#8: Expand the logarithm shown below. *
log981xy

The box that would be able to hold all the cubes if Robin's teacher had 200 cubes is given as follows:

Box B.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

Hence the volumes for each box in this problem are given as follows:

As 216 > 144, Box B is the box that could hold all of the 200 cubes.

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Answer:

2 times, with a remainder of 0.

Step-by-step explanation:
If you had 2 friends and you had to divide 18 between both you would get 9. each with no left over

Answer:

[tex](y - 4)^2 = -8(x - 2).[/tex]

Step-by-step explanation:

The equation of a parabola with a vertical axis of symmetry, vertex (h, k), and focus (h+a, k) is given by:

[tex](y - k)^2 = 4a(x - h)[/tex]

In this case, the vertex is (2, 4) and the focus is (0, 4).

Comparing this to the general equation, we have h=2, k=4, and h+a=0.

From h+a=0, we can solve for a:

a=-h = -2

Substituting the values of h, k, and p into the equation, we get:

[tex](y - 4)^2 = 4(-2)(x - 2)[/tex]

Simplifying further:

[tex](y - 4)^2 = -8(x - 2)[/tex]

Therefore, the parabola equation is[tex](y - 4)^2 = -8(x - 2).[/tex]

People at the concession stand as input Cost of their order's output.

(1) The relation in question is a function.

(II) This function is not constant. (Each category of concession has a different order cost.)

Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)

A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.

The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.

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The quadratic equation in standard form that corresponds to the given graph is [tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]

To determine the quadratic equation in standard form that corresponds to the given graph, we need to identify the key features of the parabola. From the graph, we can see that the parabola opens upwards and intersects the y-axis at the point (0, c). We can also observe that the vertex of the parabola lies at the point (h, k).

The standard form of a quadratic equation is given as follows:

[tex]f(x) = a(x - h)^2 + k[/tex]

Where (h, k) represents the coordinates of the vertex, and 'a' is a constant that determines the shape and direction of the parabola.

Looking at the graph, we can determine the vertex by identifying the x-coordinate where the parabola reaches its highest or lowest point. Let's assume the vertex is located at the point (h, k).

From the graph, it appears that the vertex lies at (-2, 4). Therefore, we have h = -2 and k = 4.

Now we can rewrite the equation as:

[tex]f(x) = a(x + 2)^2 + 4[/tex]

Next, we need to determine the value of 'a'. To do this, we can use another point on the graph. Let's consider the point (1, 0).

Plugging in the coordinates (1, 0) into the equation, we get:

[tex]0 = a(1 + 2)^2 + 4[/tex]

0 = 9a + 4

9a = -4

a = -4/9

Now we have the value of 'a'. Substituting it back into the equation, we get:

[tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]

Thus, the quadratic equation in standard form that corresponds to the given graph is:

[tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]

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The exponential regression equation is y = 11.37 * 3.87ˣ

From the question, we have the following parameters that can be used in our computation:

(-4,0.05), (-3, 0.20), (-2, 0.75)

To calculate the exponential regression equation that best fits the data shown, we use a graphing tool

An exponential function is represented as

y = abˣ

From the graphing tool, we have

a = 11.37

b = 3.87

substitute the known values in the above equation, so, we have the following representation

y = 11.37 * 3.87ˣ

Hence, the exponential regression equation is y = 11.37 * 3.87ˣ

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Answer: A

Step-by-step explanation: 32.07 cm^2

The statement "If dom(f) = Χ, then f is an n-ary functionon X" means that if the domain   of the function f is equal to the set X, then f is considered an n-ary function on X.

In other words, for each element in X,   the function f can take n arguments or inputs to produce aunique output. The term "n-ary" indicates the number of arguments that the function can accept.

A statement in mathematics is a declarative utterance that is either true or untrue but not both. A proposal is anothername for a statement. The main point is that there should be no uncertainty.

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Answer:

The statement "If dom(f) = X, then f is an n-ary function on X" means that if the domain of a function f is equal to the set X, then f is a function that takes n arguments or inputs from the set X, where the value of n depends on the specific function.

