A tank contains 350 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number

If T is the midpoint of PQ and PT = 3x+3, TQ = 7x-9, then PT = 12 units.

Determining the Value of PT

It is given that,

T is the midpoint of PQ ........ (1)

PT=3x+3 ......... (2)

TQ=7x-9 .......... (3)

From (1), the distance from P to T and the distance from T to Q will be equal.

⇒ PT = TQ [Since, a midpoint divides a line into two equal segments]

Hence, equating the equations of PT and TQ given in (2) and (3) respectively, equal, we get the following,

3x + 3 = 7x - 9

or 7x - 9 = 3x + 3

or 7x - 3x = 9 + 3

or 4x = 12

or x = 12/4

⇒ x = 3

Substitute this obtained value of x in equation (2)

PT = 3(3) + 3

PT = 9 + 3

PT = 12 units

Thus, if T is the midpoint of PQ, then the measure of PT and TQ is equal to 12 units.

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Answer:

D

Step-by-step explanation:

i got it right

Answer: D  -_-

Step-by-step explanation: Because its on edge

Answer:

60 math problems.

Step-by-step explanation:

30/2.5=12

12*5=60

Answer:

1314.110429

Step-by-step explanation:

:)

Answer:

(-0.5, 0)

Step-by-step explanation:

'B' lies on the x-axis. This means that it's y-value is zero.

'B' also is in between '-1' and '0'. This means that the x-value is -0.5.

'B' should be (-0.5, 0).

Hope this helps.

Answer:

Number = 12

Step-by-step explanation:

2n-7=n+5 (+7 to both sides)

2n=n+12 (-n to both sides)

n=12

Standard equation of the line which is parallel to the given line 4x-2y =8 and passes through the point (-2,8) is equal to y = 2x + 12.

As given in the question,

Given equation of the line which is parallel to the required equation of the line:

4x -2y = 8

⇒ 2y = 4x -8

⇒ y= 2x -4

Slope of the line by comparing with standard form y =mx +c , where m is the slope.

Slope 'm' = 2

Slope is same for the parallel lines.

Required equation of the line passes through (-2 ,8) with slope m = 2

y -y₁ = m(x-x₁)

⇒ y- 8 = 2(x-(-2))

⇒ y -8 = 2x +4

⇒ y= 2x +12

Therefore, standard equation of the line which is parallel to the given line 4x-2y =8 and passes through the point (-2,8) is equal to y =2x + 12.

The complete question is :

Write an equation of a line in standard form, that is parallel to the line

4x - 2y = 8 that passes through the point (-2, 8).

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Answer:

= 408.16 or =20000/49

Step-by-step explanation:

= (78000/ 19110) x100

= (200/49)*100

=20000/49

Answer:

52

Step-by-step explanation:

40% of 130 is 52

Answer:

13x25=455

Step-by-step explanation:

Answer:

The value of a + b = 9

Step-by-step explanation:

Step(i):-

Given expression

                     3(2m + 5) - 6(4m - 2)    

                 = 6 m + 15 -24m +12

                 = (6-24) m +27

                = -18 m +27

Step(ii):-

Given that the form  am + b

                             - 18 m + 27

where a=-18 and b = 27

The value of a + b =  - 18 + 27 = 9

Final answer:-

The value of a + b = 9

Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?

Let

x ------> students enrolled last year

we have that

100%+10%=110%=110/100=1.10

so

528=1.10x

solve for x

x=528/1.10

x=480

Answer:

15-65=-50 So the opposite would be 50.

Answer:

Not exactly sure what the question is but John would have to pay 180 to be in the class, he does not have enough for the class right now.

Moving on to step 20, you need to take a screenshot issues of the tools menu. This can usually be accessed by clicking on the "Tools" option in the menu bar of the program or application you are using.

To take a  of the tools menu in step 20, you can follow these steps:Open the tools menu in the desired application or software.Press the "Print Screen" (PrtSc) button on your keyboard. This will capture a screenshot of your entire screen.

Open an image editing software or any program that allows you to paste imagesPaste the screenshot by pressing "Ctrl" + "V" on your keyboard.Save the image in your desired format.

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Answer:

1

Step-by-step explanation:

2÷2=1

For the scores the sum of squares SS is calculated to be

A statistical measure of deviation from the mean is the sum of squares. Variance is another name for it.

The squared differences of each data point are added together to calculate it. The sum of squares is calculated by squaring the separation between each data point and the line of best fit, then adding the results.

The mean is calculated as follows

= (0 + 1 + 4 + 5) / 4

= 10 / 4

= 2.5

the variance

= (0 - 2.5)² + (1 - 2.5)² + (4 - 2.5)² + (5 - 2.5)²

= 6.25 + 2.25 + 2.25 + 6.25

= 17

the sum of squares is 17

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Therefore , the solution of the given problem of average comes out to be the average price of a pizza in 2000 was about $9 (or half of $18).

An organised collection's median value is the precise value that makes up the collection's mean. In this case, the ratio between the lowest and highest 50% of the data is a normal but rather probability measure. When finding the middle and mode, a variety of algorithms can be applied in order to identify any unusual or even amounts of values.

Here,

By dividing 72 by the interest rate, we can calculate how many years it will take an investment to double in value at a specific interest rate. This is known as the law of 72. In this instance

With an inflation rate of 3.25 percent, it takes roughly how many years for the price of a pizza to double as a result of inflation:

72 / 3.25 = 22.15 years

In light of this, we can calculate that a pizza cost $9 (half of $18) roughly 22 years ago, which corresponds to the following year:

2022 - 22 ≈ 2000

As a result of inflation running at an average of 3.25% for many years, the average price of a pizza in 2000 was about $9 (or half of $18).

