what’s 15/25 in its simplest form?

Answer:

-4x

Step-by-step explanation:

3-7=-4 just add a x

Answer:

27

Step-by-step explanation:

i think

Step-by-step explanation:

\(your \: answer \: is \: option \: c \\ 11\)

So the first three possible values of g^2 + 3 are:

3, 4, 7

The first option is the correct one.

The set of the whole numbers is {0, 1, 2, 3...}

Then the first possible value is when g = 0.

0^2 + 3 = 3

The second possible value is when g = 1

1^2 + 3 = 4

The third possible value is when g = 2.

2^2 + 3 = 7

So the first three possible values of g^2 + 3 are:

3, 4, 7

The first option is the correct one.

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Answer:

3,4,7

Step-by-step explanation:

jus took the test

Answer:

y = 5x -10

Step-by-step explanation:

The y-intercept is -10, as in, the line on the y-axis is at -10

The slope is 5, as in, the line is moving up 5 and right 1. So it should be 5/1x but you don't need the 1. You could use it, but you don't need to. Here's what it would look like if you did use it:

y = 5/1x - 10

Answer:

− 312500

Step-by-step explanation:

Whenever looking at sequences, you have to attempt to find a common factor between the members of that sequence, be it the difference between them, a common divisor, a common multiplier, etc. In this case, we can see that if we divide each member by the previous one, we get a the same number:

100/-20 = -5

-20/4 = -5

So our sequence, starting at 4 is represented by the following recursive equation:  

Hope this helps. :D

Answer:

A makes the most sence cbwt

Step-by-step explanation:

Using ϕ and the Fundamental Theorem of Calculus for Line Integrals to evaluate ∫CF⃗ ⋅dr⃗ = 17920/3.

(a) To find F⃗ -∇ϕ, we need to compute the gradient of ϕ and subtract it from F⃗ :

∇ϕ = (∂ϕ/∂x)i⃗ + (∂ϕ/∂y)j⃗

= (83(3x^2 + 6y))i⃗ + (6x)j⃗

= 249x^2 i⃗ + 6xj⃗

F⃗ -∇ϕ = (6yi⃗ + 7xj⃗ ) - (249x² i⃗ + 6xj⃗ )

= -249x² i⃗ + (6y - 6x)j⃗

Now, let's find ∇h:

∇h = (∂h/∂x)i⃗ + (∂h/∂y)j⃗

= (-8xi⃗ + j⃗)

Comparing F⃗ -∇ϕ and ∇h, we see that they are related because they have the same components. Specifically:

F⃗ -∇ϕ = ∇h

(b) To evaluate ∫CF⃗ ⋅dr⃗ using the Fundamental Theorem of Calculus for Line Integrals, we need to parameterize the path C from P(0, 6) to Q(4, 70) that lies on the contour of h.

Let's parameterize C as r(t) = (x(t), y(t)), where t varies from 0 to 1.

We can express x(t) and y(t) in terms of t as follows:

x(t) = 4t

y(t) = 6 + 64t²

Now, let's compute the differential dr⃗ :

dr⃗ = (dx/dt)i⃗ + (dy/dt)j⃗

= 4i⃗ + (128t)j⃗

Next, we evaluate F⃗ at the parameterized points on C:

F⃗ (r(t)) = 6(y(t)i⃗ + 7x(t)j⃗ )

= 6(6 + 64t²)i⃗ + 7(4t)j⃗

= (36 + 384t²)i⃗ + 28tj⃗

Now, we can compute ∫CF⃗ ⋅dr⃗ :

∫CF⃗ ⋅dr⃗ = ∫₀¹ (F⃗ (r(t)) ⋅ dr⃗) dt

= ∫₀¹ [(36 + 384t²)i⃗ + 28tj⃗] ⋅ (4i⃗ + (128t)j⃗) dt

= ∫₀¹ [(36 + 384t²)(4) + 28t(128t)] dt

= ∫₀¹ [144 + 1536t² + 3584t²] dt

= ∫₀¹ (1536t² + 3584t² + 144) dt

= ∫₀¹ (5120t² + 144) dt

= [5120(1/3)t³ + 144t] evaluated from 0 to 1

= 5120/3 + 144 - 0

= 17920/3

Therefore, ∫CF⃗ ⋅dr⃗ = 17920/3.

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Answer:

D

Step-by-step explanation:

Answer:

d) 1/16

Step-by-step explanation:

1/2 · 1/2 ·1/2 · 1/2 = 1/16

Answer:

anything :P

Step-by-step explanation:

Answer:

There are 200 teddy bears, to find this answer divide 240 by 6, which is 40, then multiply 5 times 40 and you get your answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

TB = number of Teddy Bears

D = number of Dolls

D = 240

D/TB = 6/5

240/TB = 6/5

6TB = 5*(240)

6TB = 1200

TB = 200

====

240/200 = 24/20 = 6/5:   It checks.