Step-by-step explanation:

The statement "If dom(f) = X", then f is an n-ary function on X" means that if the domain of the function f is equal to the set X, then f is an n-ary function on X.

Here's a breakdown of the terms used in the statement:

- dom(f): The domain of a function f refers to the set of all possible input values for the function. It represents the set of values for which the function is defined.

- X: In this context, X represents a set. It could be any set, and it serves as the domain for the function f.

- n-ary function: An n-ary function is a function that takes n arguments or inputs. The value of n represents the number of inputs the function expects.

Therefore, the statement is saying that if the domain of the function f is equal to the set X, then f is an n-ary function on X. It implies that the function f takes n inputs from the set X, where n is determined by the specific function.

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area of A = πr² = π7² = 153.9 m²

area of B = πr² = π9² = 254.5 m²

The vertical asymptote of the function are x = ±1/2

Given that we need to determine what is value of the vertical asymptote of the function =

(2x + 1) / (4x²-1)

To find the vertical asymptote of the function f(x) = (2x + 1) / (4x² - 1), we need to determine the values of x for which the denominator becomes zero.

This is because division by zero is undefined, and the function may have vertical asymptotes at those points.

The denominator of the function is 4x² - 1.

To find the values of x that make the denominator zero, we can set it equal to zero and solve for x:

4x² - 1 = 0

Adding 1 to both sides:

4x² = 1

Dividing both sides by 4:

x² = 1/4

Taking the square root of both sides:

x = ±√(1/4)

Simplifying further, we get:

x = ±1/2

Therefore, the values of x that make the denominator zero are x = -1/2 and x = 1/2. These are the vertical asymptotes of the function.

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Translation =

What is value of the vertical asymptote of the function =

(2x + 1) / (4x²-1)

Answer: The Mode

Step-by-step explanation:

The mode is the data value that occurs the most often in a data set

Answer:

Step-by-step explanation:

To calculate Su-Lo's score on the test, we can multiply her percentage by the total marks for the test.

Su-Lo scored 45% out of 80, so her score can be calculated as follows:

Score = Percentage × Total marks

Score = 45% × 80

To find the score, we need to convert the percentage to a decimal by dividing it by 100:

Score = (45/100) × 80

Score = 0.45 × 80

Score = 36

Therefore, Su-Lo scored 36 marks on the test.

Answer: The value of x = 1  and y = -1

Step-by Step Explanation:

We have 5x + 2y = 3 -----(i)

and 2x + 3y = -1 -----(ii)

By substitution method,

from (i), x = 3-2y/5

Putting the value of x in equation (ii),

we get, 2(3-2y/5) + 3y = -1

6 - 4y/5 + 3y =-1

6 - 4y + 15y = -5

6 - 11y = -5

-11y = -5 - 6

-11y = -11

y = -1

And, x = 3-2(-1)/5

x = 3+2/5

x = 1

Therefore,  x=1 and y=−1

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Tom's estimated travel time is approximately 13.6 hours.

Based on the given scenario, Tom is traveling a distance of approximately 340 nautical miles from Houston to New Orleans by boat. He will be using a medium-sized recreational boat with an average speed of 25 miles per hour.

To estimate the time it will take for his journey, we can use the formula:

Time = Distance / Speed

Substituting the values, we have:

Time = 340 miles / 25 miles per hour

Calculating the division, we find that Tom's estimated travel time is approximately 13.6 hours.

However, it is important to note that this estimate assumes a continuous journey without considering other factors that may affect the travel time. Various elements can impact the actual duration, such as weather conditions, water currents, navigational challenges, refueling stops, and any necessary rest breaks.

Additionally, it is essential for Tom to adhere to all boating regulations and safety guidelines to ensure a smooth and secure voyage.

To obtain a more accurate estimate, Tom should consult local boating authorities, marinas, or experienced sailors familiar with the route.

