 216 = 3 * 72; 216 = 4 * 54 ; 216 = 6 * 36; 216 = 8 * 27; 216 = 9 * 24 ; 216 = 12 * 18. And because of a commutative property: 216 = 18 * 12 ; 216 = 24 * 9 ; 216 = 27 * 8 ; 216 = 36 * 6 ; 216 = 54 * 4 ; 216 = 72 * 3 ; 216 = 108 * 2; 216 = 216 * 1.</span>

5 0

3 years ago

Read 2 more answers

Suppose a shipment of 400 components contains 68 defective and 332 non-defective computer components . From the shipment you tak

Alona [7]

Answer:

The standard deviation for the number of defective parts in the sample is 1.88.

Step-by-step explanation:

The sample is with replacement, which means that the trials are independent, and thus, the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$