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fgiga [73]
3 years ago
7

It takes a total of 6 hours to fill up an inground backyard pool using a standard house. A function can represent this situation

to represent the amount of water in the pool until it is full a function of time the hose is running. Determine the domain for the function
Mathematics
1 answer:
frez [133]3 years ago
5 0

Answer:

All real numbers between 0 and 6

Step-by-step explanation:

We know, the function represents 'the amount of water in the pool until it is full'.

That is, 'It is a function of time giving the value of amount of water in the pool until it is full'.

So, we get that,

The domain is representing the time in which the pool is filled completely.

As, we are given that,

Maximum time taken to completely fill the pool = 6 hours.

So, the domain of the functions is 'All real numbers between 0 and 6'.

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5456.3 mi to the nearest mile
blondinia [14]

Answer:

54.56

Step-by-step explanation:

The number after the point is not 5 or higher

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3 years ago
Joseph uses 30 grams of sugar and 24 grams of butter.
Nutka1998 [239]

Answer:

check step by step

Step-by-step explanation:

A) 30 divided by 24

B) 24 divided by 30

4 0
2 years ago
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Find 2× - 2y + 5z - 2x - y + 3z
natka813 [3]
<span>-3y+8z your welcome:)</span>
4 0
3 years ago
A group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decre
Dmitry [639]

Using the t-distribution, it is found that since the p-value of the test is of 0.0302, which is <u>less than the standard significance level of 0.05</u>, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.

At the null hypothesis, it is <u>tested if the consumption is not different</u>, that is, if the subtraction of the means is 0, hence:

H_0: \mu_1 - \mu_2 = 0

At the alternative hypothesis, it is <u>tested if the consumption is different</u>, that is, if the subtraction of the means is not 0, hence:

H_1: \mu_1 - \mu_2 \neq 0

Two groups of 22 patients, hence, the standard errors are:

s_1 = \frac{45.1}{\sqrt{22}} = 9.6154

s_2 = \frac{26.4}{\sqrt{22}} = 5.6285

The distribution of the differences is has:

\overline{x} = \mu_1 - \mu_2 = 52.1 - 27.1 = 25

s = \sqrt{s_1^2 + s_2^2} = \sqrt{9.6154^2 + 5.6285^2} = 11.14

The test statistic is given by:

t = \frac{\overline{x} - \mu}{s}

In which \mu = 0 is the value tested at the null hypothesis.

Hence:

t = \frac{25 - 0}{11.14}

t = 2.2438

The p-value of the test is found using a <u>two-tailed test</u>, as we are testing if the mean is different of a value, with <u>t = 2.2438</u> and 22 + 22 - 2 = <u>42 df.</u>

  • Using a t-distribution calculator, this p-value is of 0.0302.

Since the p-value of the test is of 0.0302, which is <u>less than the standard significance level of 0.05</u>, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.

A similar problem is given at brainly.com/question/25600813

4 0
3 years ago
Use integration by parts to derive the following formula from the table of integrals.
emmasim [6.3K]

Answer:

I= (x^n)*(e^ax) /a - n/a ∫ (e^ax) *x^(n-1) dx +C (for a≠0)

Step-by-step explanation:

for

I= ∫x^n . e^ax dx

then using integration by parts we can define u and dv such that

I= ∫(x^n) . (e^ax dx) = ∫u . dv

where

u= x^n → du = n*x^(n-1) dx

dv= e^ax  dx→ v = ∫e^ax dx = (e^ax) /a ( for a≠0 .when a=0 , v=∫1 dx= x)

then we know that

I= ∫u . dv = u*v - ∫v . du + C

( since d(u*v) = u*dv + v*du → u*dv = d(u*v) - v*du → ∫u*dv = ∫(d(u*v) - v*du) =

(u*v) - ∫v*du + C )

therefore

I= ∫u . dv = u*v - ∫v . du + C = (x^n)*(e^ax) /a - ∫ (e^ax) /a * n*x^(n-1) dx +C = = (x^n)*(e^ax) /a - n/a ∫ (e^ax) *x^(n-1) dx +C

I= (x^n)*(e^ax) /a - n/a ∫ (e^ax) *x^(n-1) dx +C (for a≠0)

5 0
2 years ago
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