Which is a correct interpretation of the slope of the line in this graph? (2,8) (7,6)
The volume of water in the tank is decreasing by 2 L per hour.
The volume of water in the tank is decreasing by 0.2 L per hour.
The volume of water in the tank is decreasing by 2.5 L per hour.
The volume of water in the tank is decreasing by 0,4 L per hour

Answer:

x = 9

Step-by-step explanation:

create a ratio between the triangles:

x/6 = 12/8; cross multiply

72 = 8x; divide 8 on both sides

x = 9

The dependent variable is:

(4) running for 30 minutes at a pace and at an incline adequate to keep the heart rate in the range of 70-80% of the age-adjusted maximum heart rate.

Both exercise program and percentage of the age-adjusted maximum heart rate are Dependent Variable.

Dependent variables are studied under the assumption or claim that they depend on the values ​​of other variables according to some law or rule (for example, by a mathematical function). In turn, the independent variables were not considered dependent on any other variable in the context of the associated experience.

In this sense, some common independent variables are time, space, density, mass, fluid velocity, and past values ​​of some observations of interest (e.g., population size) to predict future values ​​(dependent variable).

An example of a dependent variable is depressive symptoms, which depends on the independent variable (type of treatment). In an experiment, a researcher investigates the effect that changing an independent variable might have on a dependent variable.

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Mason's friends do not play video games are 4.

Mason asked some classmates whether they play video games.

The ratio of friends who play video games to everyone he asked is given as some fraction or decimal value.
Let's assume that the ratio is in the form of "x:y",

"x" represents the number of friends who play video games, and "y" represents the total number of friends that Mason asked.
To find out how many of his friends do not play video games,

To subtract the number of friends who play video games from the total number of friends that Mason asked.

This is because the remaining friends who were not counted in the "x" value of the ratio must be those who do not play video games.
So, the number of friends who do not play video games can be calculated as:
Total number of friends - Number of friends who play video games = y - x
The ratio of friends who play video games to everyone he asked is 3:7,

It means that out of 7 friends, 3 play video games, and 4 do not play video games.

The number of friends who do not play video games can be calculated as:
y - x = 7 - 3 = 4  

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Answer:

0+x=50

Step-by-step explanation:

you started with no money which is 0 and your mom gives you $50 which is represented by x, this could be shown as 0+x and now that you have 50 bucks it would be 0+x=50

Answer:

0+×=50

Step-by-step explanation:

if your mom gives you 50 and you started with 0 then x represents 50.

(a) To show that the magnitude of the gradient, ||▽f|| = √( (∂f/∂x)^2 + (∂f/∂y)^2 ), is isotropic, we need to demonstrate that it is independent of the direction.

Let's consider the squared magnitude of the gradient:

||▽f||^2 = (∂f/∂x)^2 + (∂f/∂y)^2

Now, let's consider a rotated coordinate system, where x' and y' axes are obtained by rotating the original x and y axes by an angle θ. In this new coordinate system, the partial derivatives can be expressed as:

∂f/∂x' = cos(θ) * (∂f/∂x) - sin(θ) * (∂f/∂y)

∂f/∂y' = sin(θ) * (∂f/∂x) + cos(θ) * (∂f/∂y)

Squaring these expressions and adding them:

(∂f/∂x')^2 + (∂f/∂y')^2 = (cos^2(θ) * (∂f/∂x)^2 - 2 * cos(θ) * sin(θ) * (∂f/∂x) * (∂f/∂y) + sin^2(θ) * (∂f/∂y)^2) + (sin^2(θ) * (∂f/∂x)^2 + 2 * cos(θ) * sin(θ) * (∂f/∂x) * (∂f/∂y) + cos^2(θ) * (∂f/∂y)^2)

= (∂f/∂x)^2 + (∂f/∂y)^2

As we can see, the squared magnitude of the gradient is the same in the original and rotated coordinate systems, indicating that the magnitude of the gradient is isotropic.

(b) The isotropic property is lost when the gradient magnitude is approximated by |▽f| ≈ |∂f/∂x| + |∂f/∂y|. This approximation assumes that the partial derivatives of f with respect to x and y are independent of each other, which may not be true in general.

