Kenneth is painting his kitchen and bathroom. He bought 5 gallons of paint to paint the two rooms. He uses 1/4 of that amount to paint the bathroom and the rest to paint the kitchen.

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:

45

Step-by-step explanation:

3 to the power of 2=9

and 9x5 =45

Answer:

5608.67 ÷ 7 = 801.24

Answer:its 1

Step-by-step explanation:

Answer:

(9³×m)3

Step-by-step explanation:

Hope it helps you

Answer:

I'm pretty sure E

Step-by-step explanation:

think about it he traveled 70 feet in 5 minutes so he would still be below sea level

Answer:

4 divided by 10 is 40% 3 divided by 10 is 30 percent

Step-by-step explanation:

for red there would be 40 percent probability and green and blue both have 30% probability.

Answer:

1543/100 is the answer

Answer:

D. f(x) = 2^x

Step-by-step explanation:

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

The base is always 2. The exponent changes and is x.

Answer: D. f(x) = 2^x

Answer:

Step-by-step explanation:

Answer: The answer is -2 it's just going to stay as -2 because y has no value.

Answer: this is the graph i wish that could help :)

Answer:

24.5

Step-by-step explanation:

Answer:

C. [tex] Cos(28) = \frac{15}{17} [/tex]

Step-by-step explanation:

Recall: SOHCAHTOA

Thus,

[tex] Cos(\theta) = \frac{Adjacent}{Hypotenuse} [/tex]

Reference angle = 28°

Adjacent = 15

Hypotenuse = 17

Plug in the values

[tex] Cos(28) = \frac{15}{17} [/tex]

Answer:

d) A[n] = A[n=1] - 2 (Your selected answer is correct)

Step-by-step explanation:

Think of the formula as:

new number = previous number minus 2

Answer:

x = 10

Step-by-step explanation:

it has 8 sides so:

total interior angle degrees = (180° x 8 sides) - 360° = 1080°

11x + 14 + 4x + 87 +2x + 70 + 4x + 31 + x + 92 + 3x + 167 + 5x + 48 + 2x + 251 = 1080°

combine like terms:

32x + 760° = 1080°

subtract 760° from both sides of the equation:

32x = 320°

divide both sides by 32:

x = 10

Answer:

10%

Step-by-step explanation:

you would do 50/5 because all the sections are even so you would get 10%.

Answer:

the inverse operation for addition is subtraction

Answer:

The digit 5 in 357 is in the tens place while the digit in the number 465 is in the ones place

Step-by-step explanation:

Good luck

Answer:

0.54 = 54% probability that this family will visit Sea World without consideration to the fact that they visited Busch Gardens.

Step-by-step explanation:

We solve this question treating these events as Venn probabilities.

I am going to say that:

Event A: Visited Busch Gardens.

Event B: Visited Sea World.

The probability of visiting Busch Gardens is 40%

This means that [tex]P(A) = 0.4[/tex]

The probability of visiting Sea World given that they visited Busch Gardens is 60%

60% of 40%, which means that:

[tex]P(A \cap B) = 0.6*0.4 = 0.24[/tex]

The agent knows the probability of this type of family visiting either Busch Gardens or Sea World is 70%.

This means that [tex]P(A \cup B) = 0.7[/tex]

Te agent wants to determine the probability that this family will visit Sea World without consideration to the fact that they visited Busch Gardens.

This is P(B).

These probabilities are related by the following equation:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Replacing the values

[tex]0.7 = 0.4 + P(B) - 0.24[/tex]

[tex]0.16 + P(B) = 0.7[/tex]

[tex]P(B) = 0.54[/tex]

0.54 = 54% probability that this family will visit Sea World without consideration to the fact that they visited Busch Gardens.

Answer:

Volume = l*w*h

Equation: 1620 = 9*9*h

1620=81h

h=20 cm

Answer:

800 cubic inches

Step-by-step explanation:

We will use the formula= V=lwh or Volume= length times width times height

so, Volume=5inches times 8 inches times 20 inches

so, volume= 5 times 8 times 20

=40 times 20

=800 cubic inches

Answer:

800

Step-by-step explanation:

Answer:   777654

Step-by-step explanation:

lol

Answer: D

Step-by-step explanation:

Answer:

455

Step-by-step explanation:

Answer: 15 10

Step-by-step explanation: