Explain why each table determine if y is proportional to x .

Mathematics

1 answer:

lesya692 [45]3 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

If y is proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

To find k divide both sides by x

k = $\frac{y}{x}$

This value must be constant for all ordered pairs, thus

k = $\frac{4}{6}$ = $\frac{2}{3}$

k = $\frac{6}{9}$ = $\frac{2}{3}$

k = $\frac{8}{12}$ = $\frac{2}{3}$

k = $\frac{2}{3}$

Since k is constant for all ordered pairs then y is proportional to x

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You are given 1000 one dollar bills and 10 envelopes. Put the bills into the envelopes in such a way that someone can ask you fo

taurus [48]

Answer:

We can do it with envelopes with amounts $1,$2,$4,$8,$16,$32,$64,$128,$256 and $489

Step-by-step explanation:

Observe that, in binary system, 1023=1111111111. That is, with 10 digits we can express up to number 1023.

This give us the idea to put in each envelope an amount of money equal to the positional value of each digit in the representation of 1023. That is, we will put the bills in envelopes with amounts of money equal to $1,$2,$4,$8,$16,$32,$64,$128,$256 and $512.

However, a little modification must be done, since we do not have $1023, only $1,000. To solve this, the last envelope should have $489 instead of 512.

Observe that:

1+2+4+8+16+32+64+128+256+489=1000
Since each one of the first 9 envelopes represents a position in a binary system, we can represent every natural number from zero up to 511.
If we want to give an amount "x" which is greater than $511, we can use our $489 envelope. Then we would just need to combine the other 9 to obtain x-489 dollars. Since $x-489\leq511$ , by 2) we know that this would be possible.