The graph represents the piecewise function:

Answer:

1.3 or 1.333333

Step-by-step explanation:

Just do it!

The equivalent expression to [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex] is given by [tex]=\mathbf{\frac{n^{10}}{16m^6}}[/tex].

From the principle of indices we get,

Addition of exponent, [tex]a^{m+n}=a^m.a^n[/tex]

Subtraction, [tex]a^{m-n}=\frac{a^m}{a^n}[/tex]

Multiplication, [tex]a^{mn}=(a^m)^n[/tex]

negative exponent, [tex]a^{-m}=\frac{1}{a^m}[/tex]

Here in the problem given expression is [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]

Calculating we get,

[tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]

[tex]=\left(4m^{1-(-2)}n^{1-6}\right)^{-2}[/tex], using addition and subtraction of indices formulae

[tex]=\left(4m^3n^{-5}\right)^{-2}[/tex]

[tex]=16^{-1}m^{-6}n^{10}[/tex], using multiplication of indices

[tex]=\frac{n^{10}}{16m^6}[/tex], using negative exponent formula

Hence the equivalent required expression is [tex]=\frac{n^{10}}{16m^6}[/tex].

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Answer:

b

Step-by-step explanation:

edge 23

Using limits, the end behavior of the functions are given as follows:

a. Rises to the left and falls to the right.

b. Rises to the left and rises to the right.

c. Falls to the left and rises to the right.

The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.

In item a, we have that, respectively, to the left and to the right.

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -5x^3 = -5(-\infty)^3 = \infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -5x^3 = -5(\infty)^3 = -\infty[/tex]

Hence it rises to the left and falls to the right.

In item b, we have that, respectively, to the left and to the right.

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 3x^6 = 3(-\infty)^6 = \infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 3x^6 = 3(\infty)^6 = \infty[/tex]

Rises to the left and rises to the right.

In item c, we have that, respectively, to the left and to the right.

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 20x^3 = 20(-\infty)^3 = -\infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 20x^3 = 20(\infty)^3 = \infty[/tex]

Falls to the left and rises to the right.

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Answer:

558, 500

Step-by-step explanation:

round 349,001 to 349,000             subtracted 1

round 209, 499 to 209, 500          added 1

349,000 + 209, 500 = 558, 500

Now, the added and subtract 1 cancel out so that is the final answer

The solution to the equation is x = 7 , -2 , Option C and D is the right answer.

An equation is a mathematical statement formed when two algebraic expression are equated by an equal sign.

It is given that the equation is

[tex]\rm 3 +\sqrt{3x - 5}= x[/tex]

Taking square on both sides

3x-5 = (x-3)²

3x-5 = x² +9 -6x

x² -9x -14 = 0

x² -7x +2x -14 = 0

x(x-7) +2(x-7) = 0

(x-7)(x+2) = 0

x =7 , x = -2

Therefore the solution to the equation is x = 7 , -2 , Option C and D is the right answer.

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Answer:

1/2

Step-by-step explanation:

since every time you divide by 2, the common ratio is 1/2

Answer:

We can use change of base rule

Answer:

450 N

Step-by-step explanation:

Since you have the VOLUME and the HEIGHT of the prism, you can calculate the AREA of the prism base :

 18 m^3 / 3 m =   6 m^2    area

Now you are given  pressure = force / area

                                      75 n/m^2 =  force / 6 m^2

        6 *75 = force = 450 N

Answer:

450 newtons

Step-by-step explanation:

To solve for the force, we first need to find the area. (Force = Pressure × Area)

[tex]Area = \frac{volume}{height} = \frac{18m^{3} }{3m} = 6m^{2}[/tex]

Now we just substitute this number into [tex]Force = Pressure * Area[/tex] and get that [tex]Force = 75newtons/m^{2} * 6m^{2} = 450 newtons[/tex]

(p.s. Units are very important! This question doesn't require any unit

conversions, but others might.)

If Five hundred ten of 650 high school students said that pizza was their favorite food. The margin of error is 0.0322.

Given:

Sample proportion=Five hundred ten=510

Sample size=650

Hence:

Margin of error=z×√p×(1-p)/n

Margin of error=2√510/650× (1-510/650)÷650

Margin of error=2√0.78461538×(1-0.78461538)÷650

Margin of error=2√0.78461538×0.21538462÷650

Margin of error=2√0.168994085÷650

Margin of error=2√0.0002599909

Margin of error=0.0322

Therefore the correct option is D.

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A function assigns the values. The input value that produces the same output value for the two functions is 1.

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

For the given tables the x is the input while f(x) and g(x) are the outputs of the respective functions. Therefore, the input for which the two given functions will return the same output is 1.

Hence, the input value that produces the same output value for the two functions is 1.

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The correct answer will be 2/33.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Well, the problem is that he does not replace the first marble after he draws it.

Therefore, yes, he has a 2/12 probability of drawing a yellow marble first, but then he has a 4/11 probability of drawing a red marble second, not 4/12.

