which of the following functions best describes this graph

Answer:

C. 30 ÷ 6 = 5

Step-by-step explanation:

A. incorrect

         6 - 5 is not equal to 11, it is equal to 1

B. incorrect

         6 × 30 is not equal to 5, it is equal to 180

C. CORRECT

         30 ÷ 6 is equal to 5

D. incorrect

         11 + 5 is not equal to 6, it is equal to 16

The probability that they are sitting around a round table in age order is 1/12. There are 10 ways for five people to sit in age order.  

Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

Five people all of different age are sitting around a round table.

Find the probability they are sitting in age order!

Let's name the 5 people 1, 2, 3, 4, 5.

There are two ways in putting them in the age order, ascending or descending.

There are 10 ways that they are sitting around a round table in the age order.

n(Age order) = 10

The total arrangements for 5 people sitting around a round table is

5! = 1 × 2 × 3 × 4 × 5

5! = 120 ways

n(S) = 120

The probability that they are sitting in age order would be

P(Age order) = n(Age order) / n(S)

P(Age order) = 10/120

P(Age order) = 1/12

Hence, the probability that five people are sitting around a round table in age order is 1/12.

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Answer:

I guess you forgot to attach something

Step-by-step explanation:

Hope it helps!!!

\(8 + 6x < 44\)

x = no. of games

The lengths of the major and minor axis are 4√6 and 4√3.

A point on a curve is described by an ellipse if its location is such that the sum of the distances between its two focal points is a constant.

(x−h)²/ b² +(y- k)² /a² = 1

Given:

(x−3)²/ 27+(y+4)² /45=1

The above equation can be compared to the standard equation of an ellipse

(x−h)²/ b² +(y- k)² /a² = 1

where, (h, k) = coordinates of the center of the ellipse

a =  length of the semi major axis

b = length of the semi minor axis

By comparison, we have;

(h, k) = (3, -4)

a = √(24) = 2 x√6

b = √(12) = 2 x√3

and, length of the major axis = 2a

length of the minor axis = 2b

Thus, The length of the major axis is

2x a = 2 × 2 x √6 = 4√6

and, length of the minor axis is

2•b = 2 × 2√3 = 4√3

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Answer: 6sqrt(5) and 6sqrt(3)

Step-by-step explanation:

I took the test and these were the correct answers.

Answer:

Step-by-step explanation: When solving the perimeter for a quadrilateral you will add up all the sides and the all sides are the same so when you figure out the number from one side you will figure the rest of it.  I think that one of the sides is 10 I'm not really sure but you you should the little square outside the shape and it should give you the answer to it.

I don't know if it is 10 or not and also the formula is P=a+b+c+d

Hope this advice helps :D

Answer:

y = 4

I hope it helps

Step-by-step explanation:

\(y \alpha \frac{1}{x} \\ y = \frac{k}{x} \\ 10 = \frac{k}{2} \\ \)

\(k = 20 \\ y = \frac{20}{x} = formula \: connecting \\ \: x \: and \: y \\ \)

\(x = 5 \\ y = \\ y = \frac{20}{x} \\ y = \frac{20}{5} \\ \)

\(5y = 20 \\ \frac{5y}{5} = \frac{20}{5} \\ y = 4\)

Answer:

$ 471.78

Step-by-step explanation:

This describes an 'ordinary annuity' ====>   FORMULA:

PV= C [  1-(1+i)^-n / i ]    Looking for C    i = .05/12   n =60   PV = 25000

 plug in the numbers and calculate   C = 471.78

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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  Among the given options (A, B, C, D), the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

In a population regression model, we are interested in modeling the relationship between a dependent variable (Y) and one or more independent variables (X1, X2, etc.). The model equation consists of the regression coefficients (β0, β1, β2, etc.) that represent the effect of each independent variable on the dependent variable, and the error term (e) that captures the unexplained variation in the data.
Among the given options, only option D includes all the necessary components of a population regression model with two independent variables (k = 2). It includes the dependent variable Y, the regression coefficients β0, β1, and β2 for the independent variables X1 and X2, respectively, and the error term e.
Options A, B, and C are incorrect because they either omit the error term or have an incomplete equation. The error term is crucial in accounting for the unobserved factors and random variation in the relationship between the variables.
Therefore, the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

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The composition of functions g and f, denoted as \(\(g \circ f\)\)is a function that maps elements from the domain of f to the codomain of g. In this case, we have \(\(g: a \to b\)\) and \(\(f: b \to c\)\), where \(\(a = b = c = \{1, 2, 3, 4\}\)\).

The function g is given by \(\(\{(1, 4), (2, 1), (3, 1), (4, 2)\}\)\), and f is given by \(\(\{(1, 3), (2, 2), (3, 4), (4, 2)\}\)\). The composition \(\(g \circ f\)\) is a function that maps elements from the domain of f to the codomain of g. In other words, it combines the mappings of g and f in a way that the output of f becomes the input for g.

