Anyone know how solve it

Answer:

The number A(t) of pounds of salt in the tank at time t = [tex]\frac{3t(100 - t)}{25}[/tex]

Step-by-step explanation:

Given - A large tank is filled to capacity with 400 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at a rate of 8 gals/min.

To find - Find the number A(t) of pounds of salt in the tank at time t.

Proof -

Given that,

Capacity of water = 400 gallons

rate in flow = 4 gal/min

rate out flow = 8 gal/min

Concentration in = 3 lbs/gal

Concentration out = (Amount of salt at time t )/ (Solution in tank at time t)

Now,

Let

A(t) = Amount of salt in the tank at time t

Now,

Initially tank has 400 gallons of water, So

A(0) = 0 ................(1)

Now,

Rate of change in the amount of salt = [tex]\frac{d}{dt} A(t)[/tex]

                                                             = (Rate in flow )( Concentration In) - (Rate out flow )( Concentration out)

                                                             = (4) (3) - (8) ([tex]\frac{A(t)}{400 - 4t)}[/tex]

                                                             = 12 - [tex]\frac{2A(t)}{100 - t)}[/tex]

⇒[tex]\frac{d}{dt} A(t)[/tex] + [tex]\frac{2A(t)}{100 - t)}[/tex] = 12

Now,

Integrating Factor, I.F = [tex]e^{\int {\frac{2}{100 - t} } \, dt }[/tex]

                                    = [tex]e^{-2ln(100 - t)}[/tex]

                                    = (100 - t)⁻²

⇒I.F = (100 - t)⁻²

The solution becomes

A (I.F) = ∫ (I.F)(12) dt + C

⇒A (100 - t)⁻² = ∫12(100 - t)⁻² dt + C

⇒A (100 - t)⁻² = -12(100 - t)⁻¹ (-1) + C

⇒A(t) = [tex]12(100 - t)+ C(100 - t)^{2}[/tex]

Now,

We have A(0) = 0

⇒C = -12/100

∴ we get

A(t) = 12(100 - t) - [tex]\frac{12}{100}[/tex] (100 - t)²

     = 12(100 - t) [ 1 - [tex]\frac{100 - t}{100}[/tex] ]

     = 12(100 - t) ([tex]\frac{t}{100}[/tex])

     = [tex]\frac{3t(100 - t)}{25}[/tex]

⇒A(t) = [tex]\frac{3t(100 - t)}{25}[/tex]

∴ we get

The number A(t) of pounds of salt in the tank at time t = [tex]\frac{3t(100 - t)}{25}[/tex]

Answer:

4, because 12/3 is 4 cause 3×4=12

Answer: 4

Step-by-step explanation: you need to divide 12 and 3 to get 4.

Answer:

y = 6x

Step-by-step explanation:

To write an equation, find the unit rate or constant of proportionality (k).

Using a point on the line, (3, 18):

Constant of proportionality, k = y/x = 18/3

k = 6

To write an equation, substitute k = 6 into y = kx.

Thus:

y = 6x

Answer:

8 degrees

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

or Subtract the same value from both sides.

Clear out any fractions by Multiplying every term by the bottom parts.

Divide every term by the same nonzero value.

Combine Like Terms.

Factoring.

Expanding (the opposite of factoring) may also help.

Recognizing a pattern, such as the difference of squares.

More items...

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Solving Equations - Math is Fun

Answer:

im so sorry bt I dont know this one

Step-by-step explanation:

Answer:

I think it is addition property

Answer:

w=2

Step-by-step explanation:

-14w + 21 = 1 - 4w

-10w + 21 = 1

-10w = -20

w = -20/-10

w=2

Answer:

20 - 10 W = 0

-7 (2w - 3) = 1 - 4w

21 - 14w = 1 - 4 w

w = 2

HOPE THIS HELPS <3 :) HAVE A NICE DAY

Answer:

vertex C could be at (6,0) or (2,8)

(I'm sorry if I'm wrong, but if not I hope this helps!)

Step-by-step explanation:

vertex C needs to be placed somewhere on the graph where it would form a right angle (and therefore a right-angled triangle as well). vertex C could be at (6,0) or (2,8). this is because at these two points vertex C will form a right angle, therefore making it a right-angled triangle.

Answer:

Step-by-step explanation:

s=7+x

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

The surface area is made up of four triangles and a square base, so the area is four times the area of the triangle plus the area of the base.

A=4(5)(6)/2+5(5)

A=60+25

A=85

Answer:

Add all three side measures together

Step-by-step explanation:

That is how you find the perimeter of most shapes.

Hope this helps! :)

Answer:

add all three aide measures together. I'm not sure but I'd someone give another answer go with it. have a nice day

Answer:

The test statistic is z = -2.82.

Step-by-step explanation:

A marketing research firm believes that more than half of adults drink mostly either regular or diet soda.

