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3 years ago

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The population of a city, P, in millions, is a function of t, the number of years since 2010, so P=f(t). What does the statement

f(5)=10 mean in terms of the population of this city?

1 answer:

Crazy boy [7]3 years ago

4 0

Answer:

$f(5) = 10$

The population of city is 10 millions in year 2015 that is 5 years after 2010.

Step-by-step explanation:

We are given the following information in the question:

The population of a city, P, in millions, is a function of t.

$P= f(t)$

where P is the population of city in millions and t is the number of years after 2010.

We have to interpret the meaning o the statement f(5) = 10.

$f(5) = 10$

Interpretation:

Comparing the relation we get,

It means that the population of city is 10 millions in year 2015 that is 5 years after 2010.

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Step-by-step explanation:

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Rena spent 6 days reading her book completing the same fraction of the book each day if she had a total of 8/9 of her book after

Artyom0805 [142]

Answer:

The fraction of the book that Rena read every day is $\frac{4}{27}$

Step-by-step explanation:

Rena spent 6 days reading her book completing the same fraction of the book every day and you want to know the fraction of the book she read each day. Knowing that Rena had a total of 8/9 of her book read after 6 days, then you simply divide the total amount of the book read during those days by 6, the number of days:

$\frac{8}{9}$ ÷6

To divide a fraction by a whole number, you must convert the whole number into a fraction, finding the reciprocal of that fraction, and multiply it by the first fraction. That is, you must find the reciprocal of the number that is after the division symbol; and then you multiply the first number (the one before the division symbol) by the reciprocal of the second number (the one after the division symbol). Remember that to find the reciprocal of a number, you simply have to change the numerator and denominator of the number.

Since 6 can be considered to be a fraction equal to $\frac{6}{1}$ , by inverting the number, then you get $\frac{1}{6}$

Then:

$\frac{8}{9}$ ÷6= $\frac{8}{9} *\frac{1}{6}$

Now you multiply the numerators and denominators of the fraction to get the new numerator and denominator of the final solution.

$\frac{8}{9}$ ÷6= $\frac{8}{9} *\frac{1}{6}=\frac{8*1}{9*6} =\frac{8}{54}$

Finally, simplifying the fraction:

$\frac{8}{9}$ ÷6= $\frac{8}{9} *\frac{1}{6}=\frac{8*1}{9*6} =\frac{8}{54}=\frac{4}{27}$

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$\frac{8}{9}$ ÷6= $\frac{4}{27}$

<u><em>The fraction of the book that Rena read every day is </em></u> $\frac{4}{27}$ <u><em></em></u>

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3 years ago

Based on historical data, your manager believes that 26% of the company's orders come from first-time customers. A random sample

scoundrel [369]

Answer:

$\hat p \sim N( p, \sqrt{\frac{p (1-p)}{n}})$

And we can use the z score formula given by:

$z = \frac{\hat p -\mu_p}{\sigma_p}$

And if we find the parameters we got:

$\mu_p = 0.26$

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And we can find the z score for the value of 0.4 and we got:

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And we can find this probability:

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And if we use the normal standard table or excel we got:

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Step-by-step explanation:

For this case we have the following info given:

$p = 0.26$ represent the proportion of the company's orders come from first-time customers

$n=158$ represent the sample size

And we want to find the following probability:

$p(\hat p >0.4)$

And we can use the normal approximation since we have the following two conditions:

1) np = 158*0.26 = 41.08>10

2) n(1-p) = 158*(1-0.26) = 116.92>10

And for this case the distribution for the sample proportion is given by:

$\hat p \sim N( p, \sqrt{\frac{p (1-p)}{n}})$

And we can use the z score formula given by:

$z = \frac{\hat p -\mu_p}{\sigma_p}$

And if we find the parameters we got:

$\mu_p = 0.26$

$\sigma_p = \sqrt{\frac{0.26(1-0.26)}{158}} = 0.0349$

And we can find the z score for the value of 0.4 and we got:

$z = \frac{0.4-0.26}{0.0349}= 4.0119$

And we can find this probability:

$P(z>4.0119) = 1-P(z$

And if we use the normal standard table or excel we got:

$P(z>4.0119) = 1-P(z$

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