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2 years ago

What is the greatest integer that always divides the difference of the squares of any two different positive odd integers?

Mathematics

1 answer:

Anastasy [175]2 years ago

4 0

Answer:

The greatest integer is 8.

Step-by-step explanation:

Odd positive integers are positively directed numbers that can not be divided into to equal values without a remainder. Examples are: 1, 3, 5, 7, 9 etc.

Given the following positive odd integers:

i. 9 and 3

$9^{2}$ - $3^{2}$ = 81 - 9

= 72

ii. 3 and 1,

$3^{2}$ - $1^{2}$ = 9 - 1

= 8

iii. 7 and 5

$7^{2}$ - $5^{2}$ = 49 - 25

= 24

iv. 21 and 13

$21^{2}$ - $13^{2}$ = 441 - 169

= 272

Therefore, it can be observed that the greatest integer that always divides the difference is 8.

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A lathe is set to cut bars of steel into lengths of 6 cm. The lathe is considered to be in perfect adjustment if the average len

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Answer:

$t=\frac{5.97-6}{\frac{0.4}{\sqrt{93}}}=-0.723$

E. -0.723

$df=n-1=93-1=92$

$p_v =2*P(t_{(92)}$

Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.

Step-by-step explanation:

Information provided

$\bar X=5.97$ represent the sample mean for the length

$s=0.4$ represent the sample standard deviation

$n=93$ sample size

$\mu_o =6$ represent the value that we want to test

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value for the test

System of hypothesis

We need to conduct a hypothesis in order to check if the lathe is in perfect adjustment (6cm), then the system of hypothesis would be:

Null hypothesis: $\mu = 6$

Alternative hypothesis: $\mu \neq 6$

since we don't know the population deviation the statistic is:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing in formula (1) we got:

$t=\frac{5.97-6}{\frac{0.4}{\sqrt{93}}}=-0.723$

E. -0.723

P value

The degrees of freedom are given by:

$df=n-1=93-1=92$

Since is a two tailed test the p value would be:

$p_v =2*P(t_{(92)}$

Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.

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3 years ago

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Do 5 2/6-2 4/6 which =_____

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Factor the common factor out of 8x^3+12x

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3 years ago

Read 2 more answers

A book sold 35,300 copies in its first month of release. Suppose this represents 6.3 of the numbers sold to date. How many copie

skelet666 [1.2K]

Answer:

560,317.460

Step-by-step explanation:

The computation of copies that have been sold is shown below:-

we assume the number of copies is x

So, the number of copies in the first month is

= $\frac{6.3}{100} x$

As per the situation the number of sold copies is 35,300 so the equation will be

$\frac{6.3}{100} x = 35,300$

$6.3x = 35,300\times 100$

$x = \frac{35,300\times 100}{6.3}$

after solving the above equation we will get the number of copied that have been sold to date

= 560,317.460

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3 years ago