A cylindrical cup with a base diameter of 4 inches and a height of 12 inches is filled with orange juice that occupies 67% of the cup. What is the volume of the orange juice in the cup?

We will see that g(x) is a reflection across the y-axis of f(x), then:

   [tex]g(x) = f(-x) = 3^{-x\\[/tex]

By looking at the graph, we can see that g(x) is a reflection across the y-axis of f(x).

So we can write:

g(x) = f(-x)

Here we know that:

[tex]f(x) = 3^x[/tex]

Then, replacing f(x) on the formula for g(x), we get:

[tex]g(x) = f(-x) = 3^{-x\\[/tex]

That is the function g(x) shown in the figure.

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Answer:

0.2

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Answer:

I believe I found your question, I hope this helps.

Step-by-step explanation:

Answer:

84.

Step-by-step explanation:

mean = total of the values  / number of numbers

If the total of the numbers = T:

14 = T / 8

T = 8*14 = 84.

Explanation:

Pick any term. Subtract off the previous one to find the common difference.

And so on. You only need to pick one of those to show as your steps to your teacher. However, doing all three subtractions is a good way to get practice in seeing how we have an arithmetic sequence. The common difference must be the same each time.

We subtract 7 from each term to get the next term, i.e. we add -7 to each term to get the next one.

Answer:

Step-by-step explanation:

for any variable to be eliminated in a simultaneous equation, the one of the coefficients must be the same in the two equations. and:

FOR OPTION A

if the first equation is multiplied by 3 , we will be having 12x-27y= 24 as the new equation 1 and since the cofficient of y or x are different in equation 1 and 2, no variable can be eliminated.

FOR OPTION B

if the second equation is multiplied by 2, our new equation 2 will be 4x+6y= 48. here, the cofficient of x in the two equations are now the same but since we're going to add, 4x+4x = 8x which does not eliminate x

FOR OPTION D

if the second equation is multiplied by three, our new equation 2 becomes 6x+9y= 72 and subtracting,-9y -9y= -18y which does not eliminate y

The probability of Ryan winning a prize would be 0.71.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Ryan is on a game show. He will choose a box to see if he wins a prize.

The odds in favor of Ryan winning a prize are 5/7.

P(Ryan wins a prize) = 5/7 = 0.71

Thus, the probability of Ryan winning a prize would be 0.71.

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Answer:

-10 6/11

Step-by-step explanation:

16/11−12/1=16/11+−12/1=16/11+−132/11=16+−132/11=−116/11

-116/11 = −10 6/11

Answer:

if a scale factor is less than 1 then your figure gets smaller

Step-by-step explanation:

The correct answer is: [A]: " Look at the graph of the relationship.  Find the y-value of the point that corresponds to x = 1 . That value is the unit rate."

The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). Also called "Ordinate".

Here, The "y-axis" is located on the "vertical axis" that represents the "dependent variable" (or, at times, the "control value") that cannot be "manipulated" / controlled/ or "selected" / since it represents the "y-value" of the corresponding coordinate to which the "x-value" happens to corresponds to at the given value for "x" .

Thus, the correct answer is: [A]: " Look at the graph of the relationship.  Find the y-value of the point that corresponds to x = 1 . That value is the unit rate."

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Answer:

Step-by-step explanation:

1. To find f(0.5), substitute the x value in the function f(x) with 0.5

            f(x) = 30x + 5

          f(0.5) = 30*0.5 + 5

                    = 15 + 5

                    = 20

At 0.5 gigabytes of data used, the cost is  $20

2)  g(x) = 10x + 20

g(0.5) =  10*0.5 + 20

           = 5 + 20

           = 25

At 0.5 gigabytes of data used, the cost is $ 25.

3)          f(x) = 50

    30x + 5  = 50

Subtract 5 from both sides

            30x = 50 - 5

            30x = 45

Divide both sides by 30

                x = 45/30

             x = 1.5

If she chooses plan 'f', she could use 1.5 gigabytes.

         g(x) = 50

   10x + 20 = 50

            10x =50- 20

            10x = 30

                x = 30/10

              x = 3

If she chooses plan 'g', she could use 3 gigabytes.

