Place the following in least to greatest. 3.24,3.45,3.429,3.024,3,5

Find the smallest positive $n$ such that \begin{align*} n &\equiv 3 \pmod{4}, \\ n &\equiv 2 \pmod{5}, \\ n &\equiv

Alex777 [14]

4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number $x$ such that taking it mod 4, 5, and 7 leaves the desired remainders:

$x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6$

Taken mod 4, the last two terms vanish and we have

$x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4$

so we multiply the first term by 3.

Taken mod 5, the first and last terms vanish and we have

$x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5$

so we multiply the second term by 2.

Taken mod 7, the first two terms vanish and we have

$x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7$

so we multiply the last term by 7.

Now,

$x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147$

By the CRT, the system of congruences has a general solution

$n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}$

or all integers $27+140k$ , $k\in\mathbb Z$ , the least (and positive) of which is 27.

3 0

3 years ago

There are over 2700 species of snakes in the world over 600 are venomous Express the fraction of species that are not venomous a

Andre45 [30]

You do 600 divided by 2700 and you end up with 22/100 or 0.22 as a decimal. So if 0.22 or 22/100 are venimous then 78/100 or 0.78 are non venimous. I understand its a bit confusing and i can simplify it for you but still I hope this helps :)

6 0

2 years ago

77 over 200 as mixed number as a decimal

e-lub [12.9K]

Every mixed number is (a whole number) + (a piece of another one).
So every mixed number must be bigger than ' 1 ', because ' 1 ' is the
smallest whole number.

77/200 is less than ' 1 ', because the numerator is less than the
denominator. So it doesn't have what it takes to be a whole number.

Every fraction is a short way to write a division problem. It means

(the top number) divided by (the bottom number).

When you actually do the division, the answer is the decimal form
of the fraction.

When you divide 77 by 200 , you get 0.385 .

6 0

2 years ago

Find the value of x and then the measure of Arc XYZ and Arc XZ. Show work on a piece of paper.

Westkost [7]

Given:

The measure of arc XY is (31x)°

The measure of arc YZ is (35x - 16)°

We need to determine the value of x, measure of arc XYZ and arc XZ.

Value of x:

From the figure, it is obvious that the arcs XY and YZ are congruent.

Thus, we have;

$31x=35x-16$