What are the domain and range of the step function with the equation below?
fx)=-3[x]​

If a ray of light is traveling at a downward angle of 45 degrees and strikes an object, the ray will reflect back at the same angle from the object.

The law of reflection say that when light fall on an object that is able to reflect the ray of light than the light will be reflected from the normal to the surface at the same angle at which the ray has fallen on to the surface.

So, when a light beam strikes an item while approaching it at a 45-degree downward angle, the beam will return at the same angle.

The angle will be measured from the surface of the object or the normal. Although it does not matter in this particular case because the angle will be same in this case measured from anywhere, the normal or the surface of the object.

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Answer:

45 degrees

Step-by-step explanation:

The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

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Answer:

your question is wrong put correct question the answer!

Answer:

The answer is 12 (A)

Step-by-step explanation:

Trust

also I took the test

Answer:

3645 to 9.29

Step-by-step explanation:

Answer:

3/5

7/13

10/7

Step-by-step explanation:

all of these are greater than 1/2

Answer:

This is a division problem.

Divide 18 by different numbers until you get 3.

The quotient of eighteen and six is three.

Step-by-step explanation:

The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

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The term that refers to the fact that the distance between two or more points is equal is "equidistant".

In geometry, the concept of equidistance is important when dealing with circles, which are sets of points that are equidistant from a single point called the center. This property is what allows circles to be defined in terms of their radius, which is the distance between the center and any point on the circle.

Equidistance is also important in other areas of mathematics and science. For example, in physics, equidistant points can be used to define a plane or surface that is perpendicular to a given line or axis. This is useful in many applications, such as designing electronic circuit boards or constructing buildings.

The concept of equidistance is not limited to mathematics and science, however. It can also be applied in everyday life. For instance, if you are planning a road trip and want to visit several destinations that are equidistant from your starting point, you can use this information to help plan your route and estimate your travel time.

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Step-by-step explanation:

law of sine :

a/sinA = b/sinB = c/sinC

with the sides and correlating angles being always opposite to each other.

we are dealing with a right-angled triangle here.

the train track is the Hypotenuse (the side opposite of the 90° angle) : 1600 ft.

the horizontal level "connection" from beginning to the end of the track is one leg, and the elevation difference at the end of the track is the second leg.

the 2 legs enclose a 90° angle, as the elevation goes straight up from the horizontal level.

so, we have

1600/sin(90) = elevation difference / sin(1.6)

sin(90) = 1

1600 = elevation difference / sin(1.6)

elevation difference = 1600 × sin(1.6) =

= 1600 × 0.027921639... =

= 44.67462196... ft

≈ 44.7 ft

Answer:

I think the answer is (A statement where two expressions are joined with an equal sign.)

Step-by-step explanation:

Answer:

Step-by-step explanation:

.6(2k-3)=3(4k+5) foil

1.2K-1.8=12k+15 subtract 1.5k from both sides

-1.8=10.8k+15 subtract 15 from both sides

-16.8=10.8k divide by 10.8

k= -1.5

18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.

19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.

If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.

The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.

The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.

This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.

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Answer:

5

Step-by-step explanation:

Area of a square= length ×length

=5in×5in

=25in^2

The area of a square is 25 in^2.

Therefore, the length

= √25 in

= 5 in

Te length is 5 in.

The values of trigonometric-ratios in the given triangle whose legs are 4 and \(4\sqrt{3}\) are:

a)sinθ=0.5

b)cosθ=0.866

c)tanθ=0.577

What is trigonometric-ratios ?

A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are their respective acronyms. These ratios show the ratio of various sides depending on the angle selected.

Given sides of triangle: 4 and \(4\sqrt{3}\)

hypotenuse=\(\sqrt{perpendicular^{2}+base^{2} }\)

                  =\(\sqrt{4^{2}+\((4\sqrt{3}) ^{2} }\)

                  =\(\sqrt{16+48}\)

                  =8

a)Sin θ=\(\frac{side opposite to the given angle}{hypotenuse}\)

Sin θ=\(\frac{4 }{8}\)

Sin θ=\(\frac{1}{2}\)

Sin θ=0.5

b)Cos θ=\(\frac{side adjacent to the given angle}{hypotenuse}\)

            =\(\frac{4\sqrt{3} }{8}\)

            =\(\frac{\sqrt{3} }{2}\)

            =\(\frac{1.732}{2}\)

Cos θ=0.866

c)tan θ=\(\frac{side opposite to the given angle}{side adjacent to the given angle}\)

            =\(\frac{4}{4\sqrt{3} }\)

            =\(\frac{1}{\sqrt{3} }\)

tan θ=0.577

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(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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In Chapter 6, Problem 10P, the constraints are derived based on the given problem scenario and the objective of the optimization problem. Without specific details about Problem 10P in Chapter 6, it is challenging to provide a precise explanation.

However, I can provide a general understanding of how constraints are typically formulated in optimization problems. In optimization problems, constraints are used to represent the limitations or restrictions on the decision variables. These constraints can arise from various sources, such as physical constraints, resource constraints, budget constraints, or technical constraints. To derive the constraints, you need to carefully analyze the problem statement and identify the conditions or limitations that must be satisfied. These conditions are then translated into mathematical inequalities or equations that relate the decision variables. For example, if the problem involves allocating limited resources among different activities, the constraints would represent the availability of those resources and ensure that the total allocation does not exceed the available amount. Similarly, if the problem involves production planning, constraints might include demand requirements, capacity limitations, or inventory constraints. In general, the process of formulating constraints requires careful consideration of the problem's requirements, objectives, and limitations. It often involves translating real-world constraints into mathematical expressions to create a well-defined optimization problem that can be solved using appropriate techniques.

