Given the domain {-4, 0, 5}, what is the range for the relation 12x 6y = 24? a. {2, 4, 9} b. {-4, 4, 14} c. {12, 4, -6} d. {-12, -4, 6}

The unit rate of the proportional relationship y = 3x is 3

The proportional relationship is given as:

y = 3x

Divide both sides by x

y/x = 3

For a proportional relationship y/x = k;

The unit rate is 3

This means that the unit rate of the proportional relationship y = 3x is 3

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Answer:

$528
If not then it might be $385

The value of given trigonometric value cos(22. 5°) is 0.387.

According to the statement

we have given that the trigonometric value and we have to find the exact value of that given value with the help of the half angle formula.

So, For this purpose, we know that the

The half angle formulas are used to find the exact values of the trigonometric ratios of the angles like 22.5°.

So,

The given value is :

cos(22. 5°)

Then the value of cos half angle formula is

[tex]cos (theta/2) = +- sqrt((1-cos theta) / 2)[/tex]

then

The value of θ/2 is 22.5 degree.

And θ is 22.5*2

θ = 45 degree

and cos 45 degree is 1/squareroot 2

And by this the value of given value become is

[tex]cos 22.5 = +\sqrt{((\sqrt{2} -1)/(2 \sqrt{2} )) } = + 0.3827[/tex]

So, The value of given trigonometric value cos(22. 5°) is 0.387.

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The minimum number of balls that we need to draw to ensure that we get at least 3 even labeled balls is 4

The total number of balls is

Total = 50

Let k represent the minimum number of balls that we need to draw to ensure that we get at least 3 even labeled balls

Using the pigeonhole principle, we have

n + 1 = k

Where n = 3

So, we have

3 + 1 = k

Evaluate the sum

4 = k

Rewrite the equation as

k = 3

Hence, the minimum number of balls that we need to draw to ensure that we get at least 3 even labeled balls is 4

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The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

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Answer:

The answer is A. V=pi r³

Step-by-step explanation:

:)

The expression for the volume of the pyramid in terms of the radius r of the cone is [tex]\pi r^3[/tex]. So, option A is correct.

The cone is a three-dimensional figure with a vertex and a flat base.

The volume of a pyramid is given by the formula:

[tex]V = \dfrac{1}{3} \times base\ area \times height.[/tex]

Given that:

The base area of the pyramid = B

The height is 3r

The base area of the pyramid is the same as that of the cone.

The base of the cone = [tex]\pi r^2[/tex]

The volume of the pyramid is calculated as:

[tex]V = \dfrac{1}{3} \times \pi r^2 \times 3r[/tex]

V =[tex]\pi r^3[/tex]

Therefore, the volume of the pyramid is [tex]\pi r^3[/tex]. So, option A is correct.

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Question 17: B. A’ (1,2), B’ (3,2), C’ (3,5)

Translating 4 to the right means that you should add 4 to the x value of your coordinate point.

Question 18: C. (3,-5)

This is because reflecting over the x-axis would mean to move down the same amount of units above the x-axis the original point is (the original point is five units above the x-axis so you just move down five units). Look at the attached picture for more help.

Question 19: A. C’ (0,-2)

We can see that the triangle has been translated 1 unit to the right and 2 units up. This would mean you add 1 to the x-value of the coordinate and add 2 to the y-value of the coordinate. I can’t see point C clearly, but I’m guessing that it’s at (-1,-4). This would give point C’ as (0,-2)

Hope this helps! Let me know if you need more help! Have a fantastic day!

Jane lost 5 points in the game.

Given that, Jane gained 25 points in the first round of a game. In the second round, she lost 40 points and in the third round, she gained 10 points.

We need to write and evaluate an expression to find how many points Jane gained or lost.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Now, for the given situation we can write an expression as follows:

25 – 40 + 10

=25 + 10 + ( -40 )

=35 -40= -5

Therefore, Jane lost 5 points in the game.