This is because there are going to only be 11 marbles left in the bag after he draws the first marble and does not replace it.

The correct answer would be:

(2/12)(4/11)

=8/132

=4/66

=2/33

Thus, the correct answer will be 2/33.

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Answer:

(fog)(a)​ = a³ - 3a² + 4a - 2

           = (a - 1)×(a² - 2a + 2)

Step-by-step explanation:

Given :

g(a) = a -1 

f(a)= a³ +a

…………………………

(fog)(a)​ = f(g(a)​))

           = g(a)³ + g(a)

           = (a - 1)³ + (a - 1)

           = (a³ - 3a² + 3a - 1) + (a - 1)

           = a³ - 3a² + 3a - 1 + a - 1

           = a³ - 3a² + 3a + a - 1 - 1

           = a³ - 3a² + 4a - 2

Second method :

(fog)(a)​ = f(g(a)​))

           = f(a - 1)

           = (a - 1)³ + (a - 1)

           = (a - 1)×[(a - 1)² + 1]

           = (a - 1)×[a² - 2a + 1 + 1]

           = (a - 1)×(a² - 2a + 2)

The answer to the question is 5 units up.

Answer:

Step-by-step explanation:

If two ratios make a proportion then it can be shown as:

Let's verify the answer choices with this method

A. 1/4 and 5/25

B. 1/4 and 7/24

C. 1/4 and 10/48

D. 1/4 and 9/36

Answer:

it depends on whether the outlier is a high outlier or a low outlier

Step-by-step explanation:

The mean of a data set is the average of the data set. So if I had the data set {5, 2, 10} the average would be (5+2+10)/3 = 5.667. Now if I added an outlier like 10,000 it would increase the mean significantly. It changes it significantly but I cannot say whether it increases or decreases it without knowing the value of the outlier, since if I had the outlier -10,000 that would decrease the mean, but I had the outlier 10,000 it would increase it. So it depends on whether the outlier is a high outlier or a low outlier

I think the answer is 90in.

In a case whereby the face of a suitcase measures 24 inches long and 18 inches wide the diagonal length of the face is 30 in.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

The suitcase measures 24 inches long and 18 inches wide

Using Pythagoras theorem,

The diagonal =[tex]\sqrt{18^{2} + 24^{2} }[/tex]

= [tex]\sqrt{900}[/tex]

=30 in.

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Answer:

[tex]3^x=5[/tex]

Step-by-step explanation:

Given:

[tex]9^x=25[/tex]

Rewrite 9 as 3²:

[tex]\implies (3^2)^x=25[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{2x}=25[/tex]

Apply the same exponent rule:

[tex]\implies (3^x)^2=25[/tex]

Square root both sides:

[tex]\implies \sqrt{(3^x)^2}=\sqrt{25}[/tex]

[tex]\implies 3^x=5[/tex]

The range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given that:-

The range for the given domain: {-2, -1, and 0} and the function is y = 3x².

The range will be the value of y at each given value of the domain.

Domain: { -2, -1, 0 }

y  =  3x²

At x = -2  →  y = 3 ( -2)² = 12

At x = -1   →  y = 3 (-1)²   = 3

At x = 0   →  y = 3 (0)    = 0

Therefore range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.

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Answer:

m=3

b=(0,5)

Step-by-step explanation:

Answer: 62.8 cubic feet

Step-by-step explanation:

R is radius

H is height

R=2ft

H=5ft

V=(3.14)(2)^2(5)

V=62.8 cubic feet

Answer:

  ia) center: (0, 0), the origin

  ib) angle: 90°

  ic) direction: CCW

  ii) LM ≅ L'M', ∠L ≅ ∠L'

  iii) (2, 1)

Step-by-step explanation:

A rigid transformation preserves size and shape of a figure, so the image is congruent to the original. The rigid transformations are rotation, reflection, and translation. Each has characteristics that allow one to determine the nature of the transformation(s) involved.

__

angle and direction

One way to determine the angle and direction of rotation of a figure is to compare a horizontal segment on the original with the corresponding segment on the image. Here, a convenient segment is NM, which is horizontal and points to the right. Its angle relative to the direction of the +x axis is 0°.

The transformed segment N'M' points upward, at an angle relative to the +x axis of 90°. This tells you the figure was rotated 90° in the CCW direction. (This is fully equivalent to a rotation of 270° in the CW direction.)

center

Points in a rotated image always remain at the same distance from the center of rotation as the original points. In most cases, the center of rotation is the origin. We can check to see if that is the case by looking at the distances of a couple of points from the origin.

  N is at coordinates (1, 1), so is √(1² +1²) = √2 from the origin

  N' is at coordinates (-1, 1), so is √((-1)² +1²) = √2 from the origin

  L is at coordinates (1, 3), so is √(1² +3²) = √10 from the origin

  L' is at coordinates (-3, 1) so is √((-3)² +1²) = √10 from the origin

This confirms that the origin is the center of rotation.

