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2 years ago

Write the condition under which the hcf of the given algebraic expression is 1

Mathematics

1 answer:

solong [7]2 years ago

6 0

Answer:

A HCF is the highest common factor between 2 or more numbers. because every number times 1 is equal to itself, every 2 numbers have a common factor of 1.

HCF between 2 numbers a,b or expressions such that a and b are not equal to 0 , will never be 0 , because of the simple fact that anything times 0 is equal to 0 , and we stated that a,b isn’t equal to 0 , so that’s a contradiction.

Since you stated that there is no common factor bigger or lower than 1 between the 2 numbers (which means that the two numbers are equal to each other and equal to 1 or 0 , think about it yourself a little bit) that means that the only factor is 1 when the two numbers are not 1 , and 0 or anything if the two numbers are 0 , because again, every number times 0 is equal to 0 .

So finally, there is not HCF if the two numbers stated are both 0 , and the only other possibility is for them to be 1 , and in this case, the HCF will be 1 .

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gizmo_the_mogwai [7]

Answer:

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Step-by-step explanation:

since it is a 45, 45, 90 triangle

both Z and Y will be the same length

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Since the length of this triangle's hypotenuse is $10\sqrt{2}$ the side length would be 10

Hope that helps :)

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3 years ago

A retail store is offering a series discount of 10/10 on a dishwasher with a list price of $346. Find the net cost after the ser

lutik1710 [3]

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3 years ago

The mean annual income for people in a certain city is 37 thousand dollars, with a standard deviation of 28 thousand dollars. A

Aloiza [94]

Answer:

$P( 31 < \bar X< 41)$

And we can ue the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using this formula we got for the limits:

$z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515$

$z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01$

So we want to find this probability:

$P(-1.515$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the annual income of a population, and for this case we know the following info:

$\mu=37$ and $\sigma=28$ and we are omitting the zeros from the thousand to simplify calculations

We select a sample size of n=50>30.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we want to find this probability:

$P( 31 < \bar X< 41)$

And we can ue the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using this formula we got for the limits:

$z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515$

$z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01$

So we want to find this probability:

$P(-1.515$

4 0

3 years ago

Write the condition under which the hcf of the given algebraic expression is 1​

Write the condition under which the hcf of the given algebraic expression is 1