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Answer:

probability result of sample space would result in 12/144

Step-by-step explanation:

as result there is 12 numbers on each dice, blth have exact same numbers, resulting in 144 combinations ti be thrown as sample space event outcome wluld be;

1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12

2/1 2/2 2/3 2/4 2/5 2/6 2/7 2/8 2/9 2/10 2/11 2/12

3/1 3/2 3/3 3/4 3/5 3/6 3/7 3/8 3/9 3/10 3/11 3/12

4/1 4/2 4/3 4/4 4/5 4/6 4/7 4/8 3/9 4/10 4/11 4/12

5/1 5/2 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/10 5/11 5/12

6/1 6/2 6/3 6/4 6/5 6/6 6/7 6/8 6/9 6/10 6/11 6/12

7/1 7/2 7/3 7/4 7/5 7/6 7/7 7/8 7/9 7/10 7/11 7/12

8/1 8/2 8/3 8/4 8/5 8/6 8/7 8/8 8/9 8/10 8/11 8/12

9/1 9/2 9/3 9/4 9/5 9/6 9/7 9/8 9/9 9/10 9/11 9/12

10/1 10/2 10/3 10/4 10/5 10/6 10/7 10/8 10/9 10/10 10/11 10/12

11/1 11/2 11/3 11/4 11/5 11/6 11/7 11/8 11/9 11/10 11/11 11/12

12/1 12/2 12/3 12/4 12/5 12/6 12/7 12/8 12/9 12/10 12/11 12/12

giving 12 matching numbers in a 144 possible rolled outcome

mathematic formula would be P(A) = n(A)/n(S)

As P(A)= probabolity of event A

n(A)= number of favouravle outcome

n(S)= total number of outcome in sample space

giving

12=2/144=0,0138888889

Answer:

A

Step-by-step explanation:

Answer:

61.9°

Step-by-step explanation:

The angles of a triangle always add up to 180°. Using this information along with the values of two of the three angles, we can set up an equation to find the measure of the third angle.

Let the measure of the third angle be represented as "x". The first angle + the second angle + the third angle must equal 180 therefore...

[tex]35.5+82.6+x=180[/tex]

Start by adding the like terms on the left side of the equation:

[tex]118.1+x=180[/tex]

Then, subtract both sides by 118.1:

[tex]x=61.9[/tex]

Therefore the measure of the third angle of the triangle is 61.9°.

There are 8855 ways in which a 4-member committee be formed from 23 members

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

The number of ways that a 4-member committee be formed from 23 members is:

Number of ways = 23! / [(23 - 4)!4!] = 8855 ways

There are 8855 ways in which a 4-member committee be formed from 23 members

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Answer:

The answer is 212,520.

Step-by-step explanation:

This is a permutation, not a combination. So, we need to follow the formula

[tex]nP_{r} =\frac{n!}{(n-r)!}[/tex]

Plug in the numbers and solve:

[tex]nP_{r}= \frac{23!}{(23-4)!}[/tex]

[tex]nP_{r}= \frac{23!}{19!}\\[/tex]

[tex]nP_{r}= \frac{25,852,016,738,884,976,640,000}{121,645,100,408,832,000}[/tex]

[tex]nP_{r}= 212,520[/tex]

Because 212,520 is an answer choice, this is the correct answer.

When calculating a nation’s digital power, the term that is used to refer to the demonstrated capabilities of a nation-state in cyber offense or defense is Cyberwarfare.

Cyberwarfare  can be regarded as the use of cyber attacks against a nation-state so as to produce significant harm.

It should be noted that Cyber Warfare is set of actions  which is been carried out by  nation or organization so as to be able to launch an attack on institutions' computer network systems.

The interests or reasons for cyberwarfares based on the Cybersecurity as well as Infrastructure Security Agency are;

In order to achieve the goals behind the cyberwarfare programs, it is usually designed to focus on spectrum of objectives which will bring harm to national interests.

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Answer:

0.213

Step-by-step explanation:

→ Convert into binomial information

x ~ B ( 12 , 0.4 )

→ Write down probability required

p ( x = 4 )

→ Evaluate

0.2128

Answer:

11.3 miles more than

Step-by-step explanation:

Looking at the graph, when x is 10 the y is 308. For the equation, if you make x 10, then y is 421. 421 is 113 more than 308. Jace travels 113 more than Jeriel on 10 gallons of gas. If you divide 113 by 10 (to get 1 gallon of gas), you would end up with 11.3 miles more than :)

The given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.

