I’ll give brainliest to the first answer

Answer:

s(t) = 160/3  ( 1 - e^(-3t / 200) )

Step-by-step explanation:

volume of pure water in tank  = 1000 L

Brine contains 0.04kg of salt/L

Inflow rate of Brine containing 0.04kg of salt/L = 5L/min

Brine containing 0.06 kg of salt/L

Inflow rate of Brine containing 0.06 kg of salt/L = 10L/min

Solution is thoroughly mixed and drains from tank at 15L/min

a) Determine the amount of salt is in the tank after t minutes

rate of salt entering = 0.2 + 0.6 = 0.8 kg/min

rate of salt leaving = s/1000 * 15

amount of salt at time (t) = s(t)

initial condition s( 0 ) = 0

ds/dt = 0.8 - 15s/1000 = 0.8 - 3s/200

200 ds/dt = ( 160 - 3s )

-200/3  In ( 160 - 3s ) = t + c

Given that ;  t = 0 , s = 0    

c =  - 200/3  In ( 160 )

∴  -200/3  In ( 160 - 3s ) = t - 200/3  In ( 160 )

- 200/3  [ In ( 60 - 3s ) - In ( 160 ) ] = t

therefore:  

In ( 160 - 3s / 160 ) = -3t/200

= ( 160 - 3s / 160 ) = e ^ (-3t/200 )

Hence amount of salt in tank after t minutes

s(t) = 160/3  ( 1 - e^(-3t / 200) )

Max is participating at a school bake sale. Each cookie he sells costs 50 cents. Unfortunately, it took 6 dollars to buy the materials for the cookies. Find how much money would it take for Max to break even.

Answer:

Step-by-step explanation:

4 years ago when Mary was 6, she was one half the age of her brother.  

 How old is her brother now?

Solution :

Let brother's age be = x

Four years ago, brothers age was = (x - 4)

Four years ago Mary was = 6

She was half the age of her brother

                                                   [tex]6 = \frac{1}{2} (x - 4)[/tex]

Answer:

Buses - 43 people

Vans - 12 people

Hi there!  

»»————-　★　————-««

I believe your answer is:  

4

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻  

[tex]\boxed{\text{Calculating the Answer...}}\\\\8^{\frac{2}{3}}\\-----------\\\text{Recall the Exponent Rule: }} a^{\frac{b}{c}} = \sqrt[c]{a^b}\\\\\rightarrow {\frac{\text{Power}}{\text{Root Index}}\\\\[/tex]

[tex]-----------[/tex]

[tex]\rightarrow 8^{\frac{2}{3}}\\\\\rightarrow \sqrt[3]{(8^2)}\\\\\rightarrow\sqrt[3]{64}\\\\\rightarrow \boxed{4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

4

Step-by-step explanation:

[tex]8^{\frac{2}{3} }[/tex]

=[tex](2)^3*\frac{2}{3}[/tex]

=[tex](2)^\frac{3*2}{2}[/tex]

=[tex](2)^\frac{6}{3}[/tex]

=[tex]2^2[/tex]

=4

Answer:

4)8 goats, 3 hens.

Step-by-step explanation:

8*4=32

3*2=6

32+6=38

Answer:

See the answers below

Step-by-step explanation:

Name two characteristics of the Fibonacci Series that you observed. ​

If we take a closer look at the Fibonacci series, we will notice the following characteristics

1.The next number is the sum of the two preceding numbers

2. Another interesting characteristic is evidenced in the convergence of the sequence

Answer:

460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{101}{\sqrt{90}} = 27.4[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 436 - 27.4 = 408.6.

The upper end of the interval is the sample mean added to M. So it is 436 + 27.4 = 463.4.

460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460

Answer:

4. (2, 3)

5. (0, 1)

7. (-1, 2)

Step-by-step explanation:

I hope this helps! Have a nice dayy! :)

You're very close. Choices D and E are two of the three answers. The third answer is choice G (-1,2)

If you plug the coordinates of the points into the inequality, you should get a true statement.

For instance, let's try the coordinates of choice G

[tex]-2x + 3y\ge 3\\\\-2(-1) + 3(2)\ge 3\\\\2 + 6\ge 3\\\\8\ge 3\\\\[/tex]

Which is true since 8 is indeed greater than 3. That verifies point G is a solution point. A similar story happens with points D and E as well.

----------

If you tried something like choice A, then,

[tex]-2x + 3y\ge 3\\\\-2*(2) + 3(-3)\ge 3\\\\-4 - 9\ge 3\\\\-13\ge 3\\\\[/tex]

Which is false because -13 is not greater than 3, and -13 is not equal to 3 either. So choice A is a non-answer. You should find that choices B, C, and F are also non-answers.