They can provide valuable insights into the specific conditions and offer guidance on potential challenges that may affect the travel time. Planning for additional buffer time is also recommended to account for unforeseen circumstances and to prioritize safety during the journey.

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The complete question may be like:

Tom plans to travel by boat from Houston, Texas, to New Orleans, Louisiana. He wants to estimate the time it will take for his journey. The distance between the two cities by water is approximately 340 nautical miles. Tom will be traveling on a medium-sized recreational boat that has an average speed of 25 miles per hour. Considering normal weather conditions and assuming a continuous journey, how long will it take Tom to reach New Orleans?

Please provide an answer based on this scenario, taking into account the distance, average speed, and any other relevant factors.

Answer:

The domain and range of the graph are the same

Step-by-step explanation:

The domain and range of the graph are both [tex][0,\infty)[/tex] because you cannot take the square root of a negative number to produce a real result, and you cannot square a real number to get a negative number.

The equation of the parabola with the given focus (2, 7) and directrix y = -1 is [tex](x - 2)^2 = 12(y - 3)^2[/tex].Option C.

To find the equation of the parabola with a focus and directrix, we can use the standard form of the equation of a parabola:

For a vertical parabola:

[tex](x - h)^2 = 4p(y - k),[/tex]

where (h, k) is the vertex, and p is the distance from the vertex to the focus and directrix.

In this case, the focus is given as (2, 7), which means the vertex is also (2, 7) since the focus and vertex lie on the axis of symmetry. Additionally, the directrix is given as y = -1, which means the directrix is a horizontal line.

First, let's determine the distance from the vertex to the focus and directrix, which is the value of p. The distance is the absolute difference between the y-coordinate of the focus (7) and the y-coordinate of the directrix (-1):

p = |7 - (-1)| = 8.

Now we can substitute the values of the vertex (h, k) = (2, 7) and p = 8 into the standard form equation:

[tex](x - 2)^2 = 4(8)(y - 7).[/tex]

Simplifying further:

[tex](x - 2)^2 = 32(y - 7).[/tex]

Expanding the equation:

[tex]x^2 - 4x + 4 = 32y - 224.[/tex]

Rearranging the terms:

[tex]x^2 - 4x - 32y + 228 = 0.[/tex]

Therefore, the equation of the parabola with the given focus (2, 7) and directrix y = -1 is  [tex](x - 2)^2 = 12(y - 3)^2.[/tex] SO Option C is correct.

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The value of x in the given right triangle HJK include the following: C. 10.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Hypotenuse, x = 5 × 2

Hypotenuse, x = 10.

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The value of the given expression:

⇒ mk = 12

⇒ m + k = 8  

The given values,

m = 6

k  = 2

We have evaluate the given expression,

mk

This is nothing but product of m and k

Since we know,

The product is the result of multiplying two or more numbers together. Assume they are two integers and, then their product is derived by multiplying both numbers together.

Therefore,

⇒ mk = 6x2

⇒ mk = 12

We have evaluate the given expression,

m + k

This is nothing but addition of m and k

Since we know that,

Addition is the process of joining two or more integers. The numbers being added are known as addends, and the result or final response obtained after the procedure is known as the total.

⇒ m + k = 6 + 2

⇒ m + k = 8          

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The solution to the given differential equation is y(x) = (C1 + C2x) * e^(3x), where C1 and C2 are arbitrary constants.

To solve the given differential equation, we need to find the function y(x) that satisfies the equation:

(D^2 - 6D + 9)y(x) = 0,

where D represents the differentiation operator.

Let's break down the solution process step by step:

Characteristic Equation

First, we'll find the characteristic equation associated with the given differential equation. For a second-order linear homogeneous differential equation of the form aD^2y + bDy + cy = 0, the characteristic equation is obtained by replacing D with λ:

λ^2 - 6λ + 9 = 0.

Solving the Characteristic Equation

Now, we solve the characteristic equation to find the values of λ. Factoring the equation, we get:

(λ - 3)^2 = 0.