Answer:

261.06 (Approx)

Step-by-step explanation:

Given:

Two number = 0.678,9.01/0.0234

Find:

Multiply

Computation:

⇒ 0.678,9.01/0.0234

⇒ 0.678 x [9.01/0.0234]

⇒ 6.10878 / 0.0234

⇒ 261.058874

261.06 (Approx)

Answer:

28 Pi

Step-by-step explanation:

circumference = 24(2)(π) = 48π

arc ABC = 360° - 150° = 210°

(210/360)(48π) = 28 Pi

Answer:

232

Step-by-step explanation:

232

We can tell if a character is direct or Indirect  by the five methods which are action, reactions, physical description,  inner thoughts,  and speech.

The Characterization in literature is the process that the authors use to develop characters and create images of characters for audience.

There are two different approaches for characterization, which are Direct Characterization and Indirect Characterization.

The methods by which we can know that a character is Direct or Indirect are :

(i) Physical description - In this the character's physical appearance is described. For example, How the character dresses might reveal something about the character.

(ii) Action - Is the character a good person or a bad person can be told by his Action .

(iii) Inner thoughts - The inner thoughts of character reveals the personality .

(iv) Reactions - The Effect on other characters also reveals about the personality of character .

(v) Speech - What character says provides a great insight for the reader.

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Answer:

19/12

Step-by-step explanation:

1.75=7/4

7/4-1/6

21/12-2/12

19/12

Answer:

19/12

Step-by-step explanation:

1.75=7/4

7/4-1/6

21/12-2/12

19/12

Answer:

It's B

Step-by-step explanation:

B

Answer:

B-----

Step-by-step explanation:

Answer:

Ais 66 and B is 40% C is 60%

Step-by-step explanation:

I know A is correct but not b or c hope this helps

The first statement is false and the second statement is true.

Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. There are two types of random variables.

A random variable that takes a finite number of possible values can be defined as a Discrete random variable. A random variable that takes an infinite number of possible values can be defined as a Continuous random variable. A continuous random variable consists of only continuous values.

Continuous random variables are defined at intervals of values. Continuous random variables are represented by the area under a curve.

⇒  The number of cars that go through the drive-in window at a local bank each hour.

The number of cars can be counted and can be an integer like 10, 20,100 etc.

∵ The number of cars is countable it is not an example of a continuous random variable        

⇒ The high daily temperature in Anchorage.

High daily temperature can be an integer or function like 60°, 120° etc

∵ The high daily temperature is an example of a continuous random variable.

Therefore, The number of cars that go through the drive-in window at a local bank each hour is not an example of a continuous random variable and The high daily temperature in Anchorage is an example of a continuous random variable.

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The complete question is

The exponential distribution may be used to predict the failure rate of certain items over time. An LED light bulb has an expected lifetime of 25000 hours. Assuming that the lifetime of the LED light bulb follows the exponential distribution, the probability that it will last more than 3 years is closest to (C) 53%. Correct answer is option C

This is because the lifetime of an LED light bulb can be estimated using the following equation : P(x > 3 years) = 1 - P(x ≤ 3 years)where x is the lifetime of the LED light bulb.If we convert 3 years to hours, we get 3 * 365 * 24 = 26280 hours. As a result, P(x ≤ 3 years) = P(x ≤ 26280 hours)

Using the formula for exponential distribution, the probability of the LED light bulb failing after 26280 hours is : Probability = 1 - e^{-λx} Where λ is the failure rate per hour and x is the length of time in hours.We can now calculate the value of λ by dividing the expected lifetime of the bulb by the total number of hours.

 λ = 1/25000 hours  This implies that the probability of the LED light bulb failing after 26280 hours is : P (x ≤ 26280 hours)

Therefore, the probability that the LED light bulb will last more than 3 years is approximately 53 percent. The Correct answer is option C

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A differential equation with some initial conditions is used to solve an initial value problem.

The required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.

Let the given equation be \($y^{1/2} dy\ dx y^{3/2} = 1\), y(0) = 9

\($(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1\) …..(1)

Divide the given equation (1)  by \($\sqrt{ y} $\)  giving

\($y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$\), which is in Bernoulli's form.

Put \($u=y^{(1+1 / 2)}=y^{(3 / 2)}$\)

Then \($(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$\).

Multiply (2) by \($\sqrt{ } y$\) and we get

\(y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1\)

(2/3) \(u^{\prime}+u=1$\) or \($u^{\prime}+(3 / 2) y=3 / 2$\),

which is a first order linear equation with an integrating factor

exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is

\(u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$\)  or

\(\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}\)

To obtain the particular solution satisfying y(0) = 4,

put x = 0, y = 4, then

8 = (9/4) + c

c = (23/4)

Hence, the required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

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An inverse-square central force field is  \(mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\\).