----------

The graph is below. Notice how points D, E and G are either in the blue shaded region or on the boundary. The boundary line is solid (due to the "or equal to" as part of the inequality sign), so points on the solid boundary line are part of the solution set. The graph is a quick way to visually confirm the answers. I used GeoGebra to make the graph.

So that's why the 3 answers are D, E and G.

Answer:

it says round to the nearest 10th so it wouldn't be 81, it would be 81.8%

Answer:

20°

Step-by-step explanation:

perpendicular from the center on a chord of a circle always bisects the chord.

AR=BR

∴m arcAC=m arc BC=20°

Answer:

{2,4,6}

Step-by-step explanation:

Hope it helps you

There are 12 month in a year :

6360 ÷ 12 = 530

Thus the labour earns Rs 530 in a month .

To find this out we will divide 6360 by 12 (as there are 12 months in an year) 6360/12 = 530 . Therefore answer = rs 530

Pls follow and mark brainliest.

Answer:

379

Step-by-step explanation:

a23 = 27 + (23-1)(16)

= 27 + (22)(16)

= 27 + 352

= 379

The answers are as follows part A = 30m+15  part B =3m+15+27m

and partC = 30m+15

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition,substraction, multiplication and division.

Part A:- Two expressions that are equivalent to the given expressions are:-

3m   +   15   +   27m

30m  +   15

Part B:  Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties.

3  (  m   +   5    +   9m   )

Open the bracket by multiplying 3 by what is in the bracket

3m   +   15   +   27m

Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m.

3   (  m    +   5   +   9m  )

Open the bracket by multiplying 3 by what is in the bracket

3m    +    15    +     27m

Collect like terms together

3m    +     27m  +   15

=   30m   +    15

To know more about Expression follow

https://brainly.com/question/723406

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this figure can be divided into three parts one is rectangle other one is semicircle and the third one is one fourth of the circle .so let's find the area of each figure one by one. For the rectangle 12×8 =96

for semicircle that is on the top it has the radius 6 which is a half of 12

so area of the semicircle is

[tex] \frac{1}{2} \pi \: r {}^{2} \\ \frac{1}{2} \times 3.14 \times 6 {}^{2} \\ 3.14 \times 18 \\ 56.52[/tex]

no that's fine. 80 of the 1/4 of the other Circle

[tex] \frac{1}{4} \pi {}^{2} \\ \frac{1}{4} 3.14 \times 8 {}^{2} \\ 3.14 \times 16 \\ 50.24[/tex]

add all these areas

96+56.52+50.24 =202.76

Answer:

x = 1, y = 2 , z = 3

Step-by-step explanation:

[tex]6x\:+\:2y\:-4z\:=\:-2 \ \ \ \ \ \ \ \ \ -----( 1 ) \:\\\\-3x-4y\:+2z\:=\:-5 \ \ \ \ \ \ ------( 2 ) \:\\\\4x-\:6y\:+3z\:=\:1 \ \ \ \ \ \ \ \ \ \ \ \ ------- ( 3 ) \\\\( 2 ) \times 2=> -6x -8y + 4z = -10 \ \ \ \ \ \ \ -----( 4)[/tex]

Now add ( 1 ) and  (4)

[tex]6x +2y -4z = - 2\\\\-6x-8y - 4z = -10\\\\=>0x -6y + 0 = - 12\\\\-6y = -12[/tex]

y = 2

Now multiply ( 1 ) by  2 and (3) by 3

[tex](1) \times 2 => 12x + 4y -8z = -4\\\\(3) \times 3 => 12x -18y +9z = 3\\\\Subtract \ the \ equation : ( 1) - ( 3) => 0x +22y -17z = -7[/tex] ------ ( 5 )

Substitute y = 2 in ( 5 ) :

[tex]22(2) - 17z = - 7\\\\ 44 - 17z = - 7\\\\ -17z = - 7 - 44\\\\ -17z = -51\\\\[/tex]

z = 3

Substitute z = 3 and y = 2 in ( 1 ) :

[tex]6x + 2y - 4z = - 2\\\\6x + 2( 2) -4( 3) = -2\\\\6x + 4 - 12 = -2\\\\6x - 8 = - 2\\\\6x = - 2 + 8 \\\\6x = 6\\[/tex]

x = 1

The values of variables, such as the height of the table can be found by writing equations of their relationships

The height of the table is 105 cm

The reason the above height value is correct is as follows;

Known parameters:

