A tank contains 2480 L of pure water. Solution that contains 0.08 kg of sugar per liter enters the tank at the rate 4 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate.
(a) How much sugar is in the tank at the begining?
y(0)= (kg)
(b) Find the amount of sugar after t minutes.
y(t)= (kg)
(c) As t becomes large, what value is y(t) approaching ? In other words, calculate the following limit. limt→[infinity]y(t)= (kg)

Answer:  The top graph.

Step-by-step explanation:  The inflection is at x = 0, since the absolute value of x starts becoming greater as x decreases.  E.g., at x = -2,

f(x) = |x| - 4

f(x) = |-2| - 4

f(x) = 2 - 4

f(x) = - 2

At x = -4

f(x) = |x| - 4

f(x) = |-4| - 4

f(x) = 4 - 4

f(x) = 0

Answer:

Olivia's puppy, it weighed 5 pounds.

Step-by-step explanation:

Answer: x=7

               ab=21

               bc=14

Step-by-step explanation:

ab=3x

bc=2x±7

ac=42

3x±2x±7=42

5x±7=42

5x=42-7

5x=35

to get the value of x you divide 35 by 5x

35÷5x=7

so the value of x is 7

ab=3x

x=7

3x=7×3x

7×3=21

x=7

2x=7×2x

2×7=14

The amount of money that Britta will pay is; SEK2500

Let the amount paid by Britta scabetala be x

Now, we are told that Britta scabetala half as much as Agda. Thus;

Amount paid by Agda = 2x

Now, Cornelia must pay SEK 1,500 less than Britta. Thus,

Amount paid by Cornelia = x - 1500

Agda must pay five times as much as Cornelia. Thus;

2x = 5(x - 1500)

2x = 5x - 7500

5x - 2x = 7500

3x = 7500

x = 7500/3

x = SEK2500

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Answer:

The correct answer is C. X= 2

Answer:

87,600 minutes

Step-by-step explanation:

Given that practice time by Jonas :

1 hour per day for 2 years :

Bradley practices : 2 hours a day more than Jonas,

How many more minutes does Bradley practice the guitar than Jonas over the course of 2 years

Number of days in a year = 365 days

2 hours per day for (2 * 365) days :

2 * (2 * 365) = 1460 hours

Recall :

60 minutes = 1 hour

(60 * 1460) = 87,600 minutes

Answer:

21. <ABC = 58 Degrees

22. <LMN = 108 Degrees

23. <RSV = 42 Degrees

24. <LHK = 101 Degrees

28. <ABX = 112 Degrees and <CBX = 68 Degrees

29. <RSQ = 32 Degrees and <TSQ = 58 Degrees

30. <DEH = 39 Degrees and <FEH = 51 Degrees

Step-by-step explanation:

21. Add the degrees the find angle ABC

37 + 21 = 58

22. Add the degrees the find angle LMN

85 + 23 = 108

23. For this problem, you are suppose to subtract the angle measure given to you (72 degrees) from the degrees of the whole angle (<RST) to find the missing angle (RSV)

114 - 72 = 42

24. GHK is a straight line, meaning it equals 180 degrees. Subtract 180 from the angle measure given (79) to find the missing angle (LHK).

180 - 79 = 101

28. ABC is a straight line, meaning it equals 180 degrees. This also means that ABX + CBX = 180. First, find x, then use x to find the measures of ABX and CBX.

(14x + 70) + (20x + 8) = 180

Add Like Terms

34x + 78 = 180

Subtraction Prop. of Eq.

34x = 102

x = 3

Now, you can find the angle measures

14 * 3 + 70 = 112

20 * 3 + 8 = 68

(Make sure to check your work! 112 + 68 does indeed equal 180!)

29. RST is a right angle, meaning it equals 90 degrees. This also means that RSQ + TSQ = 90. First, find x, then use x to find the measures of RSQ and TSQ.

(15x - 43) + (8x + 18) = 90

Add Like Terms

23x - 25 = 90

Addition Prop of Eq.

23x = 115

x = 5

Now, you can find the angle measures

15 * 5 - 43 = 32

8 * 5 + 18 = 58

(Make sure to check your work! 32 + 58 does indeed equal 90!)

30. DEF is once again a right angle, so we follow the same steps from number 29.

13x + (10x + 21) = 90

Add Like Terms

23x + 21 = 90

Subtraction Prop of Eq.

23x = 69

x = 3

Now, you can find the angle measures

13 * 3 = 39

10 * 3 + 21 = 51

(Make sure to check your work! 39 + 51 does indeed equal 90!)

Answer:

"sixty-three hundredths of a Kilometer"

Step-by-step explanation:

Decimal measurements are read based on the place of their digits. In this case, Ajay would read this measurement as "sixty-three hundredths of a Kilometer". This is because the final digit of the decimal form measurement is in the "hundredths" position. One more to the right and it would be in the "thousandths" while one more to the left would be the "tenths"

Answer:

y=2/3x-1/2 where slope is 2/3 and the y-intercept is (0, -1/2).

