can anyone help me figure out how to do this

Answer:

[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]

Step-by-step explanation:

Given that:

A country population at any given time (t) is:

[tex]\dfrac{dP}{dt}= kP+I[/tex]

where;

P = population at any time t

k = positive constant

I = constant rate of immigration into the country.

Using the method of separation of the variable;

[tex]\dfrac{dP}{kP+1}= dt[/tex]

Taking integration on both sides:

[tex]\int \dfrac{dP}{kP+I}= \int \ dt[/tex]

[tex]\dfrac{1}{k} log (kP + I) = t+c_1 \ \ \ here: c_1 = constant \ of \ integration[/tex]

[tex]log (kP + I) =k t+kc_1[/tex]

By applying the exponential on both sides;

[tex]e^{log (kP + I) }=e^{k t+kc_1 }[/tex]

[tex]KP+I = e^{kt} *e^{kc_1}[/tex]

Assume [tex]e^{kc_1 }= C[/tex]

Then:

[tex]kP + I = Ce^{kt}[/tex]

[tex]kP = Ce^{kt}-I[/tex]

[tex]P =\dfrac{ Ce^{kt}-I}{k} \ \ \---- Let \ that \ be \ equation \ (1)[/tex]

When time t = 0, The Total population of the country is also [tex]P_o[/tex]

[tex]P_o = \dfrac{Ce^{0(t)} -I}{k}[/tex]

[tex]P_o = \dfrac{Ce^{0} -I}{k}[/tex]

[tex]P_o = \dfrac{C-I}{k}[/tex]

C - I = kP₀

C =  kP₀ + I

Substituting the value of C back into equation(1), we have:

[tex]P =\dfrac{ (kP_o+1)e^{kt}-I}{k}[/tex]

[tex]P =\dfrac{ (kP_o+1)e^{kt}}{k} - \dfrac{I}{k}[/tex]

[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]

Answer: The price is now 14.40

Step-by-step explanation: The difference is 9.60

Answer:

its c i believe <3

Answer:

Mean is 6, median 5.5, mode 2

Step-by-step

Answer:

mean=8+2+7+2+6+5

=30

30÷6=5

note: divide the total with it's sum.

median=7+2

=9

9÷2= 4.5

note: median is the middle no. since there is no middle no. so just add those two no. and divide it by 2.

mode= 2

since it occurs twice

Answer: 12

Step-by-step explanation: 25.75a+7.25b=454

a+b=32

Answer:

For the first one =5.29150262

Step-by-step explanation:

8 squared - 6 squared =64-36=28

square root of 28=5.29150262

Answer:

8571 letters per day

Step-by-step explanation:

60,000/1 week is the same as 60,000/7 days so

60,000/7 = 8571.428571

is aproximately 8571 letters per day

Answer:

It is TRUE.

Other:

Brainliest? Thanks!

9514 1404 393

Answer:

  rotated vertices are (1, 1), (-2, -1), (-4, 0)

Step-by-step explanation:

When the rotation direction is not specified, it is usually taken to be counterclockwise. Rotation 270° CCW is the same as rotation 90° CW. The transformation of coordinates is ...

  (x, y) ⇒ (y, -x)

Then your rotated points become ...

  A(-1, 1) ⇒ A'(1, 1)

  B(1, -2) ⇒ B'(-2, -1)

  C(0, -4) ⇒ C'(-4, 0)

_____

In the attached, the rotated triangle is shown in red. As an example, the arc through which point C is rotated is shown.

Answer:

5 times

Step-by-step explanation:

Because he enters through the front door.

Answer:

C) $54.00

Step-by-step explanation:

300*6%*3

300*0.06*3

which is $54.

Hope this helps plz hit the crown :D

Answer:

1/2 yard is equal to 18 inches

Step-by-step explanation:

Answer: I think #2 is either A or C

Step-by-step explanation: Hope it helped! :)

Answer:

Step-by-step explanation:

False,true,true

Answer: 4.1 gallons to 8.3 gallons

Step-by-step explanation:

just took the quiz

99.7% of the cows will produce an amount of milk in the range is 5.5 gallons to 6.9 gallons option (A) is correct.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

The missing options are:

We have:

A study has shown that the daily amount of milk produced by a dairy cow is normally distributed, with a mean of 6.2 gallons and a standard deviation of 0.7 gallons.

The mean = 6.2 gallons

Standard deviation = 0.7 gallons

The range can be calculated:

Lower range = 6.2 - 0.7 = 5.5 gallons

Upper range = 6.2 + 0.7 = 6.9 gallons

Thus, 99.7% of the cows will produce an amount of milk in the range is 5.5 gallons to 6.9 gallons option (A) is correct.

Learn more about the normal distribution here:

brainly.com/question/12421652

#SPJ5

Answer:

29

Step-by-step explanation:

Answer:

Already simplified

Step-by-step explanation:

Answer:

Step-by-step explanation:

its preety simple you just have to divide 3/10 and 1/8 and you will get your two answers

Answer:

5/9

Step-by-step explanation:

The relation between the dollars and forints will be directly proportional. Then the number of dollars will be $ 85.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

Levante changes 24 650 Hungarian forints to dollars.

Then the relation between the dollars and forints will be directly proportional. Then we have

Let x be the number of the dollars. Then we have

x / 1 = 24650 / 290

    x = $ 85

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ2

Answer:

Johnson Middle School held a track and field event during the school year. Miguel took part in a four-person shot put team. Shot put is a track and field event where athletes throw (or "put") a heavy sphere, called a "shot," as far as possible.

Step-by-step explanation:

PLZZ MARK BRAINLIEST!!!!!

Answer:

-7

Step-by-step explanation:

Answer:

7i

Step-by-step explanation:

the square root of 49 is 7

i equals -1

7 squared times -1 equals -49

Answer:

60°

Step-by-step explanation:

sum of all angles is 180

and it's a right-angled triangle so there is angle = 90

so  the other acute angle = 180-30-90=60°

Answer:

60

Step-by-step explanation:

90+30= 120

180-120= 60

Answer:

It would be a I think

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

pretty sure it's

2

−

3

=

9

\frac{X}{2}-3=9

2X−3=9

2

−

3

+

3

=

9

+

3

Given:

Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).

To find:

Whether the parallelogram ABCD is a rhombus, rectangle or square.

Solution:

Distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, we get

[tex]AB=\sqrt{(-4-(-4))^2+(-1-7)^2}[/tex]

[tex]AB=\sqrt{(-4+4)^2+(-8)^2}[/tex]

[tex]AB=\sqrt{0+64}[/tex]

[tex]AB=8[/tex]

Similarly,

[tex]BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8[/tex]

[tex]CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8[/tex]

[tex]AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8[/tex]

All sides of parallelogram are equal.

[tex]AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}[/tex]

[tex]BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}[/tex]

Both diagonals are equal.

Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.

We know that, a square is special case of rectangles and rhombus.

So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.

Answer:

it would take 22 gallons of gas

Step-by-step explanation:

3 divided by 60

that’s the amount of gas per single mile

then that number times 440 (number of miles you wish to go).