The graphs below have the same shapes. What is the equation for the red graph?

Use the definitions of expectation and variance.

[tex]E(X) = \displaystyle \int_{-\infty}^\infty x f_X(x) \, dx = \frac14 \int_0^\infty x e^{-x/4} \, dx[/tex]

Integrate by parts,

[tex]\displaystyle \int_a^b u \, dv = uv \bigg|_a^b - \int_a^b v \, du[/tex]

with

[tex]u = x \implies du = dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]

Then

[tex]E(X) = \displaystyle \frac14 \left(\left(-4x e^{-x/4}\right)\bigg|_0^\infty + 4 \int_0^\infty e^{-x/4} \, dx\right)[/tex]

[tex]E(X) = \displaystyle \int_0^\infty e^{-x/4} \, dx = \boxed{4}[/tex]

(since the integral of the PDF is 1, and this integral is 4 times that)

[tex]V(X) = E\bigg((X - E(X))^2\bigg) = E(X^2) - E(X)^2[/tex]

Compute the so-called second moment.

[tex]E(X^2) = \displaystyle \int_{-\infty}^\infty x^2 f_X(x)\, dx = \frac14 \int_0^\infty x^2 e^{-x/4} \, dx[/tex]

Integrate by parts, with

[tex]u = x^2 \implies du = 2x \, dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]

Then

[tex]E(X^2) = \displaystyle \frac14 \left(\left(-4x^2 e^{-x/4}\right)\bigg|_0^\infty + 8 \int_0^\infty x e^{-x/4} \, dx\right)[/tex]

[tex]E(X^2) = 8 E(X) = 32[/tex]

and the variance is

[tex]V(X) = 32 - 4^2 = \boxed{16}[/tex]

Answer:

3.036, 3.36, 3.3661 , 3.5

Step-by-step explanation:

Look at the first 2 numbers

3.3661, 3.5, 3.36, 3.036

We can order them as 3.0 , 3.3 , 3.3 . 3.5

So 3.036 is first one

Now we have 2 of the 3.3's

One is 3.3661 and the other one is 3.3600

Because if you add a number to the end it will always be a zero and it wont change the answer

So  3.36 is second and 3.3661 is third one

3.5  is bigger than 3.3

So 3.5 is last

The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

We have given that,

A pool of possible candidates for a student council consists of 14 freshmen and 8 software.

We have to determine the how many different councils consisting of 5 freshmen and 7 sophomores are possible

[tex]_n C_r=\frac{n !}{r ! (n-r) !}_n C_r = number of combinations\\\n = total number of objects in the set\\\r = number of choosing objects from the set[/tex]

The total number of the council is

[tex]_{10} C_5\times _9 C_7[/tex]

=252(36)

=9216

The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

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Answer: 110 degrees

Step-by-step explanation:

By the exterior angle theorem.

[tex]10x-10=100-2x+2x+10\\\\10x-10=110\\\\\therefore \angle ABC=110^{\circ}[/tex]

u=-54

you have -54 because

-54(-2)=108/9=12

Answer:

u =-54

Step-by-step explanation:

-2/9u=12

To solve for u multiply each side by -9/2 to isolate u

-9/2 * -2/9 u= 12 * -9/2

u =-54

Answer:

The answer is 5

Because 200÷10 =20.

So I'm this case, 4x=20. Divide both sides by 4 and the answer is 5. So X=5

5

Answer:

Step-by-step explanation:

if 200÷10=4×u then u=?​

200 : 10 = 4u

20 = 4u

u = 20 : 4

u = 5

---------------------------

check

200 : 10 = 4 * 5

20 = 20

the answer is good

Answer:

A.4

Step-by-step explanation:

Using the sine rule

sin(α)/A equals sin(β)/B

From the question & inserting values,

sin(90°)/8 equals sin(30°)/x

∴x equals[tex]\frac{sin(30)}{sin(90)}[/tex]×8

∴x equals 4

You can learn more on the sine rule in case you get confused.

Answer:

A

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 8 ( divide both sides by 2 )

x = 4

The conclusion is a=c statement

A modus ponens argument has the same structure as a syllogism, with two premises and a conclusion:

If P, then Q.

P occurs.

Consequently, Q occurs.

The Modus Ponens rule of inference or rule of logic requires a single premise and its logical consequences. A conditional statement states that if event 1 occurs, event 2 will also occur and that event 2 will be inferred as the outcome if event 1 occurs. For instance, if A implies B and A is assumed to be true, then it follows that B must also be true according to the Modus Ponens rule.

Hence, By modus Ponens

a=b∧b=c ⇒ a=c

So, given a=b∧b=c Then

⇒a=c.

Hence the conclusion is a=c statement .