Step-by-step explanation:

-8x+12y=-6

12y=-6-(-8x)

12y=-6+8x

12y=8x-6

y=8/12x-6/12

y=2/3x-1/2

slope-intercept form is: y=mx+b where m=slope and b=y-intercept.

Answer:

SA=2 bi r h+2 bi r squared

Answer:

The answer is in the 4th quadrant

Step-by-step explanation:

I really hope this helped!!! have a great day. :)

1+C is [-4 -4].

(i) AC = [13 -32 -40]
(ii) A + B = [-5.1 2.7 -2.8]
(iii) AB = [-13.3 10.3 -10.3]
(iv) 4A + 4B = [-20.4 10.8 -11.2]
(v) A + C = [-11 -9 -10]
(vi) 1 + C = [ -4 -4]
(vii) CA = [6 11 8]
(viii) BA = [-6.3 9.9 -9.9]
(ix) B + A = [-5.1 2.7 -2.8]
(x) 4(A + B) = [-20.4 10.8 -11.2]
(a) MATLAB may refuse to do some calculations if they are not mathematically valid. For example, the product of two matrices (AB) must have the same number of columns in the first matrix as the number of rows in the second matrix.
(b) Yes, 4(A + B) = 4A + 4B.
(c) No, AB ≠ BA.
(d) Adding a scalar to a matrix adds the scalar to each element of the matrix. In this case, 1+C is [-4 -4].
(e) Yes, A + B = B + A.

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I'm sorry, but the given information is not sufficient to determine the value of Y. Please provide additional information or clarify the question further.

3.3 ÷ 0.3

3.3 = 33/10

0.3 = 3/10

33/10 ÷ 3/10 = 11

Answer:

The top is independent

The bottom is dependent

Step-by-step explanation:

     The top is independent because it does not rely on another variable. It is the "affector" and not dependent on it.

     The bottom is dependent because it does rely on another variable. It is dependent on this other variable because it will be affected by any changes in that other variable.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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Answer:

A) \(g(x)=\sqrt[3]{x+4}+3\)

Step-by-step explanation:

The transformation that occured in the graph is that the function went up 3 and left 4. Algebraically, this would be \(g(x)=\sqrt[3]{x+4}+3\)

Using translation concepts, it is found that the function g(x) is given by:

Function f(x) is given by:

\(f(x) = \sqrt[3]{x}\)

Looking at the graph, it can be seen that g(x) was shifted left 4 units, hence:

\(g(x) = f(x + 4) = \sqrt[3]{x + 4}\)

Then, it was shifted up 3 units, then:

\(g(x) = f(x + 4) + 3 = \sqrt[3]{x + 4} + 3\)

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Answer:

The measure of AB is 29

Step-by-step explanation:

If a line is drawn from a vertex of a triangle perpendicular to the opposite side to this vertex and bisects it, then the sides joining this vertex are equal in lengths

In Δ ABD

∵ Line AC ⊥ side BD

∵ BC = BD = 15

∴ C is the mid-point of The side BD

∴ Line AC is a perpendicular bisector of side BD

→ By using the rule above

∴ AB = AD

∵ AB = 5x - 11

∵ AD = 3x + 5

→ Equate them

∴ 5x - 11 = 3x + 5

→ Add 11 to both sides

∵ 5x - 11 + 11 = 3x + 5 + 11

∴ 5x = 3x + 16

→ Subtract 3x from both sides

∵ 5x - 3x = 3x - 3x + 16

∴ 2x = 16

→ Divide both sides by 2

∴ x = 8

→ Substitute the value x in the expression of side AB

∵ AB = 5(8) - 11

∴ AB = 40 - 11

∴ AB = 29

∴ The measure of AB is 29

The sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

To calculate the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator we will follow these steps:

Step 1: Calculate the amount of discount = Regular Price × Discount rate

Discount rate = 35/100

Simplifying the value we have:

Discount rate = 0.35

Amount of discount = 91 × 0.35

Amount of discount = $31.85

Step 2: Calculate the sale price

Sale price = Regular price − Amount of discount

Sale price = $91 − $31.85

Sale price = $59.15

Hence, the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

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The given statement "calculated fields must always contain at least one constant" is false because calculated fields do not necessarily have to contain a constant value.

They can involve variables, formulas, functions, or expressions that perform calculations based on the given data. The purpose of calculated fields is to derive new values or perform computations based on existing data within a system or application.

While constants can be used in calculated fields, they are not a requirement. The specific requirements and structure of calculated fields may vary depending on the context and the software or system being used.

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Answer:

\(33\%, ~\dfrac 3{10},~0.32,~ \dfrac 13\)

Step-by-step explanation:

\(33\% <\dfrac 3{10}<0.32<\dfrac 13\)

c

you need to find the slope and then y intercept

m=y2-y1/x2-x1

so m=2

now y intercept

3=2(4)+b

solve for b

u get -5

therefore

y=2x-5

The probability that there will be TWO or MORE customers in line by the Poisson distribution is 0.084.