This means that the null hypothesis is: [tex]H_{0} = 0.5[/tex]

The alternate hypothesis is: [tex]H_{a} > 0.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.5 tested at the null hypothesis:

This means that:

[tex]\mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5[/tex]

Gallup took a nationally representative sample of 2027 adults and asked them about their soda consumption. The survey shows that 950 of those surveyed drink mostly either regular or diet soda.

This means that [tex]n = 2027, X = \frac{950}{2027} = 0.4687[/tex]

Test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.4687 - 0.5}{\frac{0.5}{\sqrt{2027}}}[/tex]

[tex]z = -2.82[/tex]

The test statistic is z = -2.82.

Answer:

A. Wider and would have a smaller chance of missing the true mean.

Step-by-step explanation:

Margin of error for a confidence interval:

The margin of error for a confidence interval is given by:

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

In which z is related to the confidence level(the higher the confidence level, the higher the value of z), [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

95% confidence interval

Would be wider than the 90% confidence interval, due to the higher value of z.

Also, a x% confidence interval has a x% chance of having the true mean, and a (100-x)% probability of missing the true mean.

Then, a 95% confidence interval has a smaller(5%) chance of missing the true mean compared to the 90% confidence interval(10%). This means that the correct answer is given by option A.

Answer:

60

Step-by-step explanation:

120 + 90 + 90 + 60 = 360

Answer:

3^6

Step-by-step explanation:

Answer:

3^6

Count how many threes there are and that's the exponent

Answer: P-22 A-30

P=28 A-28

P=12 A=9

P=18 A=18

Step-by-step explanation:

1. Side lengths are 5,6,5,6- perimeter is 22 Area is 5*6= 30

2. Side lengths are 10,4,4,2,6,2- perimeter is 28 Area can be found by finding the area of the whole region (4*10) and subtracting the missing piece (2*6) so 40-12=28

3. sides are all 3- perimeter is 3*4= 12 and area is 3*3=9

4. sides are 6,3,6,3- perimeter is 18 and area is 3*6=18

9514 1404 393

Answer:

  9.70 seconds

Step-by-step explanation:

The zero of the equation can be found using the quadratic formula.

  ax² +bx +c = 0

  x = (-b ±√(b² -4ac))/(2a)

We are only interested in the positive value of x, so this will be ...

  x = (-147 -√(147² -4(-16)(80)))/(2(-16)) = (147 +√2679)/32

  x ≈ 9.7028 ≈ 9.70 . . . . seconds

The rocket will hit the ground after about 9.70 seconds.

Answer:

its equal

Step-by-step explanation:

15 times 5 (a) is 75 soooo 75 is equal to 75 maybe

Answer:

25

Step-by-step explanation:

17+8

Answer:

It's   -8

Step-by-step explanation:

DISTRIBUTE :

4x + 2( x - 2 ) = 4x + x - 12

4x + 2x - 4 = 4x + x - 12

COMBINE LIKE TERMS :

4x + 2x - 4 = 4x + x - 12

6x - 4 = 4x + x - 12

COMBINE LIKE TERMS :

6x - 4 = 4x + x - 12

6x - 4 = 5x - 12

ADD 4 TO BOTH SIDES :

6x - 4 = 5x - 12

6x - 4 + 4 = 5x - 12 + 4

ADD THE NUMBERS/ SIMPLIFY :

6x = 5x - 8

SUBTRACT 5x FROM BOTH SIDES :

6x = 5x - 8

6x - 5x = 5x - 8 - 5x

SIMPLIFY :

x = -8

Answer:

just say i did it and that it got undone

Step-by-step explanation:

Answer:

The real answer is:

3x^2 -6x+3x-6

Step-by-step explanation:

[tex]4 \frac{1}{5} + x = 4 \frac{3}{5} \\ \\ x = 4 \frac{3}{5} - 4 \frac{1}{2} \\ \\ x = \frac{2}{5} [/tex]

Step-by-step explanation:

Any answer that involes,

Step 1: Complete the Square

[tex] {x}^{2} - 10x = 39[/tex]

[tex]( \frac{ - 10}{2} ) {}^{2} = 25[/tex]

[tex] {x}^{2} - 10x + 25 = 64[/tex]

Step 2: Turn the left side into a binomial

[tex](x - 5) {}^{2} = 64[/tex]

Step 3: Solve for x.

[tex]x - 5 = + - 8[/tex]

[tex]x - 5 = 8[/tex]

[tex]x = 13[/tex]

OR

[tex]x - 5 = - 8[/tex]

[tex]x = - 3[/tex]

X=-3 or X=13

Answer:

Step-by-step explanation:

P(BorL)=(2/8)+(1/8)=(3/8)

He is expected to wear boots or loafers in the next 264 days

264(3/8)=99 of those days

Answer:

3 cm cube: 27

6 cm cube: 216

Step-by-step explanation:

First, you would need to find the volume of the 3 cm cube: 3*3*3=27

To build this cube you would need 27 1 cm cubes

For the 6 cm side cube you would need to do 6*6*6=216

So you would need 216 1 cm cubes

Hope this helps!