In your own words, explain why every natural number is also a rational number but not every rational number is a natural number.

It takes 3 hours for the cats to catch 27 fish in the pond.

Zarko can catch 5 fish per hour.

Manchu can catch 2 fish every 0.5 of an hour, so in an hour, the cat would catch 2 times that, which is 4 fish.

When working together, the cats can catch 4 + 5 = 9 fish per hour

If the cats work for x hours, then they catch 9*x fish.

To get the time that takes them to catch 27 fish we just need to solve the linear equation:

9x = 27

Solving for x:

x = 27/9 = 3

It takes 3 hours for the cats to catch 27 fish in the pond.

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The Inventory Turnover for 2021 is 5.9 times and for 2022 is 10 times.

2021

Inventory Turnover = Cost of Goods sold / Average Inventory

Cost of Goods sold = $1,165,250/[($170,000+$225,000)/2]

Cost of Goods sold = $1,165,250/($395,000/2)

Cost of Goods sold = $1,165,250/197,500

Cost of Goods sold = 5.9 times

2022

Inventory Turnover = Cost of Goods sold / Average Inventory

Cost of Goods sold = $1,525,000/[($225,000+$80,000)/2]

Cost of Goods sold =  $1,525,000/($305,000/2)

Cost of Goods sold =  $1,525,000/152,500

Cost of Goods sold = 10 times

Therefore the Inventory Turnover for 2021 is 5.9 times and for 2022 is 10 times.

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The complete question is:

Pina Colada Corp. switched to a just-in-time inventory system. Its sales and Inventory amounts for 2021 and 2022 are shown below.

                                 2021            2022

Sales revenue $3,360,000  $3,900,000

Cost of goods sold  1,165,250 1,525,000

Beginning inventory  170,000 225,000

Ending inventory        225,000  80,000

Determine the inventory turnover for 2021 and 2022.

Answer:

a)

[tex](x^{2} + 2)(x^{2} + 2)\\x^{4} + 2x^{2} + 2x^{2} + 4\\= x^{4} + 4x^{2} + 4\\[/tex]

b)

[tex](x +1)(x + 1)(x^{2} -2x +3) = (x + 1)^{2} (x^{2} -2x +3)[/tex]

Answer:

"If I know the measures of A and B, I can subtract those measures from 180 to find the measures of the other

two angles."

Step-by-step explanation:

i did it

Answer:

B. x = -6

Step-by-step explanation:

Use a graphing calculator such as desmos and enter each equation, you'll find the only one that falls on (-6, -9) and is perpendicular is B.

Answer:

B. x = -6

Step-by-step explanation:

Answer:

11 inches

Step-by-step explanation:

90 divided by 18 is 5 so each inch is worth 5 cents so 55 cents would give you 11 inches of wire because 55/5 is 11

The spring .2m far when it is compressed on being supported by a mass of 10kg.

Given: Mass of 30 kg which compresses spring by 0.6m

To find: The compression of the spring when it is supported by a mass of 10 kg

Concept: Compression springs are coiled springs that hold mechanical energy in a compressed state. When these springs are subjected to compressive loads, they compress and shorten, capturing and storing significant potential force.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

By using unitary method,

10 is 3 times less than 30.

so, 30/3=10

Also applying the same proportion over the lengths compressed,

we get, 0.6/3=.2

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Answer:

Step-by-step explanation:

a+a=a
→a+a-a=0
→a=0
(proved)

Step-by-step explanation:

[tex]a + a = a[/tex]

[tex]2a = a[/tex]

[tex]2a - a = 0[/tex]

[tex]a = 0[/tex]

Proved.

Answer:

12(x+y)=42

60(y-x)=42

Step-by-step explanation:

12(x+y)=42 (12 seconds, x+y speed each second, 42 metres)

60(y-x)=42 (1 minute = 60 seconds, x-y speed each second, 42 metres)

Answer:

(-2,-1,0,1,2)

(1,4,6,7)

Answer:

Step-by-step explanation:

Let the sides be a, b and c.

The length of one side of a triangle is 2 feet less than three times the length of its second side

The length of the third side is 3/4 of the sum of the lengths of the first two sides:

The perimeter of the triangle is 17.5 feet:

Substitute a with b in the second equation:

Now substitute a and c with b in the third equation and solve for b:

Find the value of a:

Find the value of c:

The sides of the triangle are:

Answer:

4 slices for all the brothers

Step-by-step explanation:

Answer: Look for the closes thing to 10

Step-by-step explanation:

The equation of parabola passing through coordinates A (-2,0), B (-1.5,-2.5), C (0,5), D (1, 0), E (1.5, 2.5), and F (2, 0) is y = -2.5(2x+4)², and the graph is attached.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

The coordinates of the point of parabola A (-2,0), B (-1.5,-2.5), C (0,5), D (1, 0), E (1.5, 2.5), and F (2, 0).

Calculate the equation of parabola by the formula given below,

[tex]y=a(x-h)^2+k[/tex]

Here (h, k) are the coordinates,

Put A (-2,0)

y = a[x- (-2)] ² + 0

y = a(2x + 4)²

Put B (-1.5,-2.5)

y = a[x- (-1.5)]² + (-2.5)

y = a(x + 1.5)² - 2.5

y = 2ax + 3a -2.5

Solve the above equation

a = -2.5

Thus, the equation of the parabola is,

y = -2.5(2x+4)²

Therefore, the equation of parabola passing through coordinates A (-2,0), B (-1.5,-2.5), C (0,5), D (1, 0), E (1.5, 2.5), and F (2, 0) is y = -2.5(2x+4)², and the graph is attached.