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Given Data:

The initial investment is: P=$100

The total period of investment is: t=3

The annual interest is: 6%.

For the simple interest, the expression to calculate the interest in t years is,

Here r is in percentage.

Substitute known values in the above expression.

Thus, the total intrest for 3 years will be $18.

Answer:

18x-6 is the expression equivalent to -3(-6x+2)

The global maximum value of f(x, y) on the closed triangular region occurs at either (4, 0) or (0, 4), both of which have a value of 16.

The global minimum value of f(x, y) occurs at the critical point (0, 0), with a value of 0

To find the Optimization of multivariable functions i.e, global extreme values of \(f(x, y) = x^2 - xy + y^2\) on the closed triangular region in the first quadrant bounded by the lines x = 4, y = 0, and y = x,

We need to first find the critical points of the function in the interior of the region and evaluate the function at these points, and then evaluate the function at the boundary points of the region.

To find the critical points of the function in the interior of the region, we need to solve the system of partial derivatives:

\(df/dx = 2x - y = 0\\f/dy = -x + 2y = 0\)

Solving this system of equations, we get the critical point (x, y) = (0, 0).

To check whether this point is a maximum or a minimum, we need to evaluate the second partial derivatives of f:

\(d^2f/dx^2 = 2\\d^2f/dy^2 = 2\\d^2f/dxdy = -1\)

The determinant of the Hessian matrix is:

\(d^2f/dx^2 \times d^2f/dy^2 - (d^2f/dxdy)^2 = 4 - 1 = 3\)

Since this determinant is positive and \(d^2f/dx^2 = d^2f/dy^2 = 2\) are both positive, the critical point (0, 0) is a local minimum.

Next, we need to evaluate the function at the boundary points of the region. These are:

(4, 0): f(4, 0) = 16

(0, 0): f(0, 0) = 0

(0, 4): f(0, 4) = 16

(y, y) for 0 ≤ y ≤ 4: \(f(y, y) = 2y^2 - y^2 = y^2\)

Therefore, the global maximum value of f(x, y) on the closed triangular region occurs at either (4, 0) or (0, 4), both of which have a value of 16.

The global minimum value of f(x, y) occurs at the critical point (0, 0), with a value of 0.

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Answer:

#3- a^2 +2ab +b^2

#4- a^2 -b^2

Step-by-step explanation:

Answer:

a) 3 : 4

b) 4 : 3

c) 7 : 3

d) 4 : 7

Step-by-step explanation:

(just a side note: you can write ratios in fraction form as well!)

To find the ratio between boys to girls, we would write it like this:

180/240 or  180 : 240 or  180 to 240

Although that is right, that isn't simplified.

Thus, we need to find a common factor that both the numerator and denominator share!

180 and 240 are both divisible by 60!

  180 ÷ 60 = 3

  240 ÷ 60 = 4

Therefore, you would get a simplified ratio of 3 : 4! For every 3 boys. there are 4 girls!

For part b, you simply switch the 4 and 3 around so you get 4 : 3. For every 4 girls, there are 3 boys.

Now part c involves the total amount of students...

Basically, add the number of boys and the number of girls together, and you would get 420.

    420 : 120 shows the amount of students there are to boys...but it is not in its simplest form!!

Like we did before, we have to find a common factor between the two...which is 60!

 420 ÷ 60 = 7

 120 ÷ 60 = 3

Thus, there are 7 students for every 3 boys (7 : 3)

Finally, part d! Simply the ratio:

   420 : 240

Divide both by 60 and...

You get 4 :7! For every 4 girls, there are 7 students

Hope this helps! Let me know if you have any other questions :D

Answer:

(a) 3:4

(b) 4:3

(c) 7:3

(d) 4:7

Step-by-step explanation:

(a) 3:4

180:240 = 3:4 (after simplification)

(b) 4:3

240:180 = 4:3 (after simplification)

(c) 7:3

Total number of students = 240 + 180 = 420

420:180 = 7:3 (after simplification)

(d) 4:7

Total number of students = 240 + 180 = 420

240: 420 = 4:7  (after simplification)

Answer:

About 28... I think.

Step-by-step explanation:

Answer:

the answer is -3

Step-by-step explanation:

I took the quiz on k12

Answer:

2X^2 - 7x - 2

Step-by-step explanation:

Subtract 7x-9from 2x^2-11

the 9 will be added to the -11

Answer:

The answer is 7

Step-by-step explanation:

Answer:

Gaming Functions

Step-by-step explanation:

I think your teacher is implying for you to explain the function and the "works" behind the game. Maybe talk about the game's programming or the way it's overall structured?

Answer:

y2- y1 over

x2 -x2

\( - 3 - 0 = - 3\)

\(0 - 2 = - 2\)

Step-by-step explanation:

slope is m =

\(m = - \frac{3}{2} \)

use the -3 for b and you get

\(y = - \frac{3}{2} x - 3\)

slope intercept form

To be categorized as unemployed, a person has to be without a process, presently available to work, and actively seeking out work within the previous 4 weeks.

Unemployment is a time period regarding people who are employable and actively looking for a process but are not able to discover a process. blanketed in this institution are the ones people in the group of workers who are working but no longer have the precise job.

The situation of now not having a task but being a member of the labor pressure. To be considered unemployed, someone must be jobless but actively trying to find a task by having searched within the last 4 weeks.

Hence, To be categorized as unemployed, a person has to be without a process, presently available to work, and actively seeking out work within the previous 4 weeks.

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complete question:

how do economists define unemployed workers? group of answer choices although currently working, they are not happy with their current job working on contract for a limited time not currently working not currently working but actively searching for work