The diagram shows a table, a cat and a mice

Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice

From the given diagram, we have;

Height of the table + Height of the cat - Height of the mice  = 120 cm

∴ x + y - z = 120...(1)

Height of the table + Height of the mice - Height of the cat   = 90 cm

∴ x + z - y = 90...(2)

Adding equation (1) to equation (2) gives;

x + y - z + (x + z - y) = 120 + 90 = 210

x + y - z + (x + z - y) = 210

However;

x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x

∴ x + y - z + (x + z - y) = 2·x = 210

x = 210/2 = 105

Therefore;

The height of the table, x = 105 cm

Learn more about word problems leading on simultaneous equations here:

https://brainly.com/question/16513646

Answer:

2a.

Step-by-step explanation:

6 = 2 * 3

8 = 2 * 2 * 2   - 2 is common to both sets of factors.

So the GCF of 6 and 8 is 2.

For the 2 a's it is a.

9514 1404 393

Answer:

  182 lbs

Step-by-step explanation:

You can write the proportion for the required patient weight (w) as ...

  weight/medicine = w/(174.72 mg) = (150 lb)/(144 mg)

  w = (150 lb)(174.72/144) . . . . . multiply by 174.72 mg

  w ≈ 182 lb

The patient's weight is 182 pounds.

Answer:

For cobalt-60, which has a half-life of 5.27 years, 50% remains after 5.27 years (one half-life), 25% remains after 10.54 years (two half-lives), 12.5% remains after 15.81 years (three half-lives), and so on.

Step-by-step explanation:

You can figue out the rest.

Answer:

(a+b)²=a²+b²+2ab

Step-by-step explanation:

The square of sum of two terms is equal to the squared plus squared plus times product of and . In mathematics, the plus whole squared algebraic identity is called in three ways. The square of sum of two terms identity.

Answer:

Y=x

Step-by-step explanation:

The y and x values are the same

Answer:

y = x

Step-by-step explanation:

a 45° line with the origin passing through the origin has the equation y=x.

Have a nice day.

Answer:

396

Step-by-step explanation:

It's a square.

That means that all four sides are equal.

So the two expressions you have been given are equal.

2.5x + 76.5 = 12x - 9            Subtract 2.5x from both sides.

-2.5x               -2.5x  

          76.5 = 9.5x - 9          Add 9 to both sides

           9                 9

          85.5 = 9.5x              Divide by 9.5

       85.5/9.5 = x

x = 9

That is just the value for x. It is not the answer

Side = 12x - 9

Side = 12*9 - 9

Side = 108 - 9

Side = 99

The perimeter = 4 * Side

The perimeter = 4 * 99

Perimeter = 396

Answer:

a) 2 nonsingular 2 by 2  matrices are not closed when added together hence it is not a vector space( i.e. their sum = singular and not nonsingular )

b) 2 singular 2 by 2 matrices is not  closed under addition, hence they are not a vector space. ( i.e. their sum = nonsingular )

Step-by-step explanation:

a) Prove that nonsingular 2 by 2 matrices is not a vector space

2 nonsingular matrices are not closed when added together hence it is not a vector space ( i.e. their sum = singular and not nonsingular )

vector A = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]    +  vector B =  [tex]\left[\begin{array}{ccc}0&1\\1&0\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&1\\1&1\\\end{array}\right][/tex] ( singular vector )

b) Prove that singular 2 by 2 matrices is not a vector space

2 singular 2 by 2 matrices is not  closed under addition, hence they are not a vector space. ( i.e. their sum = nonsingular )

Vector C = [tex]\left[\begin{array}{ccc}1&0\\0&0\\\end{array}\right][/tex]  + vector D = [tex]\left[\begin{array}{ccc}0&0\\0&1\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] ( nonsingular vector )

Answer:

0.2&4

Step-by-step explanation:

There are 60 minutes in one hour, so 12 divided by 60 is the answer.

0.2   kilometers * 20 = 4

Answer:

4.53

Step-by-step explanation:

Given the data :

4, 5, 10, 11, 15

The mean = 9

The standard deviation of a sample :

s = √[Σ(x - mean)²/(n-1)]

s = √[((4-9)² + (5-9)²+(10-9)² + (11-9)² + (15-9)²) / (5-1)]

s = √(25+16+1+4+36)/4

s = √20.5

s = 4.527

s = 4.53

Answer:

4.5

Step-by-step explanation:

5.1.3

Answer:

3

Step-by-step explanation:

4.5x 2 = 9

[tex]\sqrt{9}[/tex]= 3

this is an example of linear equations is one variable