For example, consider a function f(x, y) = x^2 + y^2. The gradient of this function is ▽f = (2x, 2y). The magnitude of the gradient, ||▽f||, is √(4x^2 + 4y^2) = 2√(x^2 + y^2). However, if we approximate the gradient magnitude using the given formula, we would get |▽f| ≈ |2x| + |2y| = 2|x| + 2|y|. This approximation does not accurately represent the true magnitude of the gradient and violates the isotropic property.

Therefore, when the gradient magnitude is approximated by the sum of the absolute values of the partial derivatives, the isotropic property is lost and the approximation may not provide an accurate measure of the gradient magnitude.

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The given limit can be expressed as the definite integral: lim (n→∞) n ∑(i=1 to n) i⁶/n⁷ = ∫[1/n, 1] x⁶ dx

To express the given limit as a definite integral, we need to determine the appropriate function f(x) and the integration limits b and 1.

Let's start by rewriting the given limit:

lim (n→∞) (1/n) ∑(i=1 to n) \(i^6/n^7\)

Notice that the term i⁶/n⁷ can be written as (i/n)⁶/n.

Therefore, we can rewrite the above limit as:

lim (n→∞) (1/n) ∑(i=1 to n) (i/n)⁶/n

This can be further rearranged as:

lim (n→∞) (1/n^7) ∑(i=1 to n) (i/n)⁶

Now, let's define the function f(x) = x⁶, and rewrite the limit using the integral notation:

lim (n→∞) (1/n^7) ∑(i=1 to n) (i/n)⁶ = ∫[a,b] f(x) dx

To determine the integration limits a and b, we need to consider the range of values that x can take. In this case, x = i/n, and as i varies from 1 to n, x varies from 1/n to 1. Therefore, we have a = 1/n and b = 1.

Hence, the given limit can be expressed as the definite integral:

lim (n→∞) n ∑(i=1 to n) i⁶/n⁷ = ∫[1/n, 1] x⁶ dx

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The number of students who were wearing spirit wear at the assembly is = 120.

As given in Question that 3 out of 10 students were wearing spirit were.

if we have these type of Question then we will find the fraction part for 1 student as given 3 out of 10 then  the fraction part for 1 will be = 3/10 = 0.3

for 1 student there  is 0.3 fraction of students has wear spirit wear

so for 400 students were at the assembly

for 1 fraction is 0.3

for 400 = 400*(0.3 )= 120

Here 120 students were wear spirit wear in assembly

as like type we can solve for any number of students who were in assembly . like if there is 500 student the we can do like 500*.03 = 150 students.

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Answer:

2

Step-by-step explanation:

Assume, that the number is x

Let's write an equation according to the given information:

\(2x = {x}^{2} \)

\( {x}^{2} - 2x = 0\)

Let's solve this incomplete quadratic equation:

\(x(x - 2) = 0\)

x = 0 or x - 2 = 0

x = 2

Since O isn't a natural number, the answer is 2

Answer:

VW and YZ

Step-by-step explanation:

Count the lines in between the black dots.

Answer:

Srry can't help you buddy it doesn't make cents

Step-by-step explanation:

Answer:

9 x 8/2 = 36  l     36 x 9 = Volume

Step-by-step explanation:

we know base is a triangle to to find volume is area of the base times the height and on the right side of the figure, (look at photo) the height is 9 so just do 36 times 9 to get the volume.

hope this helps :D have a good night!

Answer:

(2,3)

Step-by-step explanation:

it is the point in which they intersect

i am in algebra two so you can trust my answer. if you need more help, lmk in the comments. happy holidays and stay safe!

