A water dispenser fills 4 glasses in 32 seconds. How many glasses will be filled by the dispenser in 128 seconds?

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Ilya [14]

Answer:

ur suppose to subtract

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Researchers are interested if a school breakfast program leads to taller children. Assume that the population of all 5 year-old

DedPeter [7]

Answer:

$39-1.96\frac{1}{\sqrt{25}}=38.608$

$39+1.96\frac{1}{\sqrt{25}}=39.392$

So on this case the 95% confidence interval would be given by (38.608;39.392)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=39$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The margin of error is given by:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

And replacing we got:

$ME= 1.96 *\frac{1}{\sqrt{25}}= 0.392$

Now we have everything in order to replace into formula (1):

$39-1.96\frac{1}{\sqrt{25}}=38.608$

$39+1.96\frac{1}{\sqrt{25}}=39.392$

So on this case the 95% confidence interval would be given by (38.608;39.392)

7 0

2 years ago

What would the answer be?

NikAS [45]

Answer:

11.35%

Step-by-step explanation:

Add all of the numbers together to get the total amount of people who visited.

Add all the numbers in the teen section to find how many teens visited.

If you put teens over whole it will give you the fraction 86/758

If you divide 86 by 758 you will get 0.11345646438 .

Move the decimal two places to the right and round to get the percent 11.35.

7 0

2 years ago

I can't figure this one out...

worty [1.4K]

Answer:

the area would be 36(pi) since you can't find out the exact value of pi (22/7) and where it would terminate so thats the most exact answer you can get. The circumference would be

Step-by-step explanation:

12/2 = 6

Area = (pi)radius^2

6^2 = 36

36(pi)

Circumference: (pi)d

12(pi)

For approximate area you multiply r^2 by 3.14

For approximate circumference you multiply diameter by 3.14

5 0

3 years ago

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Which of the following is NOT a linear factor of the polynomial function?

Natalija [7]

Answer:

Among the four choices, $(x + 5)$ is the only one that is not a linear factor of this polynomial function.

Step-by-step explanation:

Let $a$ denote some constant. A linear factor of the form $(x - a)$ is a factor of a polynomial $f(x)$ if and only if $f(a) = 0$ (that is: replacing all $x$ in the polynomial $f(x) \!$ with the constant $a\!$ would give this polynomial a value of $0$ .)

For example, in the second linear factor $(x - 2)$ , the value of the constant is $a = 2$ . Verify that the value of $f(2)$ is indeed $0$ . (In other words, replacing all $x$ in the polynomial $f(x) \!$ with the constant $2$ should give this polynomial a value of $0\!$ .)

$\begin{aligned}f(2) &= 2^3 - 5\times 2^2 - 4 \times 2 + 20 \\ &= 8 - 20 - 8 + 20 \\ &= 0 \end{aligned}$ .

Hence, $(x - 2)$ is indeed a linear factor of polynomial $f(x)$ .

Similarly, it could be verified that $(x - 5)$ and $(x + 2)$ are also linear factors of this polynomial function.

Rewrite the first linear factor $(x + 5)$ in the form $(x - a)$ for some constant $a$ : $(x + 5) = (x - (-5))$ , where $a = -5$ .

Calculate the value of $f(5)$ .

$\begin{aligned}f(5) &= (-5)^3 - 5\times (-5)^2 - 4 \times (-5) + 20 \\ &= (-125) - 125 + 20 + 20 \\ &= -210\end{aligned}$ .

$f(5) \ne 0$ implies that $(x - (-5))$ (which is equivalent to $(x + 5)$ ) isn't a linear factor of this polynomial function.

3 0

2 years ago