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The value of the expression z + 3x4 using arithmetic operation where z = 15, is 27. The answer is A) 27.

The given expression is z + 3x4, where z = 15. To evaluate this expression, we substitute 15 for z and perform the multiplication. First, we multiply 3 and 4, which gives us 12. Then, we add 15 and 12 to get the final result of 27.

z + 3x4 = 15 + 3x4

= 15 + 12

= 27

Therefore, the value of the expression when z = 15, is 27. In other words, using arithmetic operation of multiplication and addition, which gives us the final answer of 27. So, the correct answer is option A).

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____The given question is incomplete , the complete question is given below:

Evaluate the expression, where z = 15

z + 3x4

A. 27

B. 32

C. 56

D. 1,304

Answer: 1719.22 mi squared

Step-by-step explanation:

you have to find the height first.

you only have r and hypotenuse

so

a^2 + b^2 = c^2

13^2 + b^2 = 29.1^2

169 + b^2 = 846.81

b^2 = 846.81 - 169

b^2 = 677.81

b = 26.03

height = 26.03

surface area formula :

          _______

πr(r+_/h^2+r^2)

                   ___________

π(13) [13 + _/26.03^2 + 13^2]

= 1719.22

The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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A root of a transformed equation that is not the root of the original equation because it was excluded from the original equation's domain is known as an extraneous solution.

What are extraneous solutions?

A "false" solution to an equation is known as an extraneous solution. Even if we appeared to follow sound procedures when solving the equation, an extraneous solution did not fulfill the original equation.

So,

When we solve an equation, an extraneous solution is a result that does not fulfill the equation. As an illustration, if we square both sides of the equation x = -1, we obtain the value x = 1, which does not satisfy the original equation, indicating that x = 1 is an extraneous solution.

when we wanted to solve the equation √x = -1.  After squaring both sides, we get a value of x = 1.

When we substitute x = 1 into the original equation, we get:

x = -1  [original equation]

√1 = -1  [substitute x = 1]

1 = -1  [this is not true]

Hence,

This equation is called an extraneous solution.

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Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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Answer:

X=8

X=4

Step-by-step explanation: Those are the solutions.

Hope this helps!!

Answer:

In standard form =>

x + y = -2

The inverse of the function and the secret code obtained from the table of values are;

A. C⁻¹(x) = (x + 9)/4

B. The secret code is; FUNCTIONS

The inverse of a specified function reverses the effect of a the specified function.

A. The specified function is; c(x) = 4·x - 9

The inverse of the function c(x) can be found as follows;

c(x) = 4·x - 9

c(x) + 9 = 4·x

4·x = c(x) + 9

x = (c(x) + 9)/4

c⁻¹(x) = (x + 9)/4

B. The table for c(x) and c⁻¹(x) are presented as follows;

c(x)   \({}\)    c⁻¹(x)

15 \({}\)        c⁻¹(x) = (15 + 9)/4 = 6

75 \({}\)        c⁻¹(x) = (75 + 9)/4 = 21

47 \({}\)        c⁻¹(x) = (47 + 9)/4 = 14

3 \({}\)          c⁻¹(x) = (3 + 9)/4 = 3

71 \({}\)         c⁻¹(x) = (71 + 9)/4 = 20

27 \({}\)        c⁻¹(x) = (27 + 9)/4 = 9

51 \({}\)        c⁻¹(x) = (51 + 9)/4 = 15

47 \({}\)        c⁻¹(x) = (47 + 9)/4 = 14

67 \({}\)        c⁻¹(x) = 67 + 9)/4 = 19

The letters are; 6 = F, 21 = U, 14 = N, 3 = C, 20 = T, 9 = I, 15 = O, 14 = N, 19 = S

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Answer:

15/16

Step-by-step explanation:

Easy Way:

To make a fraction equal to one, we multiply its reciprocal. This means that 2/3 must be multiplied by 3/2 to equal 6/6, which equals one.

Since we multiplied 3/2 to one side, we have to do it to the other side to balance it out. 5/8 times 3/2 equals 15/16 inches of rain in one hour.

Another way that is different with more steps (if your brain works this way):

In order to make a fraction into a whole number we have to multiply by its denominator. Right now, we have 2/3 of an hour. If we multiply this by 3, we can get 6/3 which simplifies to 2 hours.

We have to multiply the other side by 3 since both sides need to be balanced. 3 times 5/8 is 15/8.

This leaves us with 15/8 inches of rain falling in 2 hours. To get how much inches fall in one hour, we can divide 15/8 by two. This means multiplying 15/8 by 1/2, which equals 15/16.

The graph of y = - 3x + 1 has a slope of -3 and a y-intercept of 1

The equation is given as:

y = - 3x + 1

The above equation is a linear function

A linear function is represented as:

y = mx + c

Where m represents the slope and c represents the y-intercept

This means that the graph of y = - 3x + 1 has a slope of -3 and a y-intercept of 1

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To determine the Mean Absolute Deviation (MAD), we need the actual sales data and the forecasted values. Since the actual sales data is not provided, it is not possible to calculate the MAD accurately.

MAD is calculated by taking the average of the absolute differences between the forecasted values and the actual values. Without the actual sales data, we cannot compute the absolute differences and find the MAD.

To calculate the MAD, you will need the actual sales data and the corresponding forecasted values for each day. Then, you can calculate the absolute differences between the actual and forecasted values, take their average, and round the result to two decimal places to obtain the MAD.

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