To compute \(\(g \circ f\)\), we start with the elements in the domain of f, which is \(\(b = \{1, 2, 3, 4\}\)\). For each element x in b, we apply f to get f(x), and then apply g to get g(f(x)).

The composition \(\(g \circ f\)\) is calculated as follows:

\(\[g \circ f = \{(1, g(f(1))), (2, g(f(2))), (3, g(f(3))), (4, g(f(4)))\}\]\)

Substituting the values from the given functions, we have:

\(\[g \circ f = \{(1, g(3)), (2, g(2)), (3, g(4)), (4, g(2))\}\]\)

Now, we substitute the values of g for the respective inputs:

\(\[g \circ f = \{(1, 2), (2, 4), (3, 2), (4, 1)\}\]\)

Therefore, the composition \(\(g \circ f\)\) is given by \(\(\{(1, 2), (2, 4), (3, 2), (4, 1)\}\)\).

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Answer:

\(f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)\)

Step-by-step explanation:

The root -2 has a multiplicity of 2, and corresponds to a factor of \((x+2)^2\).

The root 1 has a multiplicity of 1, and corresponds to a factor of \((x-1)\).

The root 3 has a multiplicity of 1, and corresponds to a factor of \((x-3)\).

So, \(f(x)=a(x+2)^2(x-1)(x-3)\).

Since \(f(0)=10\),

\(10=a(0+2)^2(0-1)(0-3) \\ \\ 10=12a \\ \\ a=\frac{5}{6} \\ \\ \therefore f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)\)

Answer:438

Step-by-step explanation:

6 x108=648

2x105=210

648-210=438

Answer:

x=15 y=24

Step-by-step explanation:

This is because the rule is x goes up 3 y goes up 4

(9,12)->(x,20)

it skips one, so instead of adding 3 we add six

x=15

(15,20)->(18,y)

you follow the rule and 4.

Y=24

The triangle is the essential geometric form in the construction and support of a geodesic dome.

        A geodesic dome is a spherical structure like a round tent that is formed by the simultaneous placements of triangular structures one along the other. The triangles are placed in such a way it seems that rhombuses are placed one after the other.

         They are lightweight, and a layer of canvas or transparent material is placed over the structure to make it water-proof.

          It was first created by the American designer Richard Buckminster Fuller in the 20th century.

          Although these homes save energy and give a perfect place to live in nature, they can also pose some issues like the placement of the chimney, creating rooms within the dome, leakage in the roof, and so on.

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Answer:

24

Step-by-step explanation:

3x4x2=24

When finding the answer to this problem, you times all of the options by each other.

Answer:

4 pieces

Step-by-step explanation:

Total length of lumber = 9 feet

How many 2 1/4 foot pieces can you cut from this piece of lumber

To find the number of 2 1/4 foot pieces of lumber in a 9 feet of lumber, we will divide the total length of lumber by the length of each piece of lumber

9 ÷ 2 1/4

= 9 ÷ 9/4

= 9 × 4/9

= 36/9

= 4 pieces of lumber

Therefore, 4 pieces of 2 1/4 foot of lumber can be gotten from 9 feet of lumber

Answer:

\( x\approx 18.0\)

Step-by-step explanation:

Here, a = 30, b = 16, C = x

By law of cosines

\( {c}^{2} = {a}^{2} + {b}^{2} - 2ab \cos C \\ \\ {x}^{2} = {30}^{2} + {16}^{2} - 2 \times 30 \times 16 \: cos 30 \degree \\ \\ {x}^{2} = 900 + 256 - 960 \times \frac{ \sqrt{3} }{2} \\ \\ {x}^{2} = 1156 - 480 \times \sqrt{3} \\ \\ {x}^{2} = 324.615612 \\ \\ x = \sqrt{324.615612} \\ \\ x = 18.0170922 \\ \\ x \approx \: 18.0\)

The value of y in the right triangle is found to be 3√3 units.

Given data:

So, apply trigonometric ratios:

cos 30 = y / 6

y = cos 30 * 6

y = √3 / 2 * 6

y = 3√3

Thus, the value of y in the triangle is found to be 3√3 units.

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The correct answer is (B) u = x² + 4. Let's use the substitution u = x² + 4. Then, we have du/dx = 2x, which implies dx = du/(2x). Substituting these into the integral.

We get:

∫(2x/(x²+4)²)dx = ∫(1/u²)(du/2) = (1/2) ∫u^-2 du

Integrating this expression with respect to u, we get:

(1/2) ∫u^-2 du = (1/2) (-u^-1)/(-1) + C = (1/2) (1/(x²+4)) + C,

where C is a constant of integration. Therefore, evaluating the definite integral from 0 to 2, we obtain:

²∫₀ 2x/(x²+4)² dx = [(1/2) (1/(2²+4))] - [(1/2) (1/(0²+4))] = 1/8.

