I need help with this problem

Answer:

c. dP/dt = (1/5)P

Step-by-step explanation:

Given that the rate of change of population with respect to time dP/dt is directly proportional to the population, P, we have

dP/dt ∝ P

dP/dt = kP

Given that dP/dt = 2 million insects per day and P = 10 million insects after 5 days, So,

2 = k × 10

k = 2/10

k = 1/5

So, dP/dt = kP

dP/dt = (1/5)P

The option C is correct

The rate of change of a function with respect to the given variable.

The rate of change of population with respect to time is directly proportional to the population P. We have

[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t} \propto P\\\\\dfrac{\mathrm{d} P}{\mathrm{d} t} = kP[/tex]

[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t}[/tex] is 2 million insects per day and P = 10 million insects after 5 days. So

[tex]\begin{aligned} \dfrac{\mathrm{d} P}{\mathrm{d} t} &= kP\\2 &= 10k\\k &= \dfrac{1}{5} \\\end{aligned}[/tex]

Then

[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t} = kP\\\\ \dfrac{\mathrm{d} P}{\mathrm{d} t} = \dfrac{1}{5} P[/tex]

Thus, option C is correct.

More about the Differentiation link is given below.

https://brainly.com/question/24062595

Answer:

16-4x^2

Step-by-step explanation:

u start multiplying them by each other .

4×4= 16

4×2x= 8x

-2x×4= -8x

-2x×2x= -4x^2

now u combine like terms

8x+-8x = 0

16-4x^2

I hope u understood.... lol

Answer:

x=-192

Step-by-step explanation:

simplyfying we get

2/3x-4= 3/4x+12

so subratcing 2/3 on both sides we get

-4= 9x/12- 8x/12+12

subtracting 12 from both sides we get

-16= x/12

x= -192

if my answer helps please mark as brainliest

Answer:

15 bags

Step-by-step explanation:

She can fill 5 bags per each pound (because there are 5 [tex]\frac{1}{5}ths[/tex] per pound)

Since there are 3 pounds, and , again, each pound can fill 5 bags, she will need 15 bags.

Another way too look at it is to ask how many 1/5ths are in 3 pounds. To find this answer mathematically:

3 ÷ 1/5 = 15 because when we divide by a fraction, we need to flip it and then multiply (so 3 ÷ 1/5 is actually 3×5)

Answer:

1. y - 2 = (3/5) (x + 5)

2. y = -5x - 4

Step-by-step explanation:

Slope form - y1 - y = m (x1 - x)

Slope intercept - y = mx + b

Answer:

y=2x+3

Step-by-step explanation:

the 2 is the coefficient so everytime you add a new flower the amount will go up by 2 dollars and the $3 delivery fee is a one time fee so you only add it one time.

Answer:

100.531km

Step-by-step explanation:

figure #1

smaller part

4x7x2= 56m

larger part

4x3x7= 84m

84+56= 140m³

figure #2

smaller part

2x4x3= 24m

larger part

4x4x12= 192m

192+24= 216in³

Answer:

3

Step-by-step explanation:

[tex]\frac{y_{1} - y_{2}}{x_{1} - x_{2}} = \frac{9}{3} = 3[/tex]

creo que es 231 en total :7-2:al 231

Answer:

Answer:

[tex]3x^{2} - 7x - 6[/tex]

Step-by-step explanation:

[tex]2x^{2} - 6 + x^{2} - 7x[/tex]

[tex]3x^{2} - 7x - 6[/tex]

Answer:

17.5

Step-by-step explanation:

Those angles are supplementary, in other words, they add up to 180°

To solve you set the expressions up to 180:

(5x - 30) + 7x = 180

12x - 30 = 180

12x = 210

x = 17.5

Answer:

3,4

Step-by-step explanation:

up 3 and right 4. your welcome

Answer:

0.0045248 ;

0.1312218 ;

0.0001809 ;

0.1659729

Step-by-step explanation:

Number of Kings in deck = 4

Total number of cards in deck = 52

Picking without replacement :

A = King on first draw :

P(A) = 4 / 52

A = King on 2nd draw :

P(B) = 3 / 51

A = King on 3rd draw :

P(C) = 2 / 50

1.) P(A n B) = P(A) * P(B)

P(A n B) = 4/52 * 3/51 = 12 / 2652 = 0.0045248

2.) P(A u B) = P(A) + P(B) - P(AnB)

P(AuB) = 4/52 + 3/51 - 0.0045248 = 0.1312218

3.) P(A ∩ B ∩ C) = P(A) * P(B) * P(C)

P(A ∩ B ∩ C) = 4/52 * 3/51 * 2/50 = 0.0001809

4.) P(A U B U C) =

P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) - P(AnBnC)

P(AnC) = P(A) * P(C) = 4/52 * 2/50 = 0.0030769

P(BnC) = P(B) * P(C) = 3/51 * 2/50 = 0.0023529

4/52 + 3/51 + 2/50 - 0.0045248 - 0.0030769 - 0.0023529 + 0.0001809 = 0.1659729

Answer:

31hr

Step-by-step explanation:

Answer:

I’m doing i-Ready and my question hasn’t been answered

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

[tex]25 \times 25 - 15 \times 15 = 400[/tex]

[tex] \sqrt{400} = 20[/tex]

Answer:

b=√400

=20

Step-by-step explanation:

15^2+b^2=25^2

225 + b^2=625

b^2=625-225

b^2=400

b=√400

b=20

Answer:

12.5%

Step-by-step explanation:

hope it helps!!!

Answer:

1. 33%

2. 28

3. 62.5

Step-by-step explanation:

Answer: does

Step-by-step explanation:

Answer:

a) P(odd) = 1/2

b) P(multiple of 3) = 1/4

c) P(not 5, 6, 7) = 5/8

d) P(n < 4) = 3/8

Step-by-step explanation:

a) half of the numbers on the spinner are odd

b) there are 2 multiples of 3 (3 and 6)

c) not 5,6,7 means P(1,2,3,4,8) which is 5/8

d) P(n < 4) = P(1,2,3) = 3/8

Answer:

Step-by-step explanation:

Answer:

The length of the rectangular pen is 40ft. The width of the rectangular pen is 20ft

Answer:

7ft

Step-by-step explanation:

2W+2L=20

2(W+L)=20

2(W+(W+4))=20

4W+8=20

4W=12

W=3

or

If 20 is the total length of fencing used, the length of the fence is to be 4 ft longer than the width, and we know this is a rectangular pen (meaning it has 4 sides), we first multiply 4 (the additional ft for the length side) by two to get 8. Next we subtract 8 from the total amount of fencing (20) to get 12. Finally, since we know there are 4 sides to a rectangle, we divide 12 by 4 to get the width. Now since the length is 4 ft longer than the width, and we are looking for the length, then we add 3+4 to equal 7.

7 is the length.

Answer:

A). (1, 7)

Step-by-step explanation:

-3x – 2y = -17

9x + 2y = 23

____________+

6x = 6

x = 6/6

x = 1

9x + 2y = 23

9(1) + 2y = 23

9 + 2y = 23

2y = 23 - 9

2y = 14

y = 14/2

y = 7