what is (0.3)0 in binominal distribution

The graph of the function and its inverse is added as an attachment

Sketching the graph of the function and its inverse

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

f(x) = 3 + 2ln(x)

Express as an equation

So, we have

y = 3 + 2ln(x)

Swap x and  y in the above equation

x = 3 + 2ln(y)

Next, we have

2ln(y) = x - 3

Divide by 2

ln(y) = (x - 3)/2

Take the exponent of both sides

[tex]y = e^{\frac{x - 3}{2}}[/tex]

Next, we plot the graphs

The graph of the functions is added as an attachment

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Answer:

The volume of the cylinder is 628.318530718

Step-by-step explanation:

The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.

The radius is 5, and the height is 8. Plug these values into the equation and solve:

[tex]v =\pi *5^2*8[/tex]

[tex]v = 628.318530718[/tex]

So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32

Answer:

200π or 628

Step-by-step explanation:

Note: your picture is not clear so I am assuming the height to be 8.

r = 5

h = 8

Volume = πr²h

= π * 5² * 8

= (25*8) π

= 200π

= 200*3.14

= 628

Let's assign variables to represent the number of games won by each team:

Let x be the number of games won by Team A.
Let y be the number of games won by Team B.
Let z be the number of games won by Team C.

From the given information, we can form the following equations:

Equation 1: x + y + z = 60 (The total number of games won by the three teams is 60.)

Equation 2: x = (1/2)y (Team A won 50% as many games as Team B.)

Equation 3: x + y = 1.5z (Team A and Team B together won 50% more games than Team C.)

Now, let's solve this system of equations:

Substituting Equation 2 into Equation 3, we get:

(1/2)y + y = 1.5z
(3/2)y = 1.5z
y = (1.5z) * (2/3)
y = z

Substituting y = z into Equation 1, we have:

x + y + z = 60
x + y + y = 60
x + 2y = 60

Substituting y = z into Equation 3, we have:

x + y = 1.5z
x + y = 1.5y
x = 0.5y

Now, we can substitute x = 0.5y and y = z into Equation 1:

0.5y + 2y = 60
2.5y = 60
y = 60 / 2.5
y = 24

Substituting y = 24 into x = 0.5y:

x = 0.5 * 24
x = 12

Substituting y = 24 into the equation y = z:

z = 24

Therefore, Team A won 12 games, Team B won 24 games, and Team C won 24 games as well.

Answer:

D The base is 7 units and the height is 3 units.

Step-by-step explanation:

The answer is d I counted the width/base then the height/length and found answer.

The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;

1. ΔAJK ~ ΔSWY according to the SAS similarity postulate

2. ΔLMN ~ ΔLPQ according to the AA similarity postulate

3. ΔPQN ~ ΔLMN

LM = 12, QP = 8

4. ΔLMK~ΔLNJ

NL = 21, ML = 14

What are similar triangles?

Similar triangles are triangles that have the same shape but may have different sizes.

1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;

24/16 = 3/2

18/12 = 3/2

The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.

2. The ratio of the corresponding sides in each of the triangles are;

MN/LN = 8/10 = 4/5

PQ/LQ = 12/(10 + 5) = 12/15 = 4/5

The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule

3. The alternate interior angles theorem indicates;

Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;

ΔPQN ~ ΔLMN by the AA similarity postulate

LM/QP = (x + 3)/(x - 1) = 18/12

12·x + 36 = 18·x - 18

18·x - 12·x = 36 + 18 = 54

6·x = 54

x = 54/6 = 9

LM = 9 + 3 = 12

QP = x - 1

QP = 9 - 1 = 8

4. The similar triangles are; ΔLMK and ΔLNJ

ΔLMK ~ ΔLNJ by AA similarity postulate

ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)

ML/NL = LK/LJ = (24 - 8)/24

(24 - 8)/24 = (6·x + 2)/((7·x + 7)

16/24 = (6·x + 2)/(7·x + 7)

16 × (7·x + 7) = 24 × (6·x + 2)

112·x + 112 = 144·x + 48

144·x - 112·x = 32·x = 112 - 48 = 64

x = 64/32 = 2

ML = 6 × 2 + 2 = 14

NL = 7 × 2 + 7 = 21

MN = 2 + 5 = 7

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Answer:

This is an equation of a parabola.

[tex](y+6)^2=4(x+1)[/tex]

Step-by-step explanation:

A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).

The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.

Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.

As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.

The conic form of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

(h, k) is the vertex.(h+p, k) is the focus.x = h-p is the directrix.

To write the given equation in conic form, we need to complete the square for the y-variable.

Rearrange the equation so that the y-terms are on the left side:

[tex]y^2 + 12y = 4x - 32[/tex]

Add the square of half the coefficient of the y-term to both sides of the equation:

[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]

    [tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]

         [tex]y^2 + 12y+36 = 4x - 32+36[/tex]

         [tex]y^2 + 12y+36 = 4x +4[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex](y+6)^2=4x+4[/tex]

Factor out the coefficient of the x-term from the right side of the equation:

[tex](y+6)^2=4(x+1)[/tex]

Therefore, the equation of the given conic section in conic form is:

[tex]\boxed{(y+6)^2=4(x+1)}[/tex]

where:

(-1, -6) is the vertex.(0, -6) is the focus.x = -2 is the directrix.

The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola

Selecting the conic section of the equation

The given equation is

y² - 9x + 12y + 32 = 0

The above equation is an illustration of a parabola equation

The standard form of a parabola is

(x - h)² = 4a(y - k)²

Where

(h, k) is the center

While the general form of the equation is

Ax² + Dx + Ey + F = 0

In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form

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