Please help this seems impossible.

Prove that among 502 positive integers, there are always two integers so that either their sum or their difference is divisible

kondaur [170]

Answer:

We conlude that always exists two integers so that either their sum or their difference is divisible by 1000.

Step-by-step explanation:

We have a 502 positive integers. Therefore we have a numbers 1, 2, 3,.., 500, 501, 502.

For the sum, we can choose the numbers 502 and 488. We get

(502+488)/1000=1000/1000=1.

For the difference, we can choose the numbers 1 and 501. We get

(1-501)/1000=-500/1000=-0.5.

We conlude that always exists two integers so that either their sum or their difference is divisible by 1000.

5 0

3 years ago

Pretty sure this is super easy I'm just an idiot pls help!

KiRa [710]

The correct answer is B. monomial because all of the terms are combine-able.

8 0

3 years ago

Read 2 more answers

Which graph represents y=3 sqrt x+6- 3?

Llana [10]

Answer:

quadrilateral graph I think if you get the answer please inform me

3 0

3 years ago

What is quotient of -120 and 4 decreased by two?

o-na [289]

Answer:

-118

Step-by-step explanation: -120 + 4 - 2 = 118

4 0

3 years ago

Read 2 more answers

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 100100 engin

Margaret [11]

Answer:

Null hypothesis: $\mu \geq 7.3$

Alternative hypothesis: $\mu < 7.3$

$z=\frac{7.2-7.3}{\frac{0.81}{\sqrt{100}}}=-1.235$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so then we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=7.2$ represent the sample mean

$\sigma=0.81$ represent the population standard deviation

$n=100$ sample size

$\mu_o =7.3$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean pressure is lower than the specificated value 7.3, the system of hypothesis are :

Null hypothesis: $\mu \geq 7.3$

Alternative hypothesis: $\mu < 7.3$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{7.2-7.3}{\frac{0.81}{\sqrt{100}}}=-1.235$

4) P-value

Since is a one-side lower test the p value would given by:

$p_v =P(z$

5) Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.

7 0

3 years ago