How to find two consecutive positive even integers such that their sum is 48?

A recycling plant recycled 4.9 kg of paper and cardboard the first hour and 7.8 kg/h

Daniel [21]

Answer: R = {0kg, 59.5kg}

Step-by-step explanation:

When we have a function f(x) = y.

The set of the possible values of x is called the domain of the function, and the set of the possible values of y is called the range of the function,

In this case, we have that:

the plant recycled 4.9kg the first hour, and 7.8 kg per hour after.

So this function can be written as piecewise function, with one part for the first hour, and another part for the time after the first hour.

F(x) = 4.9kg*x if 0h < x ≤ 1h

F(x) = 4.9kg + 7.8kg/h*(x -1) if x ≥ 1h

We use (x - 1) for the second part because if x = 1 h, we must have the same result in both parts of the function.

Where x is the number of hours.

And we know that the domain is (0hours, 8 hours)

Then the minimum value of y will be:

F(0h) = 4.9kg*0h = 0kg.

And the maximum value in the range will be:

F(8h) = 4.9kg + 7.8kg*7 = 59.5kg

Then the range is:

R = {0kg, 59.5kg}

7 0

3 years ago

The cost of Internet access. How much do users pay for Internet service? Here are the monthly fees (in dollars) paid by a random

Ivanshal [37]

Answer:

$20.9-2.01\frac{7.65}{\sqrt{50}}=18.73$

$20.9+2.01\frac{7.65}{\sqrt{50}}=23.07$

The 95% confidence interval would be given by (18.73;23.07)

Step-by-step explanation:

Assuming these data

20 40 22 22 21 21 20 10 20 20

20 13 18 50 20 18 15 8 22 25

22 10 20 22 22 21 15 23 30 12

9 20 40 22 29 19 15 20 20 20

20 15 19 21 14 22 21 35 20 22

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".

Solution to the problem

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

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

First we need to find the sample mean with the following formula:

$\bar X= \frac{\sum_{i=1}^n X_i}{50}=20.9$

And in order to find the sample standard deviation we can use the following formula:

$s= \sqrt{\frac{\sum_{i=1}^n (x_i -\bar x)^2}{n-1}}=7.65$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=50-1=49$

Since the Confidence is 0.95or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that $t_{\alpha/2}=2.01$

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

$20.9-2.01\frac{7.65}{\sqrt{50}}=18.73$

$20.9+2.01\frac{7.65}{\sqrt{50}}=23.07$

So on this case the 95% confidence interval would be given by (18.73;23.07)

8 0

3 years ago

PLEASE HELP!!! 13 + 7 POINTS!!! THANK YOU!

grin007 [14]

Answer:

7 inches

Step-by-step explanation:

Using Pythagoras' theorem on the right triangle, that is

r² + 11² = 13²

r² + 121 = 169 ( subtract 121 from both sides )

r² = 48 ( take the square root of both sides )

r = $\sqrt{48}$ ≈ 7 in ( to the nearest inch )

6 0

3 years ago

The radius of a sphere is 5 yards. Find the<br> volume of the sphere.

FinnZ [79.3K]

Answer:

V = 523.6 yd³

Step-by-step explanation:

The equation for the volume of a sphere of radius r is

V = (4/3)πr³

and if we substitute 5 yds for r, we get

V = (4/3)*π*(5 yd)³, or

V = (4/3)·π·125 yd³, or approxomately

V = 523.6 yd³

3 0

3 years ago

Help ASAP thank you

sergey [27]

Answer: Choice A

g(x) = sqrt(2x)

====================================================

Explanation:

"sqrt(x)" is shorthand for "square root of x"

f(x) = 3x^2 is given

g( f(x) ) = x*sqrt(6) is also given

One way to find the answer is through trial and error. This would only apply of course if we're given a list of multiple choice answers.

------------------

Let's start with choice A

g(x) = sqrt(2x)

g( f(x) ) = sqrt(2 * f(x) ) .... replace every x with f(x)

g( f(x) ) = sqrt(2 * 3x^2 ) .... plug in f(x) = 3x^2

g( f(x) ) = sqrt(6x^2 )

g( f(x) ) = sqrt(x^2 * 6)

g( f(x) ) = sqrt(x^2)*sqrt(6)

g( f(x) ) = x*sqrt(6)

We found the answer on the first try. So we don't need to check the others.

------------------

But let's try choice B to see one where it doesn't work out

g(x) = sqrt(x + 3)

g( f(x) ) = sqrt( f(x) + 3)

g( f(x) ) = sqrt(3x^2 + 3)

and we can't go any further other than maybe to factor 3x^2+3 into 3(x^2+1), but that doesn't help things much to be able to break up the root into anything useful. We can graph y = x*sqrt(6) and y = sqrt(3x^2 + 3) to see they are two different curves, so there's no way they are equivalent expressions.

8 0

4 years ago

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