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anyanavicka [17]
3 years ago
9

The product of two rational numbers is irrational.

Mathematics
1 answer:
PtichkaEL [24]3 years ago
7 0

Answer:

The statement is false.

Step-by-step explanation:

Here we need to remember some things:

Integer numbers are closed under multiplication.

This means that for two integers a and b, the product a*b is also an integer.

A rational number is a number that can be written as the quotient of two integer numbers.

An irrational number is a number that can't be written as the quotient of two rational numbers.

Now let's see the statement:

"The product of two rational numbers is irrational."

The product of two rational numbers is written as:

\frac{a}{b} *\frac{c}{d}

Where a, c, b, and d are integers.

We can rewrite that product as:

\frac{a*c}{b*d}

Because of the first property, we know that a*c is an integer, and b*d is also an integer, so here we have a quotient of two integer numbers, so this is a rational number.

Then the product of two rational numbers is a rational number.

Then the statement is false.

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The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books check
Verdich [7]

Answer:

n=(\frac{1.960(150)}{90})^2 =10.67 \approx 11

So the answer for this case would be n=11 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma =150 represent the population standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

The confidence interval for this case is given by: (740, 920)

We can find the estimate for the mean and we got:

\bar X = \frac{740+920}{2} = 830

and the margin of error is given by :

ME = \frac{920-740}{2}= 90

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{s}{\sqrt{n}}    (a)

And on this case we have that ME =90 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} s}{ME})^2   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got z_{\alpha/2}=1.960, replacing into formula (b) we got:

n=(\frac{1.960(150)}{90})^2 =10.67 \approx 11

So the answer for this case would be n=11 rounded up to the nearest integer

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Step-by-step explanation:

20/100=1/5

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Make an argument for why (4^2)^4=(4^4)^2
Eduardwww [97]
I hate when it comes to explaining but I gave it my best!

(4^2)^4 is the same as (4^4)^2 because they’re both being squared and multiplied by the a number equaling to the same number, but written differently.

4^2=16 , whereas 4^4=256
HOWEVER
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Therefore both equal to the same number. It depends on the exponents, and multiplication. If it were to be a different exponent, then they wouldn’t have been the same
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