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Arte-miy333 [17]
3 years ago
7

Find the component form of the vector that translates P(4,5) to p'.

Mathematics
1 answer:
Veronika [31]3 years ago
4 0

Answer:

Component form : (-7 , 2)

Step-by-step explanation:

P(4 , 5) = P'(4 +x , 5+y) = P'(-3 , 7)

4 + x = -3

    x = -3 - 4

    x = -7

5 + y = 7

     y = 7 - 5

     y = 2

Vector form : -7i + 2j

Component form : (-7 , 2)

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Answer:

We conclude that young women are delaying marriage and marrying at a later age.

Step-by-step explanation:

We are given that the average age of brides marrying for the first time is 23.9 years with a population standard deviation of 4.2 years.

The sociologist randomly samples 100 marriage records and determines the average age of the first time brides is 24.9 years.

Let \mu = <u><em>average age of brides marrying for the first time.</em></u>

So, Null Hypothesis, H_0 : \mu = 23.9 years     {means that young women are not delaying marriage and marrying at a later age}

Alternate Hypothesis, H_A : \mu > 23.9 years     {means that young women are delaying marriage and marrying at a later age}

The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;

                         T.S. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample average age of the first time brides = 24.9 years

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So, <u><em>the test statistics</em></u>  =  \frac{24.9-23.9}{\frac{4.2}{\sqrt{100} } }

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The value of z test statistics is 2.381.

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Since our test statistic is more than the critical value of z as 2.381 > 2.326, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.

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