Which number is bigger: 0.135 or 0.14?

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

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] .

(c) 90% confidence interval estimate of the population standard deviation is given by ;

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

Factorize: a^4+2xa³+a²x²-y^4

mart [117]

Answer:

(a^2+ax-y) (a^2+ax+y^2)

Step-by-step explanation:

a^4+2xa³+a²x²-y^4

(a^2+ax)^2-y^4

(a^2+ax-y) (a^2+ax+y^2)

4 0

3 years ago

Read 2 more answers

An alrcraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on

rewona [7]

C(x) should be ;

C(x)=0.9x² - 306x +36,001

Answer:

$9991

Step-by-step explanation:

Given :

C(x)=0.9x^2 - 306x +36,001

To obtain minimum cost :

Cost is minimum when, C'(x) = 0

C'(x) = 2(0.9x) - 306 = 0

C'(x) = 1.8x - 306 = 0

1.8x - 306 = 0

1.8x = 306

x = 306 / 1.8

x = 170

Hence, put x = 170 in C(x)=0.9x²- 306x +36,001 to obtain the

C(170) = 0.9(170^2) - 306(170) + 36001

C(170) = 26010 - 52020 + 36001

= 9991

Minimum unit cost = 9991

5 0

3 years ago

Y^2(3y−4) + 7(3y−4) Factor the polynomial as the product of two binomials.

Usimov [2.4K]

First, factor the (3y-4) and group the remaining terms
y²(3y-4) +7 (3y-4)
(y²+7)(3y-4)
I hope this helps (:

7 0

3 years ago

Read 2 more answers

Please help solve this, I’ve tried my best. My answers are a height of 6.7 using 30-60-90 as a last resort, and the glass volume

Neko [114]

Answer:

A) To ensure the correct and exact straight height

B) 15 inches

C) 24.87 in $^{3}$

Step-by-step explanation:

Hello! Lets start!

First, it asks us to explain why the two bases must be parallel. In order to measure the correct and exact height, we must be sure that the bases are parallel, or else there would be a range of heights; in order to ensure that you are measuring a straight distance, they must be parallel!

Second, it asks us to identify the height of cone. To do this, we must make a slope! We can see that, for every time we go down 5 inches, we lose 1 inch of our base! Our slope in this situation would be -5. So, lets continue to see how long before the cone reaches its tip, in which the base would be equal to 0. At 5 inches, our base is 2 inches. At 10 inches, our base is 1 inch. At 15 inches, we do not have a base, as it equals 0! So therefore, our cone height is 15 inches.

Third, it asks us to identify the volume of the cup, which is also called a <em>circular truncated cone. </em>To do so, we can use the formula:

₁ $V = \frac{1}{3} \pi (r_{1}^2 + r_{1}r_{2} + r_2^2)h$

Lets plug in our information!

$V = \frac{1}{3} \pi (1.5^{2} + (1.5)(1) + 1^{2}) (5)\\V = 24.87$

Hope this helps! Remember, math is fun!

3 0

3 years ago

Which number is bigger: 0.135 or 0.14?￼

Which number is bigger: 0.135 or 0.14?