Answer:

\(\frac{7}{15}\)

Step-by-step explanation:

Given

\(\frac{16-4(5)}{2(6)+8}\) + \(\frac{2}{3}\)

= \(\frac{16-20}{12+8}\) + \(\frac{2}{3}\)

= \(\frac{-4}{20}\) + \(\frac{2}{3}\)

= - \(\frac{1}{5}\) + \(\frac{2}{3}\)

We require the fractions to have a common denominator of 15

Multiply the numerator/ denominator of - \(\frac{1}{5}\) by 3 and

Multiply the numerator/ denominator of \(\frac{2}{3}\) by 5

= - \(\frac{3}{15}\) + \(\frac{10}{15}\)

= \(\frac{7}{15}\)

Answer:

(3,-5)(5,7) instrumentate in inclination countercheck form. correspondingly kcharacterization forethoughtfulness (3,-5)(5,7) instrumentate in inclination countercheck form. correspondingly characterization forethoughtfulness

Step-by-step explanation:(3,-5)(5,7) instrumentate in inclination countercheck form. correspondingly characterization forethoughtfulness (3,-5)(5,7) instrumentate in inclination countercheck form. correspondingly characterization forethoughtfulness (3,-5)(5,7) instrumentate in inclination countercheck form. correspondingly characterization forethoughtfulness

Answer:

240

Step-by-step explanation:

Answer:

where is the graph .....

The maximized value of the objective function is 3

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

C = x + y

Subject to

y >= 0

x >= 0

4x + 2y <= 8

2x - y <= 0

When the graphs of these inequalities are plotted (see attachment), we have the following feasible regions

(x, y) = (0, 0) and (1, 2)

This means that

C = 0 + 0 = 0

C = 1 + 2 = 3

3 is greater than 0

Hence, the maximized value is 3

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The perimeter of the semicircular window with a radius of 20cm is the nearest tenth would be 63 cm.

What is the perimeter of the semicircle?

The perimeter of a semicircle is the total length of the curved boundary of the semicircle, which is half the circumference of the circle with the same radius. The formula for the circumference of a circle with radius r is 2πr, so the formula for the perimeter of a semicircle with radius r is:

Perimeter of semicircle = (1/2) x 2πr + 2r

= πr + 2r

= (π + 2)r

To find the perimeter of a semicircular window with a radius of 20cm, we can substitute r = 20 into the formula:

Perimeter of semicircle = (π + 2) x 20

= (3.14159 + 2) x 20

= 62.8318 cm (rounded to 4 decimal places)

Therefore, the perimeter of the semicircular window with a radius of 20cm is approximately 62.8318 cm.

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Answer:

here is your correct answer dude

Answer:

I Think B.

Step-by-step explanation:

Im Not But CARRY ON LEARNING

Answer:

Step-by-step explanation:

\(f - \frac{7}{g}=h\\\\f =h + \frac{7}{g}\)

Percentage change = 10%

We can use the formula:

Percent change = \(\frac{New-Old}{Old}\) x 100

Percent change = \(\frac{77-70}{70}\)x100

Percent change = \(\frac{7}{70}\) x 100

Percent change = 0.1 x 100

Percent change = 10%

Answer: 53.9

Step-by-step explanation:

Answer:

The inverse function h(x) = 4x + 48

Step-by-step explanation:

Here, we want to find the inverse of a function

The function is;

f(x) = x/4 -12

now, let this value equals m

so;

m = x/4 -12

we now try and make x the subject formula and this gives us the inverse.

m = (x-48)/4

4m = x -48

x = 4m + 48

substitute m for x

which implies 4x + 48

This is the inverse of the function

Answer:

D. h(x) = 4x + 48

The midpoint between the endpoints (9, -1) and (1, 15) is equal to (5, 7).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(9 + 1)/2, ((-1) + 15)/2]

Midpoint = [(10)/2, (14)/2]

Midpoint = (5, 7).

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Answer:

2.70

Step-by-step explanation:

45.00 X 6%=2.70

Answer:

Each will receive \(\frac{1}{6}th\) of the cake.

Step-by-step explanation:

Let the amount of cake = c

Lisa, Juan and Isaac are the persons who are sharing half of a cake equally.

Number of persons = 3

Part of the cake shared = \(\frac{c}{2}\)

Fraction of the cake shared by each = \(\frac{\text{Amount of cake shared}}{\text{Number of persons who shared}}\)

                                                             = \(\frac{\frac{1}{2}c}{3}\)

                                                             = \(\frac{1}{6}c\)

Therefore, fraction of total cake shared by each member will be \(\frac{1}{6}\) of the total amount of cake.

