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Anestetic [448]
2 years ago
12

P:-3x + 8x - 5x = x q: (3x)(5y) = 15xy Which of the following statements is false?

Mathematics
1 answer:
Varvara68 [4.7K]2 years ago
5 0

Answer: Statement p is false.

Step-by-step explanation:

In both cases, we need to isolate the variables:

p: -3*x + 8*x - 5*x = x

   (-3*x - 5*x) + 8*x = x

    -8x + 8*x = x

        0 = x

This will be true only for one value of x, so this is not always true, which means that the statement is false.

q: (3*x)*(5*y) = 15*x*y

let's solve the left side:

  3*x*5*y = 15*x*y

  (3*5)*(x*y) = 15*x*y

   15*x*y = 15*x*y

This is true for every value of x and y, then this statement is true.

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Answer:

X \sim N(114.8,13.1)  

Where \mu=114.8 and \sigma=13.1

We are interested on this probability

P(X>140)

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:

And we can find this probability using the complement rule:

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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 to the 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(114.8,13.1)  

Where \mu=114.8 and \sigma=13.1

We are interested on this probability

P(X>140)

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>140)=P(\frac{X-\mu}{\sigma}>\frac{140-\mu}{\sigma})=P(Z>\frac{140- 1114.8}{2.6})=P(z>1.924)And we can find this probability using the complement rule:

P(z>1.924)=1-P(z

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