To prove, we go by the right-hand side of the equation:

cot x - d/dx x.cot x.

We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.

cot x - {x. d/dx(cot x) + cot x. d/dx(x)}

= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}

= cot x + x. cosec²x - cot x

= x. cosec²x

= The left-hand side of the equation.

Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

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Answer:

heat map is the answer

Answer:

[0,+♾)

Step-by-step explanation:

|x| function is kinda like a half opened book from (0, 0) and |x+5| is from (–5, 0)

So we can't find any changes for y

so the domain is

[0, +♾)

Let's try solving the problem using the order of operations method, otherwise known as PEMDAS.

[tex]\begin{tabular}{c | l}Order of Operation & Required Operation \\\cline{1-2}1 & Parentheses () \\2 & Exponents e^{x} \\3 & Multiplication \times \\4 & Division \div \\5 & Addition + \\6 & Subtraction -\end{tabular}[/tex]

We are given this question :

[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 7 \times .8}[/tex]

Since there are no parentheses or exponents, let's multiply.

[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 5.6}[/tex]

The next step is to divide.

[tex]\mathrm {\frac{7}{4} - 112.5 + \frac{4}{5} - 5.6}[/tex]

After that, add.

[tex]\mathrm {\frac{7}{4} - 112.5 + 0.8 - 5.6}[/tex]

[tex]\mathrm {\frac{7}{4} - 111.7 - 5.6}[/tex]

Finally, subtract the remaining terms.

[tex]\mathrm {1.75 - 111.7 - 5.6}[/tex]

[tex]\mathrm {-109.95 - 5.6}[/tex]

[tex]\mathrm {-115.55}[/tex]

The final answer is -115.55.

I hope this helped solve the problem.

Good luck on your studies!

Answer:

-115.55

Step-by-step explanation:

7/4 -9÷ .08 + 4/5 -7 * .8

I would change fractions to decimals

1.75 - 9 ÷ .08  +.8 -7 * .8

Now using pemdas, multiply and divide from left to right

1.75 -112.5 +.8 -7 * .8

1.75 -112.5 +.8 -5.6

Now add and subtract from left to right

-110.75+.8 -5.6

-109.95-5.6

-115.55

Step-by-step explanation:

1: change 'sin²A' and 'cos²B' into (1-cos²A)and (1-sin²A) respectively.

2:open the brackets and put signs accordingly.

3: cancel (-1) and (+1).

4: remaining is your answer.

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

I’m going to assume that your values are in the form of:

(r,θ,z)=(4,6π,2π/3)

where

(r,θ)are the polar coordinates of the point’s projection in the xy-plane

z is the usual z-coordinate in the Cartesian coordinate system

Now solving for Cartesian coordinates:

x=rcosθ=4cos(6π)=4(0.86)=3.44

y=rsinθ=4sin(6π)=2

Now for spherical transformation, note that:

(ρ,θ,ϕ)

ρ is the distance between P and the origin

θ is the same angle used to describe the location in cylindrical coordinates

ϕ is the angle formed by the positive z-axis and line segment from the origin and point in space, note that0≤ϕ≤π

OK, now that we have that out of the way, let’s compute:

ρ=r2+z2 = 5

θ=θ=6π

ϕ=arccos(zr2+z2−−−−−−√)=arccos(35)≈0.927rad

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

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Answer:

5x^2-x+6

Step-by-step explanation:

That should work

The number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16

The equation is given as:

a+b+c+d+e+f = 2006

In the above equation, we have:

Result = 2006

Variables = 6

This means that

n = 2006

r = 6

The number of solutions is then calculated as:

(n + r - 1)Cr

This gives

(2006 + 6 - 1)C6

Evaluate the sum and difference

2011C6

Apply the combination formula:

2011C6 = 2011!/((2011-6)! * 6!)

Evaluate the difference

2011C6 = 2011!/(2005! * 6!)

Expand the expression

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006 * 2005!/(2005! * 6!)

Cancel out the common factors

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/6!