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Answer:

[tex]-6.5x+11[/tex]

Step-by-step explanation:

Expand The Brackets:

[tex]x-1+12-7.5x[/tex]

[tex]=x+(-1)+12+(-7.5x)[/tex]

Combine Like Terms:

[tex]=x+(-1)+12+(-7.5x)[/tex]

[tex]=(x+-7.5x)+(-1+12)[/tex]

Answer:

[tex]-6.5x+11[/tex]

I Hope This Helps  

The set of inequalities do not have a solution.

The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal. But to compare the values, whether it is less than or greater than, different inequalities are used.

Given:

f(x)= x²-2

g(x) = -x²+5

To derive, y ≤ x² + 5 simply change the equality sign in the function g(x).

To derive  y > x² - 2 ,  following transformation on the function f(x)

The inequalities of the graphs become

y < x² - 2 and y ≤ x² - 5

From the graph of the above inequalities it can be seen that curves of the inequalities do not intersect.

Hence, the set of inequalities do not have a solution

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Answer:

The standard deviation is about 2.915

Step-by-step explanation:

Answer:

=  2.9154759474227

Step-by-step explanation:

Based on the required width and height of the tent, the length of the cloth would have to be 14.4 ft.

The opening of the tent would be an isosceles triangle but if it is divided in two from the top, a right-angled triangle will be formed and the hypotenuse will be the length of the cloth on one side.

That length - according to the Pythagoras theorem - would be:

= √(6² + (8 /2)²)

= √(36 + 16)

= 7.2 ft

As this is the length of one side of the cloth, the length of the entire cloth is:

= 7.2 x 2

= 14.4 ft

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Answer:

[tex](g \cdot h)(x)=x^2-2x+23[/tex]

Step-by-step explanation:

For composite functions, it's important to understand what the functions mean:

[tex](g\cdot h)(x)[/tex]  which is read as "g of h, of x" means [tex]g ( \text{ }h(x) \text{ })[/tex] which is read as "g of, h of x" (with slight pauses at the comma).  This means that x goes into the h function, and the output of the h function goes into the g function.

Putting "x" into the h function

[tex]h(x)=-x+4[/tex]

Since it is just "x" going into the h function, the function as written is the output when x is the input.

Putting the h function output, into the g function

[tex]g(x)=x^2-6x+3[/tex]

[tex]g(h(x))=(h(x))^2-6(h(x))+3[/tex]

Substitute

[tex]g(h(x))=(-x+4)^2+-6(-x+4)+3[/tex]

Squaring means the something multiplied by itself

[tex]g(h(x))=(-x+4)*(-x+4)+-6(-x+4)+3[/tex]

Use distributive property; (some people know binomial distribution as "FOIL" -- First, Outer, Inner, Last):

[tex]g(h(x))=[(-x)(-x)+4(-x)+4(-x)+4*4)]+[6x+4]+3[/tex]

Simplify the binomial terms:

[tex]g(h(x))=[x^2-8x+16]+[6x+4]+3[/tex]

Group like terms:

[tex]g(h(x))=x^2-2x+23[/tex]

Remember that [tex](g\cdot h)(x)[/tex]  means [tex]g ( \text{ }h(x) \text{ })[/tex]

[tex](g \cdot h)(x)=x^2-2x+23[/tex]

So, [tex](g \cdot h)(x)=x^2-2x+23[/tex]

The graph of all the inequalities are given below.

Inequality is defined as an equation that does not contain an equal sign.

This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.

y ≥ x, the region is left to the line.

y < -(3/7)x – 7, the region is left to the line.

y ≤ (5/3)x – 8, the region is right to the line.

y ≥ 14 – (11/12)x, the region is right to the line.

y = -(3/2)x + 5, this is the equation of line.

All the graphs are shown below.

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A function assigns the values. The correct option is D.

A function assigns the value of each element of one set to the other specific element of another set.

The complete question is:

Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?

A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.

B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.

C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.

D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.

If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.

Hence, the correct option is D.

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log was used calculate big numbers before calculators

log is a re-arranged way to show a number with an exponent

example

log₂ 16 = 4 means 2^4 = 16

logx(Z) = y means x^y=Z

log(x-6)/log(2) + log(x)/log(2) = 4

(log(x-6)+ log(x))/log(2) = 4

(log(x-6)+ log(x)) = 4log(2)

(log(x-6)x) = log(16)

x=8

Answer:

2 cos (2x)

Step-by-step explanation:

[tex]\frac{4 -2 sec^2x}{sec^2x} \\=\frac{4-\frac{2}{cos^2x} }{\frac{1}{cos^2 x} } \\=\frac{\frac{4 cos^2x-2}{cos^2 x} }{\frac{1}{cos^2x} } \\=\frac{2(2 cos^2x-1)}{cos^2x} \times \frac{cos^2x}{1} \\=2(2cos^2x-1)\\=2cos(2x)[/tex]

A tessellation that uses only one type of regular polygon.

