There are 350 toy boats made in every 45 min what is the ratio

What is the remainder of x^5+2x^4+9x^3-6x^2+3x+3165 divided by x-5

riadik2000 [5.3K]

Answer:

8530

Step-by-step explanation:

The remainder is 5⁵ + 2(5)⁴ + 9(5)³ - 6(5)² + 3(5) + 3165 = 8530

4 0

2 years ago

What is the inverse of the function f(x) = 8x+1

Yanka [14]

Answer:

f⁻¹(x) = (x - 1)/8

Or

f⁻¹(x) = 1/8 x - 1/8

Step-by-step explanation:

To find the inverse of a function, switch the "x" and "y" variables, then isolate "y".

Remember "f(x)" is the same thing as "y". Change from function notation to "y".

f(x) = 8x + 1

y = 8x + 1

Switch the "x" and "y" variables

x = 8y + 1

Isolate "y". Move the "y" variable to the left for standard formatting

8y + 1 = x

8y + 1 - 1 = x - 1 Subtract 1 from both sides

8y = x - 1

$\frac{8y}{8}=\frac{x-1}{8}$ Divide both sides by 8 and simplify

$y=\frac{x-1}{8}$ Inverse equation

$y=\frac{1}{8}x-\frac{1}{8}$ Slope-intercept form

Use function notation, change "y"

$f^{-1}(x)=\frac{x-1}{8}$ Simplified

$f^{-1}(x)=\frac{1}{8}x-\frac{1}{8}$ Slope-intercept form

6 0

3 years ago

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] .

(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

What is the prime factorasation tree of 36

Oduvanchick [21]

36 = 3squared x 2squared

8 0

3 years ago

A rhombus has a base of 5.2 meters and a height of 4.5 meters. The rhombus is divided into two identical triangles. What is the

Lisa [10]

Answer:

11.7 m²

Step-by-step explanation:

What is the area of each triangle ?

A = b×h/2

= 5.2m×4.5m/2

= 23.4m²/2

= 11.7 m²

3 0

3 years ago