__

Since each point and its image are on a circle centered at the center of rotation, the line between them is a chord of that circle. The perpendicular bisector of that chord goes through the center of rotation. Here, we observe that the perpendicular bisector of NN' is the y-axis. The perpendicular bisector of LL' is a line with slope -2 through (-1, 2). It will intersect the y-axis at the origin, confirming the origin as the center of rotation.

__

A rigid transformation preserves lengths and angles, so any length or angle on the rotated figure is congruent to the original:

 LM ≅ L'M', MN ≅ M'N', NL ≅ N'L'

  ∠L ≡ ∠L', ∠M ≡ ∠M', ∠N ≡ ∠N'

__

The components of a translation vector add to the corresponding coordinates of a point.

  L +v = L'

  (1, 3) +(1, -2) = (2, 1) . . . image of point L

The measure of angle ∠ACB is 70°. Then the correct option is C.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

∠ABC + ∠BCA + ∠CAB = 180°

        60° + ∠BCA + 50° = 180°

                           ∠BCA = 180° – 110°

                           ∠BCA = 70°

Then the correct option is C.

The complete question is given below.

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.

The measure of ABC is 60

The measure of BAC is 50

The measure of ACB will be

a. 50

b. 60

c. 70

d. 120

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Answer:

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.

The measure of angle ABC is

✔ 60

°.

The measure of angle BAC is

✔ 50

°.

The measure of angle ACB is

✔ 70

°.

Step-by-step explanation:

Answer:

a) 1

Step-by-step explanation:

added in the picture

Answer:

46. 135°

47. 225°

47. 270°

48. 3/8

49. 3/4

Step-by-step explanation:

Answer:

46) 135°

47) 225°

48) 270°

49) [tex]\frac{3}{8}[/tex]   (3/8)

50) [tex]\frac{3}{4}[/tex]  (3/4)

Step-by-step explanation:

{the following is if you do not understand my drawing}

There are 4 segments that we can imagine - north, south, east, and west

We can imagine that these lines all meet a circle

There are 360 degrees to a circle. So, if we divide that by 4, we know that each segment is 90 degrees.

(Also, you can probably see that the angles are right angles, or you know that straight lines are 180 degrees, you probably know this information intuitively)

This means that each smaller segment, two in both of our four segments, is 45 degrees.

These 8 sections are each 1/8 of the total circle.

Answer:

w = 3

Step-by-step explanation:

1/w = 1 2/3 / 5      cross multiply

1 2/3 (w) = 5

w = 5 / ( 1 2/3 ) =  5 / ( 5/3) = 15/5 = 3

If the given differential equation is

[tex]\cos^2(x) \sin(x) \dfrac{dy}{dx} + \cos^3(x) y = 1[/tex]

then multiply both sides by [tex]\frac1{\cos^2(x)}[/tex] :

[tex]\sin(x) \dfrac{dy}{dx} + \cos(x) y = \sec^2(x)[/tex]

The left side is the derivative of a product,

[tex]\dfrac{d}{dx}\left[\sin(x)y\right] = \sec^2(x)[/tex]

Integrate both sides with respect to [tex]x[/tex], recalling that [tex]\frac{d}{dx}\tan(x) = \sec^2(x)[/tex] :

[tex]\displaystyle \int \frac{d}{dx}\left[\sin(x)y\right] \, dx = \int \sec^2(x) \, dx[/tex]

[tex]\sin(x) y = \tan(x) + C[/tex]

Solve for [tex]y[/tex] :

[tex]\boxed{y = \sec(x) + C \csc(x)}

which follows from [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}[/tex].

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

Answer:  [tex]\textsf{y = -1/4x - 4}[/tex]

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

Given: [tex]\textsf{Slope = -1/4, Point through = (4, -5)}[/tex]

Find:  [tex]\textsf{Equation for the line that passes through the given point}[/tex]

Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.

Plug in the values

Simplify and solve for y

Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.

Answer:

shown below

Step-by-step explanation:

a) V = h(pi)r²

let x = height

and c = the constant radius

V1 = 2x(pi)c²

V2 = x(pi)c²

let c = random number, such as 2

let x = 3

2x(pi)4

x(pi)4

pi(4) = 12.57

3 x 12.57 = 37.7

6 x 12.57 = 75.4

We can compare these ans realise that the cylinder with double the height will also have double the volume.

b) SA = h(pi)2c

SA1 = 2x(pi)2c

SA2 = x(pi)2c

let c = 2

let x = 3

2(3)(pi)(2(2))

6(pi)4

24(pi)

3(pi)(2)(2)

3(pi)(4)

12(pi)

I don't need to finish the calulation to see that this is also halved. So the surface area of the one with the double length is twice the surface area of the one with a smaller height.

Comparatively, both the volume and surface area are doubled when the height is doubled.

QED.

Answer:

This point is not on the line, NOT TRUE

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

           b represents the y-intercept

where the format of a point is (x, y)

Given: y = x - 1/2, (-5, -2)

we can plug in the point (-5, -2)

-2 = (-5) - 1/2

-2 = -5.5

-2 does not equal -5.5 so this point is not on the line

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