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jasenka [17]
3 years ago
6

A student says that if 5x2 = 20, then x must be

Mathematics
1 answer:
lutik1710 [3]3 years ago
4 0

Answer:

I agree with the student's answer. "x" cannot be -2 because then it would make -20 which is not equal to 20:

5(-2)(2) = ?

-10 x 2 = ?

? = -20

-20 ≠ 20

Step-by-step explanation:

Justificaiton:

5(x)(2) = 20

10(x) = 20

10/10(x) = 20/10

x = 2

Second Justification:

5(x)(2) = 20

5/5(x)(2) = 20/5

2x = 4

2x/2 = 4/2

x = 2

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A consumer survey indicates that the average household spendsμ= $185on groceries each week. The distribution of spending amounts
Vitek1552 [10]

Answer:

P(X>200)=P(\frac{X-\mu}{\sigma}>\frac{200-\mu}{\sigma})=P(Z>\frac{200-185}{25})=P(Z>0.6)

And we can find this probability using the complement rule and with the normal standard table or excel:

P(Z>0.6)=1-P(z

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 average household spent of a population, and for this case we know the distribution for X is given by:

X \sim N(185,25)  

Where \mu=185 and \sigma=25

We are interested on this probability

P(X>200)

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>200)=P(\frac{X-\mu}{\sigma}>\frac{200-\mu}{\sigma})=P(Z>\frac{200-185}{25})=P(Z>0.6)

And we can find this probability using the complement rule and with the normal standard table or excel:

P(Z>0.6)=1-P(z

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When an equation is written in the form ...

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