The discrete probability distribution is a Poisson distribution. It expresses the likelihood of an event occurring a particular amount of times (k) during a given time or space interval.

Its mean number of events, (lambda), is the solitary parameter in the Poisson distribution.

The formula for Poisson distribution is;

\(P(X=k)=\frac{e^{-\lambda} \lambda^{k}}{k !}\)

'X' is a Poisson distribution-based random variable.

The number 'k' represents the amount of times that event occurs.

P(X = k) denotes the likelihood that an occurrence will take place k times.

Euler's constant is 'e'. (approximately 2.718)

An average amount of times each event occurs is given by λ.

! is known as the factorial function

Now, according to the question;

k = 2.

λ = 5

e = 2.718

Substitute the values in the Poisson formula;

\(\begin{aligned}&P(X=k)=\frac{e^{-\lambda} \lambda^{k}}{k !} \\&P(X=2)=\frac{\left(2.718^{-5}\right)\left(5^{2}\right)}{2 !} \\&P(X=2)=\frac{(0.0067)(25)}{2} \\&P(X=2)=0.084\end{aligned}\)

Therefore, the probability that there will be TWO or MORE customers in line is 0.084.

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Answer: 4(x + 3)

Step-by-step explanation:

8x + 12

= 4(2x + 3)

Answer: look below :))

Step-by-step explanation: Yes, 8x + 12 can be factored as follows:

8x + 12 = 4x + 6 + 4x + 6

= (4x + 6) + (4x + 6)

= 2(2x + 3) + 2(2x + 3)

= 2(2x + 3) + 2(2x + 3)

= 4(2x + 3)

So the factored form of 8x + 12 is 4(2x + 3).

Answer:

This function does not have a vertex because it is a linear function, meaning it will be a straight line.

Step-by-step explanation:

I suggest graphing this on desmos! That site will be your best friend when it comes to graphing, anyway I hope this helped!

Answer:

  A = C²/(4π)

Step-by-step explanation:

You want a formula for the area of a circle, given its circumference.

Relevant relations for a circle are ...

  A = πr² . . . . . . . . A = area, r = radius

  C = 2πr . . . . . . . . C = circumference

Solving the circumference equation for r, we find ...

  r = C/(2π)

Substituting that into the area equation, we have ...

  A = π(C/(2π))²

  A = C²/(4π)

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The function that models the area A of a circle in terms of its circumference C is A = C²/(4π).

The formula for the circumference of a circle is C = 2πr or C = πd, where r is the radius and d is the diameter. To find a function that models the area A of a circle in terms of its circumference C, we can rearrange the formula for the circumference to solve for the radius: r = C/(2π). Substituting this value of r into the formula for the area, we get A = π(C/(2π))² = C²/(4π).

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Answer:

Step-by-step explanation:

ΔABC ≅ ΔDEF

The length AB = 28 and the length of DE = 7. Since these are corresponding sides, we know that DEF= 1/4 (ΔABC)

So, since ΔABC = 160, we know that ΔDEF will be 1/4 of that, meaning that ΔDEF is 40.

ΔDEF = 40cm²

Answer:

10 cm2

Step-by-step explanation:

The ratio per side is 28/7 = 4

When two similar figures have a ratio of 4:1, the difference between their areas is:

\((4)^{2} :(1)^{2}\)

\(16:1\)

That is, the dimension of the area of the largest figure is 16 times larger than the smallest figure.

So for this case:

the area of the larger figure is

ΔABC = 160 sq.cm

Then the area of the minor figure is:

ΔDEF= 160/16 = 10 sq.cm

Hope this helps

The sum of the two integers is 26.

An integer is a whole number (not a fractional quantity) that can be high quality, negative, or zero. Examples of integers are: -five, 1, five, eight, 97, and three,043. Examples of numbers that aren't integers are: -1.forty three, 1 three/4, 3.14, 09, and 5,643.1.

A variety of that isn't a whole range, a negative whole quantity, or 0 is defined as Non-Integer. it is any variety that isn't blanketed inside the integer set, which is expressed as { … -4, -3, -2, -1, zero, 1, 2, 3, 4 }. Some of the examples of non-integers consist of decimals, fractions, and imaginary numbers.

An integer is colloquially defined as more than a few that can be written without a fractional aspect. For instance, 21, 4, 0, and −2048 are integers, while 9.75, 5+half, and √2 are not.

(1/a  + 1/b) / (a+b) = 1/25              

(a+b)/(ab) / (a+b) = 1/25

1/ab = 1/25

This implies that ab  = 25

Since a, and b  appear to be distinct integers, the result would be that either 1*25  = 25 or 25 * 1  = 25.

Either way, their sum is 26.

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Answer:

Scale Factor: 2

Step-by-step explanation:

Need more information?

Visit MathWareHouse.com

Hope this was helpful! Thank you & have an awesome day! =)

Fer Vil, this is the solution:

0.0000653 in scientific notation is:

6.53 (The number between 1 and 10)

The power of 10 is -5 because we have to move the decimal point one to the right of the four zeros.

Therefore,

0.0000653 = 6.53 * 10^-5