If P(t) is the size of a population at time t, which of the following differential equations describes linear growth in the size of the population?

dPdt=200
Answer A: d cap p over d t is equal to 200
A

dPdt=200t
Answer B: d cap p over d t is equal to 200 t
B

dPdt=100t2
Answer C: d cap p over d t is equal to 100 t squared
C

dPdt=200P
Answer D: d cap p over d t is equal to 200 cap p
D

dPdt=100P2

A system of equations is simply a system that contains related equations of multiply variables

It took 5 seconds for the adults to go 20 yards and catch up to the kids

Let x represents the time of the race

The kids started 15 yards ahead, and they raced at 1 yard per second.

So, the kids' equation is represented as: [tex]\mathbf{k =15 + x}[/tex]

The adults' raced at 4 yards per second.

So, the adults' equation is represented as: [tex]\mathbf{a =4x }[/tex]

When they are side by side, we have the following equivalent equation

[tex]\mathbf{4x = 15 + x}[/tex]

Subtract x from both sides

[tex]\mathbf{3x = 15}[/tex]

Divide both sides by 3

[tex]\mathbf{x = 5}[/tex]

It means that, it took the adults 5 seconds to catch up with the kids

Substitute 5 for x in any of the equations to calculate the distance travelled.

[tex]\mathbf{a =4 \times 5}[/tex]

[tex]\mathbf{a =20}[/tex]

It means that, the adults catch up with the kids at 20 yards

Read more about systems of equations at:

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Answer:

The adults went 123 yards and caught up to the kids in 41 seconds

Step-by-step explanation:

ixl :)

Answer:

40 pizzas in total

Step-by-step explanation:

10×4=40

The way you typed out this sentence was a bit confusing but I think you were saying...

For a weekly car rental, a car rental company charges customers a flat fee of $100 +  and charges 10 cents for every mile traveled. write an equation for the amount of a weekly rental car that travels 15 miles (Please let me know if I am wrong)

The equation would be

10+10 +10+ 10+ 10+ 10+ 10+ 10+ 10+ 10+ 10+ 10+ 10+ 10+ 10 = 150 cents

so they would be charging $1.50

Hoped this helped!

Have a great day/night! :)

Answer:last one

Step-by-step explanation:

A random number generator picks a number from 6 to 66 in a uniform manner, its resultants are  mathematically given as

Generally, the equation for Mean is mathematically given as

[tex]X=\frac{a+b}{2}\\\\Therefore\\\\X=\frac{6+66}{2}[/tex]

X=36

b)

Generally, the equation for standard deviation is mathematically given as

[tex]\sigma=\sqrt{\frac{b-a}{12}^2}\\\\Therefore\\\\\sigma=\sqrt{(\frac{66-6}{12})^2}\\\\\sigma=\sqrt{25}\\\\[/tex]

[tex]\sigma=5[/tex]

c)

The probability that the number will be exactly 19

[tex]p(x=19)=\frac{19-6}{66-6}[/tex]

p(x=19)=0.2167

d)

The probability that the number will be between 28 and 46 is P(28 < x < 46)

[tex]P(28 < x < 46) =\frac{46-6}{66-6} -(\frac{28-6}{66-6})[/tex]

P(28 < x < 46) =0.3

e)

The probability that the number will be larger than 48 is P(x > 48)

[tex]P(x > 48)=1-P(x\leq 48)[/tex]

Therefore

[tex]P(x > 48)=1-(\frac{48-6}{66-6})[/tex]

P(x > 48)=0.3

f)

[tex]P(x > 17 | x < 62) = P(x\leq 62-P(x leq 17))[/tex]

Therefore

[tex]P(x > 17 | x < 62) =\frac{62-6}{66-6}-(\frac{17-6}{66-6})[/tex]

P(x > 17 | x < 62) =0.75

g)

The 49th percentile

[tex]p(x\leqk=k.(1/66-6))[/tex]

Therefore

[tex]0.49=k*(1/(66-6))[/tex]

k=29.4

h)

The maximum for the lower quartile

P(xl)=h*1/60

0.25=h*1/60

h=15

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Answer:

4.61

did that help??

Step-by-step explanation:

[tex]2 \dfrac 16 + 3 \dfrac 49 \\\\\\= 2 + \dfrac 16 + 3+ \dfrac 49\\\\\\ = 5+\dfrac{11}{18}= 5 \dfrac{11}{18}[/tex]

Answer:

78 buttons left

Step-by-step explanation:

I multiplied 24 children by 3 buttons because each child took 3 buttons and I got 72 buttons taken.

Then I subtracted 150 buttons which is the starting number by 72 buttons (the amount taken by the child's) to get 78 buttons left in the box. ( I just separated negative 72 buttons into -50 and -22 to make it easier)

Answer:

Where is it?

Step-by-step explanation:

Answer:

0.573

Hope that helps :)

Answer:

(1/2, 1/4)

Step-by-step explanation:

This is gonna be long. The x coordinate of a parabola's vertex = -b/2a. Now we have to find the equation of the parabola. Using the given points and plugging them into y=ax^2 + bx + c, we can determine:

0 = c

0 = a + b

-20 = 25a + 5b

After rearranging and solving, we get:

b = -a

-20 = 20a

a = -1

b = 1

y = -x^2 + x

Now we can find the x coordinate of the vertex, which is 1/2. After plugging this into our parabola, we get a y coordinate of -1/4 + 1/2 = 1/4. Therefore, the vertex is located at (1/2, 1/4).

[tex]\huge\mathfrak\pink{answer} [/tex]

Answer:

175000.(or around that number)

Step-by-step explanation:

half of 350,000 is 175000.

Answer:

136 inches or 354.44cm

Step-by-step explanation:

17*8 = 136

Answer:

136 inches

Step-by-step explanation:

17 X 8 = 136 inches

9514 1404 393

Answer:

  1

Step-by-step explanation:

Any (non-zero) number divided by itself is 1.

_____

This is a fact that has many uses in problem solving and units conversion.

Answer:

1.98 I think sorry if it's wrong

Answer:

line them up straight with the bottom number and the top number.

Step-by-step explanation:

cheese : pepperoni : sausage : mushroom =

10 : 7 : 5 : 8

so, in total there are 10+7+5+8 = 30 "business pieces".

to get the total number of pizzas, we need to see how many pizzas are sold per "business piece" ?

we get this from the 35 orders of pepperoni pizzas.

these 35 orders represent 7 "business pieces".

that means 1 "business piece" = 35/7 = 5 pizzas.

that means that 30 "business pieces" are 5×30 = 150

so, in total, 150 pizzas were ordered.

Answer:

28

Step-by-step explanation:

the ratio is written as copies/dollars.

14/4=x/8

since we can multiply 4 by 2 to get 8, multiply 14 by 2 as well.

14/4=28/8

The answer to your question is in the image above.

Answer:

x=-16

y=-11

Explanation:

2x-4y=12

x-3y=17

first multiply all the numbers of the bottom equation by -2

2x-4y=12

-2x+6y=-34

then cancel the x's, and add the other numbers

2y=-22

solve for y

y=-11

plug y into either the original top or bottom equations

2x-4(-11)=12

2x+44=12

2x=-32

x=-16

or

x-3(-11)=17

x+33=17

x=-16

The required value of the given numerical expression is 118, as evaluated by including the PEMDAS rule in the expression.

Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.

The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.

The given numerical expression would be below as:

⇒ 3⋅23 + 52 − 18 ÷ 6

Using the PEMDAS rule in the above expression,

⇒ 3⋅23 + 52 − 18 ÷ 6

Apply the multiplication operation,

⇒ 69 + 52 − 18 ÷ 6

Apply the division operation,

⇒ 69 + 52 − 3

Apply the addition operation,

⇒ 121 − 3

Apply the subtraction operation to get

⇒ 118

Therefore, the evaluated value of the given expression would be 118.

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We first compute the partial derivatives of f(x, y):

f(x, y) = 5x² + 5y² - 10x + 21

∂f/∂x = 10x - 10

∂f/∂y = 10y

The critical points of f occur where both ∂f/∂x and ∂f/∂y are equal to zero. This only happens at the point (x, y) = (1, 0). (And this point does lie inside R.)

Next, compute the Hessian matrix H(x, y) for f :

[tex]H(x, y) = \begin{bmatrix}\frac{\partial^2f}{\partial x^2} & \frac{\partial^2f}{\partial x\partial y} \\ \frac{\partial^2 f}{\partial y\partial x} & \frac{\partial^2f}{\partial y^2}\end{bmatrix} = \begin{bmatrix}10&0\\0&10\end{bmatrix}[/tex]

Since det(H(x,y)) = 100 is positive for all x and y, this means the critical point (1, 0) is a local minimum, and we have f(1, 0) = 16.

Next, we check for extrema along the boundary of R, which is comprised of a semicircle with radius 2 and the line segment connecting (-2, 0) and (2, 0).

• Parameterize the semicircular portion by

x(t) = 2 cos(t)

y(t) = 2 sin(t)

with 0 ≤ t ≤ π. Then

f(x(t), y(t)) = 20 sin²(t) + 20 cos²(t) - 20 cos(t) + 21

which is simplifies to a function of one variable t,

g(t) = 41 - 20 cos(t)

Find the extrema of g over the interval [0, π] : we have critical points when

g'(t) = 20 sin(t) = 0

which happens at t = 0 and t = π. At these points, we get local extreme values  of

•• t = 0   =>   x = 2 and y = 0   =>   f(2, 0) = 21

•• t = π   =>   x = -2 and y = 0   =>   f(-2, 0) = 61

• Over the line-segment portion, we take y = 0, so f(x, y) again reduces to a function of one variable:

f(x, 0) = 5x² - 10x + 21

Completing the square, we have

5x² - 10x + 21 = 5 (x - 1)² + 16

which has a maximum value of 16 when x = 1 (and this happens to be the critical point (1, 0) we found earlier).

So, over the region R, f(x, y) has

• an absolute maximum of 61 at the point (-2, 0), and

• an absolute minimum of 16 at (1, 0)

m = 180 - CBE = 180 - [ 360 - BDC - BED - (180 - DCE - DEC)]  = 180 - [ 360 - 90 -90 - (180 - 13*2)] = 154

P/s: 180 - DCE - DEC = CDE

ok done. Thank to me :>

Answer:

d

Step-by-step explanation:

Answer:

  (-1, 4)

Step-by-step explanation:

Rotation 180° negates both coordinates:

  (x, y) ⇒ (-x, -y)

The direction (clockwise or counterclockwise) is irrelevant. It is the same as reflection across the center of rotation (the origin).

  (1, -4) ⇒ (-1, 4) . . . . after rotation 180°

Answer:

-2

Step-by-step explanation:

-4x-2x ≤ 17-5

-6x ≤ 12 | /(-6)

x ≥ -2

Answer:

x=120 y=60

Step-by-step explanation:

Interior angle of a hexagon = 120

Straight line = 180

180-120=60

Answer:

yes its correct

Step-by-step explanation:

but for the check where did you get the 12? you might want to redo that part but otherwise its right

Answer:

Yes, Kathy does  have enough juice.

Step-by-step explanation:

Kathy does have enough because quarts are a little bigger than liters, so the 3 quarts she has will cover the liters.