The first runner covers 30 yards in 4 seconds, a speed of 5 yards per second. The second runner covers a distance of 20 yards in 4 seconds but starts 10 yards ahead. Both runners have a speed of 5 yards per second.

The first runner maintains a constant speed of 5 yards per second and covers a distance of 30 yards in 4 seconds. The second runner also has a speed of 5 yards per second but starts 10 yards ahead. Therefore, the second runner covers a shorter distance of 20 yards in the same 4 seconds.

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The length of the line segment B'C' is 3 units.

We can see that from the given graph that,

The coordinates of the points are:

B = (-2, 6)

C = (-2, 3)

If we translate the points 5 units to the right then the changed coordinates will be -

B' = (-2 + 5, 6) = (3, 6)

C' = (-2 + 5, 3) = (3, 3)

So the length of the B'C' is given by,

B'C' = √((3 - 3)² + (6 - 3)²) = √(0² + 3²) = √(0 + 9) = √9 = 3 units.

Hence the length of the line segment B'C' is 3 units.

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Answer:

I'm not sure.

Step-by-step explanation:

The gradient vector field F generated by the function ϕ(x,y)=x2 + y2Consider the curve r(t)=⟨t2, e2t⟩ and let θ be the angle between F and T(t), the unit tangent vector for r(t), at time t=2. cos(θ) = √(2/(2 + e4)).

To compute the gradient vector field of a scalar function, use the formula \(\nabla \phi\), where \(\nabla\) is the gradient operator, which can be expressed as a vector.\[\nabla \phi

= \langle \frac{\partial \phi}{\partial x}, \frac{\partial \phi}{\partial y} \rangle\]The gradient vector field F generated by the function

ϕ(x,y)=x2 + y2 is given by,

\[\nabla \phi = \langle 2x, 2y \rangle

= 2\langle x, y \rangle\]Now, find the unit tangent vector T(t),

which is given by the derivative of the curve r(t), normalized by its magnitude.

\[T(t) = \frac{r'(t)}{\|r'(t)\|}

= \frac{\langle 2t, 2e^{2t} \rangle}{\sqrt{4t^2 + 4e^{4t}}}

= \frac{1}{\sqrt{t^2 + e^{4t}}}\langle t, e^{2t} \rangle\]Thus, \[T(2)

= \frac{1}{\sqrt{4 + e^4}}\langle 2, e^4 \rangle

= \langle \frac{2}{\sqrt{4 + e^4}}, \frac{e^4}{\sqrt{4 + e^4}} \rangle\]

Finally, find cos(θ) by taking the dot product of F and T(t).\[F(2)

= 2\langle 2, 0 \rangle

= \langle 4, 0 \rangle\]Hence,\[\cos \theta

= \frac{F(2)\cdot T(2)}{\|F(2)\|\|T(2)\|}

= \frac{8/\sqrt{4 + e^4}}{4/\sqrt{2 + e^4}}

= \sqrt{\frac{2}{2 + e^4}}\]

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The area of the shaded region is about 100.48 square units, rounded to the nearest hundredth.

A two-dimensional surface or region can be measured using the mathematical notion of area. Common square units used to describe it include square metres, square feet, and square inches. A flat surface's area is typically calculated by multiplying its length and breadth.

To find the area of the shaded region, we need to subtract the area of the smaller circle from the area of the larger circle.

Let's first find the area of the larger circle with radius 6. The formula for the area of a circle is \(A = \pi r^2\), where A is the area and r is the radius. So, for the larger circle:

A_larger = \(\pi (6)^2\)

A_larger = \(36\pi\)

Now, let's find the area of the smaller circle with radius 2. Using the same formula, we have:

A_smaller =\(\pi (2)^2\)

A_smaller = \(4\pi\)

To find the shaded region, we subtract the area of the smaller circle from the area of the larger circle:

A_shaded = A_larger - A_smaller

A_shaded = \(36\pi - 4\pi\)

A_shaded =\(32\pi\)

To round to the nearest hundredth, we can use the approximation π ≈ 3.14:

A_shaded ≈ 32(3.14)

A_shaded ≈ 100.48

Therefore, the area of the shaded region is about 100.48 square units, rounded to the nearest hundredth.

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