I really need help with this statistical/variable question, i am really struggling and would be super happy if someone could answer

Answer:

[tex]dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex] g/min

Step-by-step explanation:

The mass flow rate dA(t)/dt = mass flowing in - mass flowing out

Since water is pumped in at a rate of 3 L/min, and it contains no salt, the concentration in is thus 0 g/L. the mass flow in is thus 0 g/L × 3 L/min = 0 g/min.

Let A(t) be the mass present at any time, t. The concentration at any time ,t is thus A(t)/volume = A(t)/210. Since water flows out at a rate of 3 L/min, the mass flow out is thus, A(t)/210 g/L × 3 L/min = A(t)/70 g/min.

So, dA(t)/dt = mass flowing in - mass flowing out

dA(t)/dt = 0 g/min - A(t)/70 g/min

dA(t)/dt =  - A(t)/70 g/min

 Since the tank initially contains 30 g of salt, the initial mass of salt in the tank is 30 g. So A(0) = 30

So, the initial value problem is thus  

dA(t)/dt =  - A(t)/70 , A(0) = 30

Separating the variables, we have

dA(t)/A(t) = -dt/70

Integrating both sides, we have

∫dA(t)/A(t) = ∫-dt/70

㏑A(t) = -t/70 + C

taking exponents of both sides, we have

A(t) = exp(-t/70 + C)

A(t) = exp(-t/70)expC

[tex]A(t) = e^{-t/70}e^{C}\\A(t) = Ce^{-t/70} whereC = e^{C}[/tex]

A(0) = 30, So

[tex]A(0) = Ce^{-0/70}\\30 = Ce^{0}\\C = 30[/tex]

[tex]A(t) = 30e^{-t/70}[/tex]

The rate at which the number of grams of salt in the tank is changing at time t is

[tex]dA(t)/dt = \frac{d30e^{-t/70} }{dt} \\dA(t)/dt = -\frac{30e^{-t/70} }{70}\\dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex]

So, the rate at which the number of grams of salt in the tank is changing at time t is

[tex]dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex] g/min

Answer:

110.1

Step-by-step explanation:

Answer:

(3.5, 2)

Step-by-step explanation:

From the attachment, we have:

[tex]H = (1,1)[/tex]

[tex]J= (2,3)[/tex]

[tex]K=(6,3)[/tex]

[tex]L = (5,1)[/tex]

Required

Determine the point of intersection

To do this, we simply calculate the midpoints of the diagonals; which are:

HK and JL

Midpoint is calculated as:

[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]

For HK:

[tex]M = \frac{1}{2}(1+6,1+3)[/tex]

[tex]M = \frac{1}{2}(7,4)[/tex]

[tex]M = (3.5,2)[/tex]

For JL:

[tex]M = \frac{1}{2}(2+5,3+1)[/tex]

[tex]M = \frac{1}{2}(7,4)[/tex]

[tex]M = (3.5,2)[/tex]

For both diagonals, the coordinate of the midpoint is (3.5, 2).

Hence, the point of intersection is: (3.5, 2)

Answer:

the answer is y=21

Step-by-step explanation:

hope this helps:)

Answer:

y=21

Step-by-step explanation:

92 = 5y - 13

92 + 13 = 5y - 13 + 13

105 = 5y

105/5 = 5y/5

21 = y

Hope this helps!

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9514 1404 393

Answer:

  divide by x

Step-by-step explanation:

To answer your question, you can get from A to B by dividing by x:

  [tex]5x=3x\\\\\dfrac{5x}{x}=\dfrac{3x}{x}\qquad\text{only if $x\ne0$}\\\\5=3[/tex]

However, this is only a valid operation if x ≠ 0. In this equation, x = 0, so that division is not valid.

__

A better approach to the solution is to put the equation in standard form:

  f(x) = 0

You can get there by subtracting 3x from both sides.

  5x -3x = 3x -3x

  2x = 0

Now, you can legitimately divide by 2 to find ...

  x = 0 . . . . . . . . the reason why dividing by x is not allowed

Answer:

Check pdf

Step-by-step explanation:

Answer:

The maximum rent each will pay is $1,333.

Step-by-step explanation:

They want the monthly rent to be no more than $3,999.

It will be split evenly between all of them, with each contributing with x.

This means that the maximum rent each will pay is given by:

[tex]3x = 3999[/tex]

[tex]x = \frac{3999}{3}[/tex]

[tex]x = 1333[/tex]

The maximum rent each will pay is $1,333.

Answer:Ok Don't freak out What do you need help with

Step-by-step explanation:

Answer:

Cavalieri's principle tells us that if 2 figures have the same height and the same cross-sectional area at every point along that height, they have the same volume.

Answer:

13

Step-by-step explanation:

5²+12²=c²

25+144=c²

169=c²

c=√169

c=13

2y

Step-by-step explanation:

16y^5-3/4)

16y²/4)

4y²)1/2

2y

Answer:

x=8 x=16

Step-by-step explanation:

Given function:

Thinks:

Rewrite as:

Thereform, x=8 and x=16.

