There was 1500ml of orange juice in the carton. Molly used 1/4litre at breakfast. How much orange juice was left in the carton.?

where's the diagram?

Answer:

a. dy/dt = - 2y/(200 + 2t)  where y(0) = 100 g

b. y = 20000/(200 + t)

Step-by-step explanation:

a. Write an IVP to determine y, the number of grams of salt in the tank at time, t.

Let y be the mass of salt.

The net flow into the tank dy/dt = mass flow in - mass flow out

Since only water flows into the tank, the mass flow in = 0 g/min

Let m be the mass of salt in the tank at time t. Since the volume of the tank is 200 L and water flows in at a rate of 4 L/min and out at a rate of 2 L/min, the net rate of increase of the volume of the tank is rate in - rate out = 4 L/min - 2 L/min = 2L/min. So, in time, t, the volume of the water in the tank increases by  2t. So, the volume of the tank in time, t is V = 200 + 2t.

So, the concentration of salt in the tank at time t is mass/volume = m/(200 + 2t).

Since the well mixed solution leaves at a rate of 2 L/min, the mass flow out is concentration × volume flow out =  y/(200 + 2t) × 2 = 2y/(200 + 2t)

The net flow into the tank dy/dt = mass flow in - mass flow out

dy/dt = 0 - 2y/(200 + 2t)

dy/dt = - 2y/(200 + 2t)

Since the initial mass of salt in the tank is 100 g, y(0) = 100 g

So, the initial value problem IVP is

dy/dt = - 2y/(200 + 2t)  where y(0) = 100 g

b. Solve an IVP to determine, the number of grams of salt in the tank at time, t.

Solving the IVP, we have

dy/dt = - 2y/(200 + 2t)  where y(0) = 100 g

Separating the variables, we have

dy/y = - 2dt/(200 + 2t)

Integrating both sides, we have

∫dy/y = - ∫2dt/(200 + 2t)

㏑y = - ㏑(200 + t) + ㏑C

㏑y + ㏑(200 + t) = ㏑C

㏑[y(200 + t)] = ㏑C

y(200 + t)] = C

y = C/(200 + t) since y(0) = 100, we have

100 = C/(200 + 0)

100 = C/200

C = 100 × 200

C = 20000

So, y = C/(200 + t)

y = 20000/(200 + t)

9514 1404 393

Answer:

Step-by-step explanation:

A local minimum is where the curve stops going down and starts going up. It is the bottom of any U-shaped spot. Here, those are identified with dots at the coordinates (-1, -2) and (3, -1).

(a) the x-values at which f has a local minimum are -1 and 3.

(b) the local minimum values of f are -2 and -1 at those x-values.

Answer:

In 24 years.

Step-by-step explanation:

Let the sum of money be 100 which amounts to 200 ( doubles itself ) in 6 years time. Interest on 100rs. Is 100. Putting the following in simple interest formula. You get :

[tex]100=\dfrac{100\times R\times 6}{100}\\\\R=\dfrac{100}{6}[/tex]

Now when 100 will become 5 times i.e 500 the interest will be 400rs.

Putting in simple interest formula:

[tex]400=\dfrac{\dfrac{100\times 100}{6T}}{100}\\\\T=\dfrac{2400}{100}\\\\=24\ yrs[/tex]

So, in 24 years, it will become 5 times.

Answer:

56+35=180 then solve it thanks

Answer:

Step-by-step explanation:

we have a two right triangle, with one side 115

lets say that the other side of the big right triangle is y

-in the big triangle find the third angle

180 -90 -35 = 55, because the sum of all interior angles in a triangle is 180

tan 55 = opp. /adj= y / 115

y = 115 * tan 55

-in the small right triangle

tan 56 = opp./ adj. = 115 / y-x

y-x = 115/ tan 56 , subtract y from both sides

- x=  -y +( 115/tan 56), multiply by -1 both sides

x= y -(115/tan56), substitute y for 115 * tan 55

x= (115*tan 55)- (115/tan56)

x≅86.6685

Answer:

Obtuse Scalene Triangle

Step-by-step explanation:

Sum of the squares of the smaller 2 sides < longest side squared = Obtuse Scalene Triangle

10% of 360 is 18 more than 5% of 360.

