A committee of 7 members is to be chosen from 6 Chartered Accountants,

4, Find a number x such that x = 1 mod 4, x 2 mod 7, and x 5 mod 9.

olchik [2.2K]

4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.

Start with

$x=7\cdot9+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 4, the last two terms vanish and we're left with

$x\equiv63\equiv64-1\equiv-1\equiv3\pmod4$

We have $3^2\equiv9\equiv1\pmod4$ , so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.

$x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 7, the first and last terms vanish and we're left with

$x\equiv72\equiv2\pmod7$

which is what we want, so no adjustments needed here.

$x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 9, the first two terms vanish and we're left with

$x\equiv140\equiv5\pmod9$

so we don't need to make any adjustments here, and we end up with $x=401$ .

By the Chinese remainder theorem, we find that any $x$ such that

$x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}$

is a solution to this system, i.e. $x=149+252n$ for any integer $n$ , the smallest and positive of which is 149.

3 0

2 years ago

On Monday, the temperature at 10 a.m. at Sam’s house was –6° Fahrenheit. The

Alika [10]

Answer:

8

Step-by-step explanation:

to find the answer, subtract the second amount (2) from the first amount (-6), -6 - 2 = -8, the temperat decreased by 8

6 0

2 years ago

Read 2 more answers

Solve the equation 0.2(d-6)=0.3d+5-3+0.1d for d

WINSTONCH [101]

Answer:

d= -16

Step-by-step explanation:

To answer this question you'll have to first simplify the equation to

0.2d+-1.2=0.3d+5-3+0.1d

then combining like terms you get

0.2d-1.2=(0.3d+0.1d)+(5+-3)

0.2d-1.2=0.4d+2

then subtract 0.4d from both sides leaving you with

-0.2d-1.2=2

then add 1.2 to both sides

-0.2d=3.2

after you divide both sides by -0.2

leaving you with the answer

D= -16

7 0

2 years ago

Read 2 more answers

the legs of a right triangle are 4 units and 7 units. What is the length of the hypotenuse? Select one: a. square root 33 units

Mrac [35]

$\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{4^2+7^2}\implies c=\sqrt{65}$

4 0

3 years ago

Read 2 more answers

. If cosec x = √10, cos x =

lorasvet [3.4K]

Step-by-step explanation:

Hey, there!!

Answer: See in pictures.

I hope you are searching this.....

5 0

2 years ago