What is the median of the data? 30, 29, 16, 11, 16, 20, 21, 13, 15, 15, 23, 30
A. 26
B. 15
C. 16
D. 18

Note that the given set of ordered pairs are an example of a mathematical function. (Option A)

An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. By situating a point on the Cartesian plane, it enhances visual comprehension. The numeric values of an ordered pair might be integers or fractions.

A function is a collection of ordered pairs in which each input (or "x" value) corresponds to exactly one output (or "y" value). In this provided set of ordered pairs: (-2, 1), (-1, 0), (1, 0), (2, 0), there is only one matching value of y for each value of x.

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Answer:

To subtract or add a fraction you must first find a common deniminator between the two.

you can use 10 as a common denomonator in this case.

3 x 2 = 6

5 x 2 = 10

your new fraction to replace 3/5 is 6/10

Now, your equation would be 7/10 - 6/10 = 1/10

Your answer is 1/10

Since this journalist writes n articles and gets 200(n + 7) for each article. If he gets N52000 altogether, the number of articles which he wrote is equal to 253 articles.

In order to determine the number of articles that was written by this journalist, we would simplify the expression and then determine the value of n as follows;

52,000 = 200(n + 7)

Opening the bracket through expansion, we have the following:

52,000 = 200n + 1,400

Subtracting 1,400 from both sides of the expression, we have the following:

52,000 - 1,400 = 200n + 1,400 - 1,400

Rearranging the expression, we have the following:

200n = 52,000 - 1,400

200n = 50,600

Dividing both sides of the expression by 200, we have the following:

n = 50,600/200

n = 253 articles.

In this context, we can reasonably infer and logically deduce that the total number of articles that was written by this journalist is equal to 253 articles.

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Answer:

-4 is the slope

Step-by-step explanation:

y= mx + b

m being the slope

Hope this helps!

Answer: m= -4

Step-by-step explanation:

y=mx+b

b is your y-intercept

mx is your slope

the equation of y = -4x + 3 would be -4x

Answer:

A bag of almonds that weighs 1.6 ounces will cost $0.51 x 1.6 = $<<0.51*1.6=0.816>>0.816.

Step-by-step explanation:

The new temperature of Moscow is - 16°C dropped - 8°C from - 8°C.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The temperature in Moscow is - 8°C.

Now, The temperature falls by 8°C.

Therefore the resultant temperature can be obtained by subtracting the temperature drop from the initial temperature of Moscow which is,

= - 8°C - 8°C.

= - 16°C.

So, The new temperature is - 16°C.

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You can prove the difference of two cubes identity. a³ – b³ = (a – b)(a² + ab + b²) based on the following responses:

A. Use the distributive property to multiply the factors on the right side of the equation.

B. Simplify the product by combining like terms.

C. Show that the right side of the equation can be written exactly the same as the left side.

D. Show that the right side of the equation simplifies to a cubed minus b cubed.

In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

a³ – b³ = (a - b)(a² + ab + b²)

a³ – b³ = a(a² + ab + b²) - b(a² + ab + b²)

Next, we would combine like terms:

a³ – b³ = a³ + a²b + ab² - a²b - ab² - b³

a³ - b³ = a³ - b³.

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Complete Question:

Explain how you can prove the difference of two cubes identity. a³ – b³ = (a – b)(a² + ab + b²)

Which of the following did you include in your response? Check all of the boxes that apply.

Use the distributive property to multiply the factors on the right side of the equation.

Simplify the product by combining like terms.

Show that the right side of the equation can be written exactly the same as the left side.

Show that the right side of the equation simplifies to a cubed minus b cubed.

The amount received after 3 years is ₹12950.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]

Given that, principal = ₹10,000, rate of interest =9% and time period = 3 years.

Now, amount =10000(1+9/100)³

= 10000(1.09)³

= 10000×1.295

= ₹12950

Therefore, the amount is ₹12950.

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Answer:

Use Mathpapa to find your answer.

Step-by-step explanation:

It's a good, and powerful program.

Correct option is C, the resultant vector will be [tex]\vec{p} + \vec{q}[/tex].

A vector is something that possesses both magnitude and direction. A vector is a directed line segment in geometry, with an arrow pointing in the direction and a length equal to the vector's magnitude.

A quantity or phenomenon known as a vector has two distinct properties: magnitude and direction. The phrase also specifies the mathematical or geometrical representation of such a quantity.

Examples of vectors in nature include velocities, moments of inertia, forces, electromagnetic fields, and weight.

Vectors are typically employed in air and sea navigation.

Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

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Answer:

To simplify the expression 2√20 - 2√5, you can start by applying the rule that the square root of a product is the product of the square roots of the factors. This means that you can rewrite √(20) as √(4*5) = 2√(5).

Applying this rule, the expression simplifies to:

2√(5) - 2√(5) = 2√(5) - 2√(5) = 0

Therefore, the simplified expression is equal to 2√(5).

Step-by-step explanation:

Answer: here’s the answer!

Step-by-step explanation: hope this helps!

Answer:

x=10

Step-by-step explanation:

3(x-2)+4=28

3x-6+4=28

3x-2=28

3x=30

x=10

The volume of 3 cones = The volume of one cylinder.

The volume of 2 cones = The volume of one sphere.

The volume of 1 sphere = 2/3 the volume of one cylinder.

The volume of one cone = 1/3 the volume of one cylinder.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3πr²h.

We have,

Volume of a cylinder = πr²h

Volume of a cone = 1/3 πr²h

Volume of a sphere = 4/3 πr³

Now,

The radius is the same.

Height of cone and cylinder = 2r

The new volume:

Volume of a cylinder = 2πr³

Volume of a cone = 2/3 πr³

Volume of a sphere = 4/3 πr³

Thus,

Volume of 3 cones = 2πr³ = volume of one cylinder

Volume of 2 cones = 4/3 πr³ = volume of one sphere

Volume of 1 sphere = 4/3 πr³ = 2/3 x volume of a cylinder

Volume of one cone = 2/3 πr³ = 1/3 x volume of cylinder

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On solving the provided question, we can say that -the  given graph is a starlight lined .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here,

in the graphs we have been given a straight line,

so its a straight line graphs

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Answer:

x=7

Step-by-step explanation:

(x+1)/4=2

x+1=2*4

x+1=8

x=7

Answer:

To find the x-intercepts and y-intercepts of a function, we need to find the values of x and y at which the function crosses the x-axis or y-axis.

X-intercepts:

The x-intercepts occur when y = 0, so we can set f(x) = 0 and solve for x:

3x³-12x²-15x = 0

This is a cubic equation, we can use factoring, synthetic division or use a numerical method like the Newton-Raphson method to solve for x.

Y-intercepts:

The y-intercepts occur when x = 0, so we can substitute x = 0 into the function to find the y-intercept:

f(0) = 3(0)³ - 12(0)² - 15(0) = 0

So the y-intercept of the graph is at the point (0,0)

In summary, the x-intercepts are the solutions of the equation 3x³-12x²-15x = 0 and the y-intercept is (0,0)

Please note that, if the equation has complex roots, the graph will not cross the x-axis and hence it will not have any real x-intercepts.

Step-by-step explanation:

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

There are 3  2 colored flags and 2 3 colored flags.  

2 colored flags to total flags is 3/5

For constant A to be -4 (option 1) the system of equations have exactly one real solution.

NOTE: We are working with the problem statement: Y=-3 Y=Ax2+4x-4 In the system of equations above, a is constant. For which of the following values of a does the system of equations have exactly one real solution?

We have given, y=-3

y= Ax^2+4x-4

Therefore, -3= Ax^2+4x-4

or, Ax^2+4x-1=0

For second order equation of ax^2+bx+c=0 have a solution for

x= [-b± (√b^2-4ac)]/2a]   [Ax2 + Bx + C = 0 is the Sridharacharya equation, where a, b, and c are real values and a 0. The Sridharacharya formula, which is stated as x = (-b (b2 - 4ac)) / 2a, provides the answer to the Sridharacharya equation.]

For single solution b^2-4ac=0

here, Ax^2+4x-1=0

4^2 - 4a(-1)=0

16+4a=0

a= -(16)/4

a= -4

option A is correct .

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This is only true equation when A is equal to -2. Therefore, the correct answer is B) -2.

B) -2

The given system of equations can be written as:

Y = A*x^2 + 4*x - 4

We can solve this equation by using the Quadratic Formula. The Quadratic Formula states that the solutions to the equation are given by:

x = [-b +/- sqrt(b^2-4ac)]/2a

where a, b, and c are the coefficients of the equation. In this case, a = A, b = 4, and c = -4.

Substituting these values into the equation, we get:

x = [-4 +/- sqrt(4^2-4*A*(-4))]/2A

Simplifying this, we get:

x = [-4 +/- sqrt(16 + 16A)]/2A

For the system of equations to have two real solutions, the value of the square root must be greater than or equal to zero. This means that 16 + 16A must be greater than or equal to zero.

This is only true when A is equal to -2. Therefore, the correct answer is B) -2.

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Answer:

A)  Exponential function

[tex]\textsf{B)} \quad y = 2(2)^x[/tex]

C)   12

Step-by-step explanation:

Given points:

In a linear function, the y-values have equal differences.  

In an exponential function, the y-values have equal ratios.

From inspection of the given points, we can see that y doubles each time x increases by 1 unit, therefore the data models an exponential function.

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

As the function doubles, the base is 2.

Substitute one of the points (1, 4) and b = 2 into the formula and solve for a:

[tex]\implies 4=a \cdot 2^1[/tex]

[tex]\implies 4=2a[/tex]

[tex]\implies a = 2[/tex]

Substitute the found values of a and b into the formula to create the exponential function to represent the given data:

[tex]y=2(2)^x[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]

Station 2:  (2, 8)

Station 4:  (4, 32)

To determine the average rate of change between station 2 and station 4 find the average rate of change over the interval 2 ≤ x ≤ 4.

Therefore, a = 2 and b = 4:

[tex]\implies \textsf{Rate of change}=\dfrac{f(4)-f(2)}{4-2}=\dfrac{32-8}{4-2}=\dfrac{24}{2}=12[/tex]

On solving the provided question, we can say that in the line, The value of x is 5; the length of in inches is 5; the length of ec in inches is 15

A line is an endlessly long object without breadth, depth, or curvature in geometry. Consequently, a line is a one-dimensional entity, while it may also exist in two-, three-, and more-dimensional regions. In common use, a line segment with two points serving as its ends is referred to as a line. A line is a single-dimensional, straight form with no thickness that can go on forever in both directions. To indicate that a line has no "wobble" anywhere along its length, it is frequently referred to as a straight line or an ancient accurate line.

here,

The value of x is 5

The length of in inches is 5

The length of ec in inches is 15

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The vertex of the quadratic expression will be at (7, -109). The parabola opens upward, then the minimum value of the expression will be - 109.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The quadratic expression is given below.

⇒ x² - 14x - 60

Convert the expression into a vertex form. Then we have

⇒ x² - 14x - 60

⇒ x² - 14x + 49 - 49 - 60

⇒ (x - 7)² - 109

The vertex of the quadratic expression will be at (7, -109). The parabola opens upward, then the minimum value of the expression will be - 109.

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A: If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent.

The total number of students in the school is 1100

From the question, we have the following parameters that can be used in our computation:

Number of students that play a sport = 528

Proportion of students that play a sport = 48%

Using the above as a guide, we have the following:

Number of students that play a sport = Proportion of students that play a sport * number of students in the school

Substitute the known values in the above equation, so, we have the following representation

48% * number of students in the school = 528

Express as decimal

This gives

0.48 * number of students in the school = 528

Divide both sides by 0.48

number of students in the school = 528/0.48

Evaluate

number of students in the school = 1100

Hence, the students are 1100

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Answer:

See the graph below

Step-by-step explanation:

The probability that each guest got one roll of each type is 3/1, which is a fraction with a numerator of 3 and a denominator of 1. Since the numerator and denominator are relatively prime integers, the value of m + n is 3

The equation for the probability that each guest got one roll of each type is m/n, where m and n are relatively prime integers.

We can expand this equation to

m/n

= 3/1.

Since the numerator and denominator are relatively prime integers, we can solve for m + n by multiplying both sides of the equation by 1.

Multiplying both sides of the equation by 1 gives us

m + n = 3.

Therefore, the value of

m + n is 3.

Let m = numerator and n = denominator in the probability of m/n.

Given that each guest got one roll of each type, the probability is m/n.

The numerator and denominator are relatively prime integers, so m and n have no common factors.

Therefore,

m + n = 3.

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Answer:

3x + 1

Step-by-step explanation:

1/5/2023

7:25PM

answer........................

3x +1

No, this is not the solution for the following system of equation

When two or more equations are solved simultaneously, they are referred to be a system of equations. The objective is to identify the values of the variables that satisfy each of the equations in the system. These equations frequently have many variables.

Here is an illustration of a set of equations:

x + y = 7

x - y = 1

To determine whether a given point (x, y) is a solution to a system of equations, we need to substitute the values of x and y into the equations of the system and see whether the equations are satisfied.

In this case, we want to check if (1, 1) is a solution to the system of equations:

6x + 14y = 20

8x + y = 6

We substitute the given x and y values into the system of equations:

6(1) + 14(1) = 20

8(1) + 1 = 9

And see if the two equations are true

6 + 14 = 20 is true

8 + 1 = 6 is false

So (1, 1) is not a solution to the system of equations.

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