4) Function 'g' would be better for a $50 monthly budget as she could get more gigabytes than function 'f'

The correct answer is option 3 which is the equation for the line of best fit of this data is y = 25x.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Given that:-

The equation of the line will be calculated as:-

The intercept of the line will be;-

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{500-250}{20-10}=25[/tex]

The equation of the line is given as:-

y - y₁ = m( x - x₁ )

Putting the coordinates:-

y - 250 = 25 ( x - 10 )

y - 250 = 25x - 250

y = 25x

Therefore the correct answer is option 3 which is the equation for the line of best fit of this data is y = 25x.

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Answer:

Step-by-step explanation:

we are given a right triangle and the measure of its two legs .

x represents the length of the hypotenuse.

……………………………………………………………………

Then (by applying the Pythagorean theorem) we obtain :

[tex]x=\sqrt{24^{2}+7^{2}}[/tex]

  [tex]=\sqrt{576+47}[/tex]

  [tex]=\sqrt{625}[/tex]

  [tex]=25[/tex]

Answer:

There are 0 solutions to this problem because it cannot be re-arranged logically enough to come to a new conclusion.

Answer:

0

Step-by-step explanation:

If we try to solve this question, we get no solutions:

First we subtract 5 from both sides :

9x = 9x + 2

Now we subtract 9x from both sides :

0 = 0 +2

0 = 2 ❌

This is why this equation has no solutions

Hope this helped and have a good day

Answer:

increasing to the certain point

Step-by-step explanation:

Potato head

Step-by-step explanation:

12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..

Answer:

B

Step-by-step explanation:

A dog might be around
b) 25 kgs

You need to find the least common multiple of 8 and 6.

[tex]8=2^3\\6=2\cdot3\\\\\text{lcm}(8,6)=2^3\cdot3=24[/tex]

Therefore, the answer is 24 days.

The surface area of the given shape is 285.01 ft²

From the question, we are to calculate the surface area of the given shape.

The given shape in the diagram is a cone.

The surface area of a cone is given by the formula,

[tex]S = \pi r(r+l)[/tex]

Where S is the surface area

r is the radius

and [tex]l[/tex] is the slant height

First, we will calculate the slant height of the cone

[tex]l^{2}=9^{2} +5.6^{2}[/tex] (Pythagorean theorem)

[tex]l^{2}=81+31.36[/tex]

[tex]l^{2}=112.36[/tex]

[tex]l}=\sqrt{112.36}[/tex]

[tex]l=10.6 \ ft[/tex]

∴ The slant height is 10.6 ft

Now, for the surface area

[tex]S = \pi \times 5.6(5.6+10.6)[/tex]
[tex]S = \pi \times 5.6(16.2)[/tex]

[tex]S = 90.72\pi \ ft^{2}[/tex]

[tex]S = 285.0053 \ ft^{2}[/tex]

S ≅ 285.01 ft²

Hence, the surface area of the given shape is 285.01 ft²

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The y-intercept of g(x) is (0, -3) and there are no asymptotes for g(x).

The function is given as g(x) = 2x - 3 and we need to find the y-intercept and the asymptote of this function g(x).

Y-intercepts of a given function are the points on the y-axis that the given function passes through.

In y-intercept points we always have x=0.

Asymptotes are straight lines on the graph that meets the given function as it moves towards infinity.

Asymptotes occur only when the given function is a rational function or when one term of the function approaches zero as one term approaches infinity.

Find the y-intercept of g(x).

We have,

g(x) = 2x - 3

Since x = 0.

we get,

g(x) = 0 - 3

g(x) = -3 or y = -3

Thus the y-intercept of g(x) is (0, -3)

Find the asymptotes of g(x).

We see that g(x) is not a rational function and when x approaches infinity g(x) does not approach zero.

Hence we can say that g(x) has no asymptotes.

The y-intercept and asymptotes of g(x) are (0, -3) and no asymptotes.

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To find the y-intercept of g(x), we set x = 0 and solve for y:g(0) = 2^0 - 3 = -2Therefore, the y-intercept of g(x) is (0, -2).To find the asymptote of g(x), we take the limit of g) as x approaches negative or positive infinity:lim x→-∞ 2^x - 3 = -3 (the asymptote is y = -3 as x approaches negative infinity)lim x→+∞ 2^x - 3 = +∞ (the graph of g(x) goes arbitrarily high as x approaches positive infinity, so there is no horizontal asymptote)Therefore, the asymptote of g(x) is y = -3.

