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Temka [501]
3 years ago
8

What is the answer to this problem 1.5(x + 4) – 3 = 4.5(x – 2)?

Mathematics
2 answers:
erastova [34]3 years ago
7 0

Answer:

x = 4

Step-by-step explanation:

1.5(x + 4) – 3 = 4.5(x – 2)

Distributive property

1.5x + 6 - 3 = 4.5x - 9

1.5x + 3 = 4.5x - 9

1.5x - 4.5x = -9 -3

-3x = -12

  x = 4

MakcuM [25]3 years ago
6 0

Expand

1.5x + 6 - 3 = 4.5x - 9

Simplify 1.5x + 6 - 3 to 1.5x + 3

1.5x + 3 = 4.5x - 9

Subtract 1.5x from both sideds

3 = 4.5x - 9 - 1.5x

Simplify 4.5x - 9 - 1.5x to 3x - 9

3 = 3x - 9

Add 9 to both sides

3 + 9 = 3x

Simplify 3 + 9 to 12

12 = 3x

Divide both sides by 3

12/3 = x

Simplify 12/3 to 4

4 = x

Switch sides

<u>x = 4</u>

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Answer:

P(X>1000)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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If we apply this formula to our probability we got this:

P(X>1000)=P(\frac{X-\mu}{\sigma}>\frac{1000-\mu}{\sigma})=P(Z>\frac{1000-950}{50})=P(z>1)

And we can find this probability using the complement rule and the normal standard table and we got:

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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 problem

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

X \sim N(950,50)  

Where \mu=950 and \sigma=50

We are interested on this probability

P(X>1000)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

P(X>1000)=P(\frac{X-\mu}{\sigma}>\frac{1000-\mu}{\sigma})=P(Z>\frac{1000-950}{50})=P(z>1)

And we can find this probability using the complement rule and the normal standard table and we got:

P(z>1)=1-P(z

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