2 years ago

Prove that there exists a pair of consecutive integers such that one of these integers is a perfect square

Mathematics

1 answer:

mr Goodwill [35]2 years ago

7 0

Horrible wording but I'll say 0 squared and 1 squared

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A sequence is defined recursively using the formula f(n + 1) = –0.5 f(n) . If the first term of the sequence is 120, what is f(5

balu736 [363]

Hello,

$f(1)=120\\
 f(2)=-\frac{1}{2}*120=-60\\ 
 f(3)=-\frac{1}{2} *(-60)=30\\ 
 f(4)=-\frac{1}{2} *(30)=-15\\ 
 f(5)=-\frac{1}{2} *(-15)=\frac{15}{2}\\
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A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random

Harlamova29_29 [7]

Answer with explanation:

Given : Sample mean = $\overline{x}=\text{48.47 pounds}$

Standard deviation : $\sigma=\text{ 3.1 pounds.}$

Sample size : n = 36

Claim : $\mu\neq50$

∴ $H_0:\mu=50$

$H_1:\mu\neq50$

Since the alternative hypothesis is two tail , then the test is two tail test.

By using a z statistic and a 0.05 level of significance. Reject $H_0$ if z < -1.960 or is z> 1.960.

Then , the test static for population mean is given by :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$z=\dfrac{48.47-50}{\dfrac{3.1}{\sqrt{36}}}\approx-2.96$

We reject $H_0$ since $-2.96\leq -1.96$ . We have statistically significant evidence at $\alpha=0.05$ to show that the mean amount of garbage per bin is not different from 50.