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We have an exponential growth. The domain is the set of all real numbers and the range is R: (0, ∞).

Here we have the exponential function:

[tex]h(x) = 125^x[/tex]

Notice that the base, 125, is larger than 1, which means that we have an exponential growth.

Now, the domain of any exponential equation is the set of all real numbers.

For the range, as x tends to negative infinity, the function will tend to zero.

And as x tends to infinity, h(x) also tends to infinity.

So the range is R: (0, ∞).

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Answer:

just multiply 20.50 by 8 and how many days she work in a week

Volume

Volume

The half life of the radioactive Rutherford-265 is;

13.1 hours.

It follows from the task content that the given function represents the decay function of the radioactive material. Since half-life corresponds to the point at which only half of the starting material remains, hence we have;

(1/2) = e ^(-0.053t)

By taking the natural log of both sides, we have;

-0.6931 = -0.053t

Hence, t = -0.6931/ -0.053 = 13.1 hours.

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(a) The differential equation

[tex]y' + \dfrac14 y = 3 + 2 \cos(2x)[/tex]

is linear, so we can use the integrating factor method. We have I.F.

[tex]\mu = \displaystyle \exp\left(\int \frac{dx}4\right) = e^{x/4}[/tex]

so that multiplying both sides by [tex]\mu[/tex] gives

[tex]e^{x/4} y' + \dfrac14 e^{x/4} y = 3e^{x/4} + 2 e^{x/4} \cos(2x)[/tex]

[tex]\left(e^{x/4} y\right)' = 3e^{x/4} + 2 e^{x/4} \cos(2x)[/tex]

Integrate both sides. (Integrate by parts twice on the right side; I'll omit the details.)

[tex]e^{x/4} y = 12 e^{x/4} + \dfrac8{65} e^{x/4} (8\sin(2x) + \cos(2x)) + C[/tex]

Solve for [tex]y[/tex].

[tex]y = 12 + \dfrac8{65} (\sin(2x) + \cos(2x)) + Ce^{-x/4}[/tex]

Given that [tex]y(0)=0[/tex], we find

[tex]0 = 12 + \dfrac8{65} (\sin(0) + \cos(0)) + Ce^0 \implies C = -\dfrac{788}{65}[/tex]

and the particular solution to the initial value problem is

[tex]\boxed{y = 12 + \dfrac8{65} (\sin(2x) + \cos(2x)) - \dfrac{788}{65} e^{-x/4}}[/tex]

As [tex]x[/tex] gets large, the exponential term will converge to 0. We have

[tex]\sin(2x) + \cos(2x) = \sqrt2 \sin\left(2x + \dfrac\pi4\right)[/tex]

which means the trigonometric terms will oscillate between [tex]\pm\sqrt2[/tex]. So overall, the solution will oscillate between [tex]12\pm\sqrt2[/tex] for large [tex]x[/tex].

(b) We want the smallest [tex]x[/tex] such that [tex]y=12[/tex], i.e.

[tex]0 = \dfrac8{65} (\sin(2x) + \cos(2x)) - \dfrac{788}{65} e^{-x/4}[/tex]

[tex]\dfrac{788}{65} e^{-x/4} = \dfrac{8\sqrt2}{65} \sin\left(2x + \dfrac\pi4\right)[/tex]

[tex]\dfrac{197}{\sqrt2} e^{-x/4} = \sin\left(2x + \dfrac\pi4\right)[/tex]

Using a calculator, the smallest solution seems to be around [tex]\boxed{x\approx21.909}[/tex]

Answer:

16 days

Step-by-step explanation:

OK, The pet snail only moves a foot per day because at night it falls again, SO ima going with 16 days.

[<Answer>] (2):
Hello! I'm Avery. And I'm here to help! :)

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[<The Explanation>}:

Sally has  pet snail that fell into a well.

(Depth of the well = 16 feet)

Snail climbs up 5 feet but each night it slides back down 4 feet.

So the snail climbs up per day = 5 feet - 4 feet = 1 feet.

Number of days snail took to reach at 11 feet = 11 × 1 = 11 feet

Remaining distance to cover by the snail = 16 - 11 = 5 feet

Number of days to cover remaining 5 feet to reach the top of the well = 1 day

Therefore, snail will take 12 days to reach the top of the well.

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[<Ending>] <3

Hope this helps and if it's wrong, you can't sue me! :D

Bye! Hope this works for you :)

Have a nice day! - Avery <3

Answer:

The first answer

4x-2y=0

Based on the various assets and liabilities that the family has, the debt ratio can be calculated to be D. 54.1%.

the debt ratio can be found as:

= Total debt / Total assets

Solving:

= (5,500 + 210,000 + 180,000+ 25,000) / (3,000 + 13,000 + 320,000 + 25,000 + 15,000 + 64,000 + 39,000)

= 258,500 / 479,000

= 54.1%

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Answer:

9.6 lbs per acre

Step-by-step explanation:

96lbs for 10acres

96 divided by 10= 9.6 lbs per acre.