Answer:

4x^2 - 4x - 3

Step-by-step explanation:

f(x) = 2x - 1

g(x) = x^2 - 4

g(f(x)) = ?

[substitute the x of g(x) with f(x)]

g(x) = x^2 - 4

g(f(x)) = (2x - 1)^2 - 4

[solve]

[binomial * binomial = quadratic equation]

[use FOIL method (first, outer, inner, last)]

g(f(x)) = (2x - 1)(2x - 1) - 4

g(f(x)) = (2x*2x) + (-2x) + (-2x) + (1) - 4

[combine like terms]

g(f(x)) = 4x^2 - 2x - 2x + 1 - 4

g(f(x)) = 4x^2 - 4x - 3

Answer:

Graph D

Step-by-step explanation:

Move the constant to the opposite side of the equation and group terms that include the same variable.

g(x) + 1 = x^2 + 2x

Finish the square. Remember to keep the equation balanced by using the same constants on both sides.

g(x) + 1 + 1 = x^2 + 2x + 1

g(x) + 2 = x^2 + 2x + 1

Rewrite as perfect squares

g(x) + 2 = (x + 1)^2

Equation in vertex form:
g(x) = (x + 1)^2 - 2

The vertex:

(-1, -2)

* This a minimum *

Answer:

square root function; y = -√(x + 2) - 1

Step-by-step explanation:

the graph shown is a square root function

the parent of a square root function is y = √x

you transform this equation using y = a√(x - h) + k

it is reflected across the x axis so you put the negative before the a

since there is no dilation the a is blank

y = -√(x - h) + k

the h is the horizontal shift

it went 2 to the left so that is -2

that makes it y = -√(x - -2) + k

which is also y = -√(x + 2) + k

the k is the vertical shift

it went 1 down

that makes it y = -√(x + 2) - 1

that is your equation

Hi student, let me help you out! :)

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

We need to translate "five times the sum of a number and -23" into an algebraic expression.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So in this case we should add a number (let it be x) and -23:

[tex]\star~\large\pmb{x+-23}[/tex]

Which is the same thing as

[tex]\star~\large\pmb{x-23}[/tex]

Now we multiply this little expression by 5, which gives us

[tex]\star~\large\pmb{5(x-23)}[/tex]

The parentheses around the  expression indicate that we multiply 5 by the entire expression, and not just one term.

Hope it helps you out! :D

Ask in comments if any queries arise.

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Answer:

909

Step-by-step explanation:

sqrt(30² + 3²) = x

hence the number in the box should be 909

Answer:

909

Step-by-step explanation:

Using pythagoras theorem :

a² + b² = x²

30² + 3² = x²

900+9 = x²

909 = x²

x = √909

Hence the number in the box should be 909

Hope this helped and brainliest please

If these coordinates are translated two units down, we will subtract 2 units from the y axis to have A(2, -1), B(0, -3) and C(2, -3)

Translation is a transformation technique of changing the position of an object on the xy-plane.

Given the following coordinate of a triangle expressed as:

A(2, 1)

B(0, -1)

C(2, -1)

If these coordinates are translated two units down, we will subtract 2 units from the y axis to have:

A(2, -1)

B(0, -3)

C(2, -3)

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The maximum value of the objective function is 330

The given parameters are:

Max w = 5y₁ + 3y₂

Subject to

y₁ + y₂ ≤ 50

2y₁ + 3y₂ ≤ 60

y₁ , y₂ ≥ 0

Start by plotting the graph of the constraints (see attachment)

From the attached graph, we have:

(y₁ , y₂) = (90, -40)

Substitute (y₁ , y₂) = (90, -40) in w = 5y₁ + 3y₂

w = 5 * 90 - 3 * 40

Evaluate

w = 330

Hence, the maximum value of the function is 330

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Answer:

The problem is with the arrangement of the ratios

PQ is the whole line but PR is a part of it only so you need QR to the ratio of PR

Answer:

[tex]\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

x^2 + 44^2 = 55^2

x^2 + 1936 = 3025

3025-1936 = 1089

sqrt(1089) = 33

x = 33

Answer:

X=33

Step-by-step explanation:

this is a right traingle so you can use pythagorean theorem

A^2 +B^2 =C^2

A^2 +44^2= 55^2

A^2 + 1936= 3025 subtract 1936 from both sides

A^2= 1089 now square root both sides

A=33

Answer:

10

Step-by-step explanation: