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3 years ago

Least common denominator of 7/9 and 2/3

2 answers:

8 0

First of all, we need to think what is the Greatest Common Factor of 3 and 9.

The answer is 3 because both sets of factors have the highest factor of 3.

Next we have to multiply the Greatest Common Factor to 3. So, 3 x 3= 9.

The answer isn’t just 9, your answer can be in fractions, I heard this saying when I was in middle school, “Whatever you do to the bottom, you have to do it to the top”.

If we follow that saying, we can get our answer. So 3 was what we were multiplying by to get 9, so we have to do it to the numerator.

7x3= 21, But sometimes they trick you, you cannot do 7x3 because the denominator is the LCD, (Least Commen Denominator”.

So that answer is the same, 7/9.

The saying we used before has to go into our next problem, 3 was the number we used to multiply, so we will multiply 2 by 3 and 2 by 2.

2 x 2= 4
2 x 3= 6

For that equation, the answer is 4/6.

So we learned that to solve this problem, we need to use Greatest Common Factor, Multiplication for basic problems, and Least Common Denominator.

We also learned how to find the answer and it showed us what to do Step by Step.

For anymore information, please ask me in comments below and I would be glad to help, I also recommend if your busy, ask your teacher of guidance counselor or any adult that has at least a high school diploma.

Thank you for asking, we appreciate it and we love to help you even more!

Have a great evening everyone and stay Brainly! :))

Margaret [11]3 years ago

7 0

Answer: 9

Step-by-step explanation: The common denominator will be the least common multiple for the two denominators.

To find the least common multiple or lcm of 3 and 9, begin by listing the first few multiples for each number.

Multiples of 6

1 × 9 = 9

2 × 9 = 18

3 × 9 = 27

Notice that we skipped 0 × 9 in our list of multiples. That's because 0 × 6 is 0 according to the zero property of multiplication and our least common multiple can't be 0.

When listing the multiples of 3, it's a good idea to keep an eye on the list of multiples for 9 so that we will notice when we find a least common multiple.

Multiples of 3

1 × 3 = 3

2 × 3 = 6

3 × 3 = 9

Notice that in both lists, we have the least common multiple which is 9.

Therefore, the least common denominator of 9 and 3 is 9.

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Answer:

a) $P( X$

We want this probability:

$P( X >64)$

And using the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

We got:

$P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316$

b) For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674$

And if we solve for a we got

$a=42 +0.674*5.5=45.707$

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.

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".

Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(42,25.5)$

Where $\mu=42$ and $\sigma=5.5$

And we want this probability:

$P( X$

And using the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

We got:

$P( X$

We want this probability:

$P( X >64)$

And using the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

We got:

$P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316$

Part b

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674$

And if we solve for a we got

$a=42 +0.674*5.5=45.707$

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.

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I think

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