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3 years ago

Three rational numbers between 5/31 and 6/31

Mathematics

1 answer:

Ludmilka [50]3 years ago

6 0

Answer:

$\dfrac{26}{155}$ , $\dfrac{27}{155}$ , and $\dfrac{28}{155}$ .

Step-by-step explanation:

What is a rational number? By definition, a rational number can be represented as the fraction of two integers.

The goal is to find three fractions in the form $\dfrac{p}{q}$ between $\dfrac{5}{31}$ and $\dfrac{6}{31}$ .

$\dfrac{5}{31} < \dfrac{p}{q} < \dfrac{6}{31}$ .

At this moment, there doesn't seems to be a number that could fit. The question is asking for three of these numbers. Multiple the numerator and the denominator by a number greater than three (e.g., five) to obtain

$\dfrac{25}{155} < \dfrac{p}{q} < \dfrac{30}{155}$ .

Since $p$ and $q$ can be any integers, let $q = 155$ .

$\dfrac{25}{155} < \dfrac{p}{155} < \dfrac{30}{155}$ .

$\implies 25 < p < 30$ .

Possible values of $p$ are 26, 27, and 28. That corresponds to the fractions

$\dfrac{26}{155}$ , $\dfrac{27}{155}$ , and $\dfrac{28}{155}$ .

These are all rational numbers for they are fractions of integers.

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3 years ago

What is 65.5 percent as a decimal

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

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What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?

Oksanka [162]

Answer:

As x approaches ∞, y approaches -∞

As x approaches -∞, y approaches ∞

Step-by-step explanation:

$f(x) = -x^5 + 9x^4 - 18x^3$

F(x) is a fifth degree (odd function ) with negative leading coefficient

If exponent is odd and leading coefficient is negative then end behavior is

As x approaches ∞, y approaches -∞

As you go on the right , f(x) goes down

As x approaches -∞, y approaches ∞

As you go on the left , f(x) goes up

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Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in

Law Incorporation [45]

Answer:

(a) 900

(b) [567.35 , 1689.72]

(c) [23.82 , 41.11]

Step-by-step explanation:

We are given that a sample of 20 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 30 rooms i.e.;

Sample mean, $xbar$ = 290 Sample standard deviation, s = 30 and Sample size, n = 20

(a) Point estimate of the population variance is equal to sample variance, which is the square of Sample standard deviation ;

$\sigma^{2}$ = $s^{2}$ = $30^{2}$

$\sigma^{2}$ = 900

(b) 90% confidence interval estimate of the population variance is given by the pivotal quantity of $\frac{(n-1)s^{2} }{\sigma^{2} }$ ~ $\chi^{2} __n_-_1$

P(10.12 < $\chi^{2}__1_9$ < 30.14) = 0.90 {At 10% significance level chi square has critical

values of 10.12 and 30.14 at 19 degree of freedom}

P(10.12 < $\frac{(n-1)s^{2} }{\sigma^{2} }$ < 30.14) = 0.90

P( $\frac{10.12}{(n-1)s^{2} }$ < $\frac{1 }{\sigma^{2} }$ < $\frac{30.14}{(n-1)s^{2} }$ ) = 0.90

P( $\frac{(n-1)s^{2} }{30.14}$ < $\sigma^{2}$ < $\frac{(n-1)s^{2} }{10.12}$ ) = 0.90

90% confidence interval for $\sigma^{2}$ = $[\frac{19s^{2} }{30.14} , \frac{19s^{2} }{10.12}]$

= $[\frac{19*900 }{30.14} , \frac{19*900 }{10.12}]$

= [567.35 , 1689.72]

Therefore, 90% confidence interval estimate of the population variance is [567.35 , 1689.72] .

P( $\sqrt{\frac{(n-1)s^{2} }{30.14}}$ < $\sigma$ < $\sqrt{\frac{(n-1)s^{2} }{10.12}}$ ) = 0.90

90% confidence interval for $\sigma$ = $[\sqrt{\frac{19s^{2} }{30.14}} , \sqrt{\frac{19s^{2} }{10.12}} ]$

= [23.82 , 41.11]

Therefore, 90% confidence interval estimate of the population standard deviation is [23.82 , 41.11] .

7 0

3 years ago