From Newton's second law of motion,

mass × acceleration = Force acting on the mass

Resolving the force F along x and y directions and applying Newton's second law of motion,

Using,

\(r = \sqrt{x^2+y^2}\)

​

Therefore,

\(m\frac{d^2x}{dt^2} =-|F|cos \theta\)

\(mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}\)

Where \(r = \sqrt{x^2+y^2}\)

​ and cos⁡θ = \(\frac{x}{\sqrt{x^2+y^2} }\)

Similarly using,

\(r = \sqrt{x^2+y^2}\)

we get,

 \(m\frac{d^2y}{dt^2} = -|F|sin\theta\)

\(mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}\)

Where \(r = \sqrt{x^2+y^2}\)

​ and sinθ = \(\frac{y}{\sqrt{x^2+y^2} }\)

Therefore we showed that holds

\(mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\\)

Hence the answer is an inverse-square central force field is  \(mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\\).

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Answer:

20m square units

Step-by-step explanation:

The area of a traingle  = bh/2............... Equation 1

Where b = lenght of the base, h = heigt of the triangle.

From the question,

The area of triangle GHK = m square units., let the base and the heigth of the triangle be x and y respectively

Therefore,

b = x, h = y

Substitute these values into equation 1

m = xy/2................... Equation 2

If the height of the triangle increase to five times the current height, and the length of the base increase to four times the current length.

Therefore,

height of the larger triangle = 5y, base of the larger triangle = 4x

Substitute these values into equation 1

Area of the larger triangle = (5y×4x)/2

Area of the larger triangle = 20xy/2................. Equation 3

Substitute equation 2 into equation 3

Area of the new triangle = 20m square units.

Answer:

Expression A: |-10 - (-4)|

Expresion B: |-10+4|

Step-by-step explanation:

The distance (which you can get by counting on the numberline) is 6. This mean that the value derived wiithin the absolute value must be either 6 or -6. Answers of 4 and negative 4 get you this answer.

Given equation is ln(4x + 5) + 4x = 25. We are required to find an integer n so that the interval (n, n+1) contains a solution to this equation.

To solve this equation, we have to use numerical methods. We can use the trial and error method or use graphical methods to find the solution.Let's consider the graphical method:First, let's plot the graphs of y = ln(4x + 5) + 4x and y = 25 and see where they intersect. We can use the Desmos graphing calculator for this.Step 1: Visit the Desmos Graphing Calculator website.Step 2: Enter the equations y = ln(4x + 5) + 4x and y = 25 in the given field.Step 3: Adjust the window of the graph to see the intersection points, which are shown in the image below.Image of the graph shown on Desmos calculator.The graph of y = ln(4x + 5) + 4x intersects the graph of y = 25 in the interval (4, 5).Thus, n = 4.Therefore, the solution is as follows:n = 4.

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The moment of inertia for an area is a measure of an object's resistance to rotational forces and is calculated using an integral involving the distance of small area elements from a reference axis.

Moment of inertia for an area, also known as the second moment of area or area moment of inertia, is a fundamental geometric property of a shape that reflects how its mass is distributed relative to a specific reference axis. It plays a crucial role in mechanics, as it is directly related to an object's resistance to bending and torsion.

In mathematical terms, the moment of inertia for an area is calculated using an integral of the form:

I = ∫(y^2 + z^2) dA

Where I represents the moment of inertia, y and z are the distances of a small area element dA from the reference axis (usually the centroid of the shape), and the integral is computed over the entire area of the shape.

The moment of inertia has units of length to the fourth power (L^4), and its value depends on both the shape's geometry and the axis around which it is calculated. For simple shapes like rectangles, circles, and triangles, the moment of inertia can be calculated using standard formulas. However, for more complex shapes, numerical methods like finite element analysis or integral calculus might be required.

In summary, the moment of inertia for an area is a measure of an object's resistance to rotational forces and is calculated using an integral involving the distance of small area elements from a reference axis. It plays a crucial role in mechanics and is essential in understanding an object's behavior under bending and torsion.

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Using proportions, the estimate of the per capita consumption from 2011 was 29.25 gallons.

A proportion is a fraction of the total amount, the measures are related using a rule of three.

The amount in 2012 was an increase of 5.3% from 2011,

105.3% = 1.053 of x,

The consumption per capita was 30.8 gallons,

hence:

1.053x = 30.8

x = 30.8/1.053

x = 29.25 gallons.

(ii) The sales in 2011

= 9.1 billion gallons in 2011.

(iii) The per capita consumption from 2011

= 9.1 / 11.8

= 0.77 billion

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Answer:

How are you doing today