From this, we see that λ = 3 (with a multiplicity of 2).

General Solution

The general solution of the differential equation is given by:

y(x) = C1e^(λ1x) + C2xe^(λ2*x),

where C1 and C2 are arbitrary constants, and λ1, λ2 are the distinct roots of the characteristic equation.

In our case, since we have repeated roots, the general solution simplifies to:

y(x) = C1e^(3x) + C2xe^(3*x).

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The perimeter of the given window is 48 centimeter.

From the given figure,

Perimeter of window = 2(Length+Breadth)

= 2(10+14)

= 2×24

= 48 centimeter

Perimeter of house = 2(Length+Breadth)

= 2(37+35)

= 2×72

= 144 centimeter

Perimeter of roof = 2(Length+Breadth)

= 2(37+5)

= 2×42

= 84 centimeter

Therefore, the perimeter of the given window is 48 centimeter.

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This equation represents the value of the stock, V(t), in dollars, t years after 1940, taking into account the 7% annual Growth rate V(t) = $1.25 * (1 + 0.07)^t.

The value of the stock, V(t), in dollars, t years after 1940, we can use an exponential growth equation since the stock's value grows by 7% each year after 1940.

formulate the equation step by step:

1. We know that the initial value of the stock in 1940 is $1.25. This initial value serves as the starting point for our equation.

2.We are given that the value of the stock grows by 7% each year. This means that for every year that passes, the stock's value increases by 7% of its previous value.

3. In mathematical terms, if V(0) represents the initial value in 1940 ($1.25), then the value of the stock after t years can be represented as:

V(t) = V(0) * (1 + r)^t,

where r is the growth rate expressed as a decimal (in this case, 7% = 0.07).

4. Plugging in the given values, our equation becomes:

V(t) = $1.25 * (1 + 0.07)^t.

This equation represents the value of the stock, V(t), in dollars, t years after 1940, taking into account the 7% annual growth rate.

For example, if we wanted to find the value of the stock 10 years after 1940, we would substitute t = 10 into the equation:

V(10) = $1.25 * (1 + 0.07)^10.

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Answer:

Mr Kalada's present age is 45 years old

Step-by-step explanation:

a) The volume of the hemisphere is V₁ = 261.80 km³

b) The volume of the hemisphere is V₂ = 1,526.81 feet³

Given data ,

a)

Let the volume of the hemisphere be represented as V₁

where the radius of the hemisphere is r₁ = 5 km

And , volume of hemisphere is V = ( 2/3 )πr³

On simplifying , we get

V₁ = ( 2/3 )π ( 5 )³

V₁ = 261.80 km³

b)

Let the volume of the hemisphere be represented as V₂

The diameter of the hemisphere = 18 feet

where the radius of the hemisphere is r₁ = 9 feet

And , volume of hemisphere is V = ( 2/3 )πr³

On simplifying , we get

V₂ = ( 2/3 )π ( 9 )³

V₂ = 1,526.81 feet³

Hence , the volume of the hemisphere is solved

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Answer:

plane

point

line

Step-by-step explanation:

Based on the options provided, the kinds of symmetry in a 2D number can be:

Therefore, the possible kinds of symmetry in a 2D number can be

plane symmetry,

point symmetry, or

line symmetry.

Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

Answer: 3:25

Step-by-step explanation:

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100

------------ = 12/100
1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

---------  = 3/25  

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:  

3  

25   =  3:25

Answer:

Step-by-step explanation:

Hello!

We want to know the area of the original circle - the now circle.

The original circle's diameter is 110 meters.

To figure out the area you use this formula: [tex]r^2*pi[/tex]

The diameter is 107 meters, so the equation is [tex]55^2[/tex][tex]*\pi[/tex].

The area is about 9503.3 meters.

The next area is the "now circle".

The now circle's diameter is 107 meters.

When you use this formula, you end up with  [tex]53.5^2*\pi[/tex].

The area is about 8892 meters.

So it's just basic subtraction!

I'll let you figure out the rest.

:)