The definition of a polygon is given as a closed two-dimensional figure with three or more straight lines.

When we cover a surface with a pattern of a flat geometric shapes such that there should have no overlaps or gaps, then the surface is called a tessellation.

A regular tessellation is tessellation made up by using only one type of regular polygon. These are made up of entirely congruent regular polygons all that joining vertex to vertex.

Hence, A is the correct option.

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Answer:

please see photo for detailed analysis.

Answer:

2nd option

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

         = [tex]\frac{4x+5+7x-6-8x+2}{3}[/tex]

         = [tex]\frac{3x+1}{3}[/tex]

         = [tex]\frac{3x}{3}[/tex] + [tex]\frac{1}{3}[/tex]

        = x + [tex]\frac{1}{3}[/tex]

Answer:

[tex]\fbox {all real numbers}[/tex]

Step-by-step explanation:

7x + 8 = 1/6 (42x + 48)

7x + 8 = 7x + 8

x = all real numbers

Part 1

[tex](f\circ g)(x)=f(g(x))=\frac{\frac{1}{x}}{\frac{1}{x}-3}[/tex]

Multiplying the numerator and denominator by x,

[tex](f\circ g)(x)=\boxed{\frac{1}{1-3x}}[/tex]

Part 2

The domain for this function is all values of x except for when the denominator equals 0 (because then, it would be undefined).

The denominator is equal to 0 when x=1/3, so the domain is [tex]\boxed{x \neq \frac{1}{3}}[/tex]

Answer:

6x + 7y = 14

7x + 8y = 27

6 7. x = 14

7 8. y = 27

option B

Answer:

212520 different committees

Step-by-step explanation:

Candidates

For a President: 23

For a Vice President: 22

For a Secretary: 21

For a Treasurer: 20

Number of ways: (23)(22)(21)(20) = 212520

Hope this helps

Answer:

To whom it may concern the answer to this problem would be 212,520.

Step-by-step explanation:

Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...

[tex]_{n}_P_{r}=\frac{n!}{(n-r)!} \\_{23} _P_{4}=\frac{23!}{(23-4)!} \\_{23}_P_{4}=\frac{23!}{19!} \\_{23}_P_{4}=\frac{23*22*21*20*19!}{19!} \\_{23}_P_{4}=\frac{212,520}{1} \\_{23}_P_{4}=212,520[/tex]

Remember that the 19! cancel each other out. Hope this helps!

Answer:

  (a)  5440.42 g

Step-by-step explanation:

The amount remaining (Q) is given in terms of the initial amount (Q₀) by the exponential decay formula ...

  Q = Q₀(1/2)^(t/330) . . . . . where t is in days

__

The amount after 540 days is ...

  1750 g = Q₀(1/2)^(540/330) = 0.321666Q₀

  Q₀ = (1750 g)/(0.321666) ≈ 5440.42 g

The initial quantity was about 5440.42 grams.

The solution of the system of linear equation by substitution method is (3,1).

The method of substitution is the method for solving the linear equation where the value of one variable of one equation is placed in the place of that variable in another equation.

Given here the linear equations are

Equation 1: 6x+2y=20

Equation 2: 2x-3y=3

in equation 1 the value of y will be

6x+2y=20

⇒2y=20-6x

⇒y=(20-6x)/2

⇒y=10-3x

substituting the value of y in the equation 2, we will get

2x-3y=3

⇒2x-3(10-3x)=3

⇒2x-30+9x=3

⇒11x-30=3

⇒11x=30+3

⇒11x=33

⇒x=33/11

⇒x=3

putting the value of x in value of y in equation 1

y=10-3x

⇒y=10-3(3)

⇒y=10-9

⇒y=1

The solution of the system of linear equation by substitution method is (3,1).

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Answer:

The correct graph of the following condition. {(x, y) : x - y6} is depicted in the graph attached.

A graph is a diagram showing the relation between variable quantities each measured along one of a pair of axes at right angles.

In this case, the correct graph of the following condition. {(x, y) : x - y6} is depicted in the graph attached.

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According to the function transformations, the value of h is -2

The complete question is in the attachment

The functions are given as:

[tex]f(x) = (2.5)^x[/tex]

[tex]g(x) = (2.5)^{x-h[/tex]

From the question, we understand that the function f(x) is translated to the left to get g(x)

From the attached graph, we can see that the function h(x) is 2 units to the left of f(x).

This transformation is represented by:

(x, y) => (x + 2, y)

So, we have:

x - h = x + 2

Evaluate the like terms

h = -2

Hence, the value of h is -2

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Answer:H=-2

Step-by-step explanation: