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tekilochka [14]

2 years ago

10

A survey of 280 homeless persons showed that 63 were veterans

1 answer:

Oxana [17]2 years ago

7 0

Answer:

Step-by-step explanation:

223

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The length of the hypotenuse of a 45°-45°-90° triangle is 22. Find the length of one leg.

Shkiper50 [21]

Check the picture below.

8 0

3 years ago

What is the average distance of earth to the sun in km

dybincka [34]

The average distance is 3.23!! I found this question very interesting thanks!

7 0

2 years ago

Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64

tino4ka555 [31]

a.

$x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}$

By Fermat's little theorem, we have

$x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5$

$x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7$

5 and 7 are both prime, so $\varphi(5)=4$ and $\varphi(7)=6$ . By Euler's theorem, we get

$x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5$

$x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7$

Now we can use the Chinese remainder theorem to solve for $x$ . Start with

$x=2\cdot7+5\cdot6$

Taken mod 5, the second term vanishes and $14\equiv4\pmod5$ . Multiply by the inverse of 4 mod 5 (4), then by 2.

$x=2\cdot7\cdot4\cdot2+5\cdot6$

Taken mod 7, the first term vanishes and $30\equiv2\pmod7$ . Multiply by the inverse of 2 mod 7 (4), then by 6.

$x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6$

$\implies x\equiv832\pmod{5\cdot7}\implies\boxed{x\equiv27\pmod{35}}$

b.

$x^5\equiv3\pmod{64}$

We have $\varphi(64)=32$ , so by Euler's theorem,

$x^{32}\equiv1\pmod{64}$

Now, raising both sides of the original congruence to the power of 6 gives

$x^{30}\equiv3^6\equiv729\equiv25\pmod{64}$

Then multiplying both sides by $x^2$ gives

$x^{32}\equiv25x^2\equiv1\pmod{64}$

so that $x^2$ is the inverse of 25 mod 64. To find this inverse, solve for $y$ in $25y\equiv1\pmod{64}$ . Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that $(-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}$ .

So we know

$25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}$

Squaring both sides of this gives

$x^4\equiv1681\equiv17\pmod{64}$

and multiplying both sides by $x$ tells us

$x^5\equiv17x\equiv3\pmod{64}$

Use the Euclidean algorithm to solve for $x$ .

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that $(-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}$ , and so $x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}$

5 0

3 years ago

What’s the hypotenuse?

Karolina [17]

Answer:

c = 10 feet

Step-by-step explanation:

Use the Pythagorean theorem: a^2 + b^2 = c^2

<u>Step 1: Plug in the information</u>

(6)^2 + (8)^2 = c^2

36 + 64 = c^2

100 = c^2

sqrt(100) = sqrt(c^2)

<em>10 = c</em>

<em />

Answer: c = 10 feet

7 0

3 years ago

At the end of the day, a bakery gives everything that is unsold to food banks for the needy. If it has 12 apple pies left at the

juin [17]

Answer:

462 ways

Step-by-step explanation:

The formula to use in solving this problem is given as the Combination formula

The Combination formula is given as

C(n , r) = nCr = n!/r! (n - r)!

We are told that a food bakery has 12 pies unsold at the end of the day which they intend to share to 6 food banks

n = 12, r = 6

In order to ensure that at least 1 food bank gets 1 pie, we have:

n - 1 = 12 - 1 = 11

r - 1 = 6 - 1 = 5

Hence,

C(11, 5) = 11C5

= 11!/ 5! ×(11 - 5)!

= 11!/5! × 6!

= (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/ (5 × 4 × 3 × 2 × 1) ×( 6 × 5 × 4 × 3 × 2 × 1)

= 462 ways

3 0

3 years ago