Expand the denominator

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/720

Evaluate the quotient

2011C6 = 9.12 * 10^16

Hence, the number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16

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The results of subtraction of functions are listed below:

There three fundamental binary operators (addition, multiplication, composition) and two secondary binary operators (subtraction, division) for functions. The subtraction is operation derived from addition, defined by the following expression:

(h - f) (x) = h(x) - f(x)       (1)

Now we proceed to develop each expression:

i) (h - f) (x):

ii) m(x) = (g - j) (x):

iii) m(3):

m(3) = 3² + 10 · 3 + 5

m(3) = 9 + 30 + 5

m(3) = 44

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The integer value of the given integers is 20.

According to the statement

we have given that the some integers values like a = 3, b = 2, c = 10 and we have to find the intresult = c *b it means integer result = c *b

So, For this purpose we know that the

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

And here integer a = 3 and b = 2 and c = 10 and we have to find the value of c *b then

intresult = c *b

Substitute the values in it then

intresult = 10 *2

intresult = 20.

So, the intresults is 20 from the given numbers.

Hence, The integer value of the given integers is 20.

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Angles are said to be produced whenever two or more straight lines intersect. Some types of angles are right angle, obtuse angle, acute angle, etc. Thus, the required proof is stated below:

Prove: <A > <C

           <B > <D

An obtuse angle is a given angle that is greater than [tex]90^{o}[/tex] but less than [tex]180^{o}[/tex]. While an acute angle is a given angle that is less than [tex]90^{o}[/tex].

Thus extend AB to F, such that BF = CD.

Draw a perpendicular from a to intersect CD at point E.

So that;

<BAD = <BAE + <DAE (addition property of an angle)

Such that;

<A is an obtuse angle, while <C is an acute angle. Thu,

<A > <C (different types of angles)

Also,

<ADC = <CDF - <ADF (subtraction property of angles)

But both angles B and D are acute angles.

So that;

<B > <C (comparison of measures of two angles)

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[tex]\boldsymbol{\sf{3n\left(\dfrac{1}{4}\right)=16\dfrac{1}{2} } }[/tex]

Multiply both sides of the equation by 4, the lowest common denominator of 4.2.

[tex]\boldsymbol{\sf{ 12n\times\left(\dfrac{1 }{4}\right)=2(16\times2+1) }}[/tex]

Multiply 12 and 1/4, because once multiplied, we get the following 12/4.

[tex]\boldsymbol{\sf{\dfrac{12}{4}n=2(16\times2+1) \ \ \longmapsto \ \ [Divide \ 12 \div 4.] }}[/tex]

[tex]\boldsymbol{\sf{3n=2(16\times2+1) \ \ \longmapsto \ \ [ Multiply \ 16\times 2] }}[/tex]

[tex]\boldsymbol{\sf{3n=2(32+1) \ \longmapsto \ \ [Add] }}[/tex]

[tex]\boldsymbol{\sf{3n=2\times33 \ \ \longmapsto \ \ [Multiply] }}[/tex]

[tex]\boldsymbol{\sf{3n=66}}[/tex]

Divide both sides by 3.

[tex]\boldsymbol{\sf{n=\dfrac{66}{3} \ \longmapsto \ \ [Split] } }[/tex]

[tex]\boxed{\boldsymbol{\sf{n=22}}}[/tex]

Once the exercise is solved, we find that the value of n is 22.

The area of the shaded region shown in the image is 14π unit²

An equation is an expression that shows the relationship between two or more numbers and variables.

Area of semicircle = π*diameter² / 4

The area of the shaded region is the sum of the area of the individual semi circles shown in the diagram.

Area of shaded region = area of SR + area of QR + area of PQ

Area of shaded region = (1/2) * π(4²/4) +  (1/2) * π(2*4²/4) + (1/2) * π(2 * 2 * 4²/4) = 14π

The area of the shaded region shown in the image is 14π unit²

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The given statement simpson’s paradox occurs whenever including a lurking variable causes you to rethink the direction of an association is true.

Since, we know that

A variable that we did not include in our analysis, that could susbtantially change our intepretation of the data if we did include it, is called a lurking variable.

Including a lurking variable may

And,

When including a lurking variable causes you to re-think the direction of an association, this is called Simpson's paradox.

Hence, the given statement simpson’s paradox occurs whenever including a lurking variable causes you to rethink the direction of an association is true.

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