The percentage is defined as ratio expressed as a fraction of 100.

What are Arithmetic operations?

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Given data as :

10% of 360

5% of 360

Firstly, we have to determine 10% of 360,

⇒ 10% of 360

⇒ (10/100)360

⇒ (0.10)360

So, 10% of 360 is 36.

⇒ 5% of 360

⇒ (5/100)360

⇒ (0.05)360

So, 5% of 360 is 18.

Since 10% of 360 is more than 5% of 360

So, substract 18 from 36, and

⇒ 36 - 18

⇒ 18

Hence, 10% of 360 is 18 more than 5% of 360.

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Answer:

A.

Step-by-step explanation:

the equation of the parabola shown in the graph is y=x²-5, then the inequality is y≥x²-5 (inside the parabola).

Answer:

Multiply the product of 16,544 x 7 by 10 as it id the same as multiplying 16,544 x 70.

Answer:

Exponential growth formula. a represents the initial value.

Step-by-step explanation:

The value of "b" will determine the growth or decay behavior of the exponential function.

An exponential function can be represented in the form:

f(x) = a * b^x

where "a" is the initial value or the value of the function when x = 0, and "b" is the base of the exponential function.

If we want an exponential function with an initial value of 2, we can set "a" equal to 2:

f(x) = 2 * b^x

The value of "b" will determine the growth or decay behavior of the exponential function. Without further information or constraints on the value of "b," we cannot determine the specific exponential function. Additional information, such as the growth/decay factor or a specific point on the function, is needed to determine the value of "b" and fully define the exponential function.

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Answer:

2/3

Step-by-step explanation:

We know that (a/b) ^ (1/2) is a^ (1/2)  / b^ 1/2

( 4/9) ^ 1/2

4^1/2

-----------

9 ^ 1/2

2

----

3

===========================================

Explanation:

There are 3 ways to select the single math book and 4*3/2 = 12/2 = 6 ways to pick the two other books that are either physics or history (order doesn't matter). This is effectively because we have 3+1 = 4 books that are either physics or history, and we're using the nCr combination formula.

Overall, there are 3*6 = 18 ways to select the three books such that one is math, and the other two are either physics or history.

-------------------

There are 3+3+1 = 7 books total. Since we're selecting 3 of them, we use the nCr formula again and you should get 35.

Or you could note how (7*6*5)/(3*2*1) = 210/6 = 35

This says there are 35 ways to select any three books where we can tell the difference between any subject (ie we can tell the difference between the math books for instance).

-------------------

We found there are 18 ways to get what we want out of 35 ways to do the three selections. Therefore, the answer as a fraction is 18/35

Answer:

jhshejwjabsgsgshshsnsjs

Answer:

Step-by-step explanation:

Put the equation into center-radius form.

x² + y² + 8x - 12y + 24 = 0

x² + y² + 8x - 12y = -24

(x²+8x) + (y²-12y) = -24

(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24

(x+4)² + (y-6)² = 28

Center: (-4,6)

radius: √28

The parabola opens upward with the y- intercept being at y=7 (0,7) and the x- intercepts on x= -2,-4 / (-2,0), (-4,0). The axis of symmetry is on x=-3, and the vertex is on (-3,-1).

Answer:

Given E(t)=1100(100-t)+580(100-t)^2

Put t = 99.5, we get

E(99.5)=1100(100-99.5)+580(100-99.5)^2

E(99.5)=1100(0.5)+580(0.5)^2

E(99.5)=1100(0.5)+580(0.25)

E(99.5)=550+145

E(99.5)=695m

Step-by-step explanation:

It can be concluded that -

E(99.5) = 695

E(100) = 0

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as follows -

E(t) = 1100(100 - t) + 580(100 - t)²

The given function is -

E(t) = 1100(100 - t) + 580(100 - t)²

At → E(99.5)

E(99.5) = 1100(100 - t) + 580(100 - t)²

E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²

E(99.5) = 1100(0.5) + 580(0.5)²

E(99.5) = 550 + 145

E(99.5) = 695

At → E(100)

E(100) = 1100(100 - t) + 580(100 - t)²

E(100) = 1100(100 - 100) + 580(100 - 100)²

E(100) = 0

Therefore, it can be concluded that -

E(99.5) = 695

E(100) = 0

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minus sign ironically makes it go to the right

because the function crosses the y axis at -13

It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of  transformation, we have to compare the two equations and look for changes.

In the equation y = x - 13, we subtract 13 from the value of x.

This means that the graph of y = x is shifted 13 units downwards,

since every point on the graph has 13 subtracted from its y-coordinate.

Hence,  It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

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Answer:

39-13=26

Step-by-step explanation:

plus(minus)=minus

Answer:

10x^3 + 7x^2 + 3x + 15

Step-by-step explanation:

hope this helps have good day.

Answer:

the fellow is correct

Step-by-step explanation:

I would have done it but without the symbols I can't

Answer:

Step-by-step explanation:

yeah of course..your answer is true.. it's part d and there is no solution for that system...w and v both of them remove in solution of system and we don't have any unknown variable for solving.

9514 1404 393

Answer:

  D. no solutions

Step-by-step explanation:

The first equation can be simplified to standard form:

  0.5(8w +2v) = 3

  4w +v = 3 . . . . . . . eliminate parentheses

__

The second equation can also be simplified to a comparable standard form:

  8w = 2 -v +4w

  4w +v = 2 . . . . . . add v -4w

__

Comparing these two equations, we find the variable expressions to be the same, but the constants to be different. If any set of variable values were to satisfy one of these equations, it could not satisfy the other equation. There are no solutions to the system.

Answer:

This shows that the mean increases by 2.95

Step-by-step explanation:

Assume the given data is 2, 5, 6, 8

Mean = 2 +5+6+8/4

Mean = 21/4

Mean = 5.25

If number 20 is added, the data becomes 2, 5, 6, 8, 20

New mean = 2 +5+6+8+20/4

New mean = 41/5

New mean = 8.2

Taking the difference in the mean:

Difference = 8.2 - 5.25

Difference = 2.95

This shows that the mean increases by 2.95

NB: The data used was assumed since we are not given any data in question

Answer:

The answer is A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Subtracting second equation from first, term by term , gives

(8x - 4x) + (3y - 3y) = (14 - 8) , that is

4x + 0 = 6, so

4x = 6 → B

Answer:

y = 3

Step-by-step explanation:

6sin(30) = 3

Answer:

Step-by-step explanation:

Answer:

f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.

Step-by-step explanation:

The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.

* if x>1, then x-1>0.

* Also since the parabola opens up, then y>5.

So let's solve y=(x-1)^2+5 for x.

Subtract 5 on both sides:

y-5=(x-1)^2

Take square root of both sides:

Plus/minus sqrt(y-5)=x-1

We want x-1>0:

Sqrt(y-5)=x-1

Add 1 on both sides:

Sqrt(y-5)+1=x

Swap x and y:

Sqrt(x-5)+1=y

x>5

y>1

Answer:

0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Poisson distribution with an average of three errors per page

This means that [tex]\mu = 3[/tex]

What is the probability that a randomly selected page does not need to be retyped?

Probability of at most 3 errors, so:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]

Then

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]

0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.

Answer:

100 in²

Step-by-step explanation:

4 triangles, each of them has area = 10*5/2

so total area = (10*5/2)*4

= (10*5*2)

= 100 in²

Answered by GAUTHMATH

The lateral surface area of the pyramid is 100 in²

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The pyramid has four triangular faces and one rectangular base we need to calculate the lateral surface area so we will calculate the area of the four triangles and sum up all the triangles.

4 triangles, each of them has an area = 10 x ( 5/2 )

So total area = (10 x 5/2) x 4

Total area = (10 x 5 x 2)

Total area = 100 in²

Therefore the lateral surface area of the pyramid is 100 in²

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Answer:

x = 0.6 * 50

Step-by-step explanation:

x = 60% of 50

x = 60% * 50

x = 0.6 * 50

Answer:

60% of 50 = 60 / 100 × 50 = ⅗ × 50 = 150 / 5 = 30

________

x% of y = x / 100 × y = xy / 100