Answer:

I think it's C im not certain

Answer:

139

Step-by-step explanation:

x^2 + y^3 2+x = 3^2 + 5^3 + 2 + 3

= 9 + 125 + 5

= 139!

Answer:

34.4

Step-by-step explanation:

(54/11) --> ratio of one side of the larger triangle to the smaller one multiplied by 7 = 34.36363636... Rounding it to the nearest tenth is 34.4

Given:

The coordinates of the points are B(-4,3), G(-2, 4), H(1, -2), L(-1, -3).

To find:

Whether GL and BH are parallel or not by using their slopes.

Solution:

If a line passes through the two points, then the slope of the line is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using the slope formula, the slope of GL is

[tex]m_1=\dfrac{-3-4}{-1-(-2)}[/tex]

[tex]m_1=\dfrac{-7}{-1+2}[/tex]

[tex]m_1=\dfrac{-7}{1}[/tex]

[tex]m_1=-7[/tex]

Using the slope formula, the slope of BH is

[tex]m_2=\dfrac{-2-3}{1-(-4)}[/tex]

[tex]m_2=\dfrac{-5}{1+4}[/tex]

[tex]m_2=\dfrac{-5}{5}[/tex]

[tex]m_2=-1[/tex]

We know that slopes of parallel lines are always equal.

The slopes of GL and BH are -7 and -1 respectively but they are not equal, therefore GL and BH are not parallel lines.

Options A and D are true for the inverse matrices.

We need to determine which statement about inverse matrices is true.

The inverse of the matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity. For a matrix A, its inverse is [tex]A^{-1}[/tex], and  [tex]A.A^{-1}=I[/tex] A = I, where I is the identity matrix. The matrix whose determinant is non-zero and for which the inverse matrix can be calculated is called an invertible matrix.

The matrix should have a non-zero determinant for getting the inverse of it.

An inverse matrix should be a square matrix.

The inverse of the matrix can be calculated by two approaches:

1) Adjoint method

2) Row/Column elementary method

Therefore, options A and D are true for the inverse matrices.

To learn more about the inverse matrices visit:

https://brainly.com/question/15118736.

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Answer:

B. Team B has a larger median and the same interquartile range.

The correct statement is,

D. Team B has a smaller median and the same interquartile range.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We know that;

Based on the given data, the correct comparison of Team B to Team A is A. Team B has a larger median and a smaller interquartile range.

This is because the median score for Team B is 70, which is higher than the median score for Team A, which is 70.

The interquartile range for Team B is smaller because the scores are more tightly clustered around the median, indicating less variability in scores compared to Team A.

Thus, The correct statement is,

D. Team B has a smaller median and the same interquartile range.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

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Answer:6

Step-by-step explanation:

Angle 2, angle 6, angle 4, and angle 8 have the same measure that is 78 degrees and this can be determined by using the corresponding angle property.

GIven :

The following steps can be used in order to determine the other angles whose measure is 78 degrees:

Step 1 - The corresponding angle property is used in order to determine the other angles whose measure is 78 degrees.

Step 2 - According to the given figure, angle 2 and angle 6 are corresponding angles. Therefore, the measure of angle 6 is also 78 degrees.

Step 3 - Angle 8 is the opposite angle of angle 6 therefore, the measure of angle 8 is 78 degrees.

Step 4 - Angle 4 is the opposite angle of angle 2 therefore, the measure of angle 2 is 78 degrees.

Therefore, the correct options are B), D), and F).

For more information, refer to the link given below:

https://brainly.com/question/10714897

Answer:

1st one: 16

2nd one: 16

3rd one: 64

4th one: 27

5th one: 1000

Step-by-step explanation:

Have a great day

Answer:

It gains 8 cm

Step-by-step explanation:

Answer:

We know that all the sides of a square are equal. Perimeter of a square is 4 times of s side. Perimeter of a square = 4 × length of a side.

Step-by-step explanation:

Answer:

8.66

Step-by-step explanation:

If it helps, volume is LENGTH x WIDTH x HEIGHT, and for a triangular prism, each side is the same. :)

Answer:

1

Step-by-step explanation:

Answer:

the three consecutive numbers are 14, 15, 16

Answer:

Since the consecutive numbers, so the first one is x, the next one is x+1, and so on....I hope this will help

Step-by-step explanation:

x + (x + 1) + (x + 2) = 45

x + x + 1 + x + 2 = 45

3x + 3 = 45

3x = 42

x = 14

Now that we know x = 14, let's add one to it.

x + 1 = 14 + 1 = 15.

Now we have our middle number, which is 15. You can always check your answer by adding 14 + 15 + 16 = 45. Whoo!

I think 710 is the answer

266+266+89+89= 710

1/3 * 7/9 kg = (1 * 7)/(3 * 9) kg = 7/27 kg

He used 7/27 kg of sugar.

Answer:

72.8

Step-by-step explanation:

16 is 8 times 2. 36.4 times 2 would be 72.8