Thus, the correct answer is (B) u = x² + 4.

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Answer:

option c.

...............

Answer: 14500

Step-by-step explanation:

Let the price of the mobile phone before the GST was added be represented by x.

Therefore,

x + (12% × x) = 16240

x + 0.12x = 16240

1.12x = 16240

x = 16240/1.12

x = 14500

The price of the mobile phone before the GST was added was 14500

The slope of the line is undefined.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-4, 6) and (-4, 1)

Now,

Since, The equation of line passes through the points (-4, 6) and (-4, 1)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - 6) / (-4 - (-3))

m = - 5 / 0

m = ∞

Thus, The slope of the line is undefined.

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Answer:

  27 cm

Step-by-step explanation:

You want the distance from the vertex of an ellipse to the opposite focus if the semi-major axis is 15 cm, and the minor axis is 18 cm.

The square of the distance from the center to either focus is the difference of the squares of the semi-axes. The semi-minor axis is half the  diameter of the ellipsoid.

  c² = 15² -(18/2)² = 225 -81 = 144

  c = √144 = 12 . . . . . cm

The distance from the vertex (V) to the opposite focus is the distance from vertex to center plus the distance from center to focus:

  15 cm +12 cm = 27 cm

The kidney stone should be located 27 cm from the vertex for greatest effect.

Explanation:

The test statistic for proportion is equal to:

Where p' is the sample proportion, p is the value in H0, and n is the size of the sample.

In this case, p = 0.72, n = 51 and p' can be calculated:

Then, replacing these values, we get:

The given differential equation is not linear because it involves the product of x and t. However, it is separable, and we can integrate both sides to find the solution.

The given equation is 9xt(dx/dt) = e^x. To determine whether this equation is separable, linear, or both, we need to rearrange it into a standard form.

Dividing both sides by 9xt, we get:

(dx/dt) = e^x / 9xt

This equation is not linear because it involves the product of x and t in the denominator. However, it is separable because we can separate the variables x and t by writing the equation as:

9xt(dx/dt) = e^x

9x dx = e^x dt/t

Integrating both sides, we get:

4.5x^2 = ln|t| + C

where C is the constant of integration.

Therefore, the given equation is separable but not linear.

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Answer:

267x2 -8x -8 where

x=- 4± 2√ 538/267

Step-by-step explanation:

x2 - 2x -89x2 - 16x2 - 163x2 + 10 x + 8

= x2  -89x2 - 16x2 - 163x2  - 2x+ 10 x + 8

= -267x2+8x +8

= 267x2 -8x -8

First the like terms are arranged and then added . All the co efficients of x2 are added and x are added separately.

Using the quadratic equation to find the value of x

a= 267 , b= -8 and c= -8

x= -b±√b²- 4ac/ 2a

x= -8±√64 +8544/534

x= -8±√8608/534

x=-8±√ 2 x 2 x 2 x 2 x 2 x 269/534

x=-8± 4√ 2 x 269/534

x=- 4± 2√ 2 x 269/267

x=- 4± 2√ 538/267

Answer:

  12

Step-by-step explanation:

You want the least common multiple of 3 and 4.

3 and 4 have no common factors, so their least common multiple (LCM) is their product:

  3·4 = 12

The LCM of 3 and 4 is 12.

__

Additional comment

If the numbers have a common factor, then the LCM is their product, divided by the greatest common factor.

For example, 4 and 6 have a common factor of 2. Their LCM is 4·6/2 = 12.

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The length of the ramp needed to make an angle of 20 degrees with the ground and reach a loading platform 1.15 meters above the ground is approximately 3.16 meters.

To find the length of the ramp needed to make an angle of 20 degrees with the ground and reach a loading platform 1.15 m above the ground, we can use trigonometry.

Let's denote the length of the ramp as L. We can use the trigonometric relationship of tangent to solve for L.

Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height of the loading platform (1.15 m), and the adjacent side is the length of the ramp (L).

We have the equation:

tan(20 degrees) = opposite/adjacent

tan(20 degrees) = 1.15/L

To solve for L, we can rearrange the equation:

L = 1.15 / tan(20 degrees)

Using a calculator, we can find the value of tan(20 degrees) ≈ 0.3640. Substituting this value into the equation, we get:

L = 1.15 / 0.3640

L ≈ 3.16 meters (rounded to two decimal places)

Therefore, the length of the ramp needed to make an angle of 20 degrees with the ground and reach a loading platform 1.15 meters above the ground is approximately 3.16 meters.

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